The Casimir Effect: From a Laboratory Table to the Universe

A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Field Theory".

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 58909

Special Issue Editor

Prof. Dr. Galina L. Klimchitskaya
E-Mail Website
Guest Editor
1. Pulkovo Observatory of the Russian Academy of Sciences, 196140 Saint Petersburg, Russia
2. Peter the Great Saint Petersburg Polytechnic University, 195251 Saint Petersburg, Russia
Interests: astrophysics; atomic physics; condensed matter physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will present a comprehensive picture of the Casimir effect as a multidisciplinary subject that plays an important role in diversified areas of physics ranging from quantum field theory, atomic physics, condensed matter physics, and applications in nanotechnology to gravitation, cosmology, and the structure of the Universe. The broad role of the Casimir effect results from the fact that it is governed by the zero-point and thermal fluctuations of quantized fields, which are inherent to any physical system. During the last few years, many new experiments on measuring the Casimir force were performed, and the related theory was generalized for arbitrary geometries, material properties, and out of thermal equilibrium situations. On the one hand, Casimir-operated micromechanical chips have been created and, on the other hand, the Casimir effect was invoked in investigations of the brane cosmology and dark energy. The Special Issue will contain both research and review articles on all these aspects of the Casimir effect, as well as a discussion of unresolved problems and plans for the future.

Prof. Dr. Galina L. Klimchitskaya
Guest Editor

Universe 2021 Best Paper Award for Special Issue “The Casimir Effect: From a Laboratory Table to the Universe” (500 CHF)

 
Winner announcement date: 28 February 2023
download description

Dear Colleagues,

To honor the excellent papers published in the Special Issue “The Casimir Effect: From a Laboratory Table to the Universe”, we are pleased to launch a new Best Paper Award. The winning paper will receive an award. The winning paper will be selected after a thorough evaluation by an Award Committee consisting of senior scholars from the Universe Editorial Board.

Eligibility for the awards:
– ONLY papers published in the Special Issue “The Casimir Effect: From a Laboratory Table to the Universe” will be considered.
– Papers published by Guest Editors will not be granted this award.

Selection Criteria:

Papers will be selected by the journal Award Committee according to the following criteria:
– Scientific merit and broad impact;
– Relevance to the SI and journal scope;
– Originality of the research objectives and/or the ideas presented (for research article);
– Creativity of the study design or uniqueness of the approaches and concepts (for research article);
– Comprehensiveness will be considered for review articles;
– Citations (data source: Web of Science (Clarivate Analytics)) and download rates in 2022.

Prizes:

The winner (corresponding author) will receive the following:
– 500 CHF;
– An electronic certificate.

The winning paper will be announced on the journal website in February 2023. If you want to know more details about the Special Issue or submit a paper, please follow this link:
https://www.mdpi.com/journal/universe/special_issues/TCEFALTU

Keywords

  • Casimir force
  • zero-point energy
  • precise measurements
  • thermal fluctuations
  • nanodevices
  • brane cosmology

Published Papers (31 papers)

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Editorial

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4 pages, 181 KiB  
Editorial
Editorial to the Special Issue “The Casimir Effect: From a Laboratory Table to the Universe”
Universe 2021, 7(8), 266; https://doi.org/10.3390/universe7080266 - 26 Jul 2021
Viewed by 1401
Abstract
This Special Issue presents a comprehensive picture of the Casimir effect as a multidisciplinary subject that plays an important role in diversified areas of physics ranging from quantum field theory, atomic physics and condensed matter physics to elementary particle physics, gravitation and cosmology [...] Read more.
This Special Issue presents a comprehensive picture of the Casimir effect as a multidisciplinary subject that plays an important role in diversified areas of physics ranging from quantum field theory, atomic physics and condensed matter physics to elementary particle physics, gravitation and cosmology [...] Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)

Research

Jump to: Editorial, Review

13 pages, 1362 KiB  
Article
Puzzling Low-Temperature Behavior of the Van Der Waals Friction Force between Metallic Plates in Relative Motion
Universe 2021, 7(11), 427; https://doi.org/10.3390/universe7110427 - 09 Nov 2021
Cited by 3 | Viewed by 1008
Abstract
This paper presents the results of calculating the van der Waals friction force (dissipative fluctuation-electromagnetic force) between metallic (Au) plates in relative motion at temperatures close to 1 K. The stopping tangential force arises between moving plates along with the usual Casimir force [...] Read more.
This paper presents the results of calculating the van der Waals friction force (dissipative fluctuation-electromagnetic force) between metallic (Au) plates in relative motion at temperatures close to 1 K. The stopping tangential force arises between moving plates along with the usual Casimir force of attraction, which has been routinely measured with high precision over the past two decades. At room temperatures, the former force is 10 orders of magnitude less than the latter, but at temperatures T<50 K, friction increases sharply. The calculations have been carried out in the framework of the Levin-Polevoi-Rytov fluctuation electromagnetic theory. For metallic plates with perfect crystal lattices and without defects, van der Waals friction force is shown to increase with decreasing temperature as T4. In the presence of residual resistance ρ0 of the metal, a plateau is formed on the temperature dependence of the friction force at T0 with a height proportional to ρ00.8. Another important finding is the weak force-distance dependence ~aq (with q<1). The absolute values of the friction forces are achievable for measurements in AFM-based experiments. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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43 pages, 1529 KiB  
Article
Next Generation Design and Prospects for Cannex
Universe 2021, 7(7), 234; https://doi.org/10.3390/universe7070234 - 09 Jul 2021
Cited by 12 | Viewed by 2428
Abstract
The Casimir And Non-Newtonian force EXperiment (Cannex) implements the unique geometry of macroscopic plane parallel plates that guarantees an optimum sensitivity with respect to interfacial forces and their gradients. Based on experience from the recently completed proof-of-principle phase, we have started [...] Read more.
The Casimir And Non-Newtonian force EXperiment (Cannex) implements the unique geometry of macroscopic plane parallel plates that guarantees an optimum sensitivity with respect to interfacial forces and their gradients. Based on experience from the recently completed proof-of-principle phase, we have started a re-design of the setup aiming to reduce systematic effects and maximize the achievable sensitivity. Several propositions have been made to measure Casimir forces in and out of thermal equilibrium, hypothetical axion and axion-like dark matter interactions, and forces originating from chameleon or symmetron dark energy interactions. In the present article, we give details on the design for the next implementation stage of Cannex and discuss the experimental opportunities, as well as limitations expected for this new setup. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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34 pages, 867 KiB  
Article
Unifying Theory for Casimir Forces: Bulk and Surface Formulations
Universe 2021, 7(7), 225; https://doi.org/10.3390/universe7070225 - 04 Jul 2021
Cited by 8 | Viewed by 1953
Abstract
The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, [...] Read more.
The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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10 pages, 274 KiB  
Article
Vacuum Interaction of Crossed Cosmic Strings
Universe 2021, 7(7), 217; https://doi.org/10.3390/universe7070217 - 30 Jun 2021
Cited by 4 | Viewed by 1134
Abstract
In this paper, we consider the vacuum energy of a scalar field in the spacetime of two non-parallel cosmic strings. To this end, we obtain metrics for orthogonal straight cosmic strings and for slightly nonparallel strings. In the first case, we derive the [...] Read more.
In this paper, we consider the vacuum energy of a scalar field in the spacetime of two non-parallel cosmic strings. To this end, we obtain metrics for orthogonal straight cosmic strings and for slightly nonparallel strings. In the first case, we derive the separation-dependent part of the vacuum energy in the leading order of string tension. The dependence of the vacuum energy on separation differs from that known for parallel strings. For two strings inclined at a small angle to each other, the approximation used simply reproduces the result for parallel strings, since the angle dependence enters the next to leading order. The results are compared with the Casimir interaction between two inclined cylinders. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
17 pages, 396 KiB  
Article
Scalar Radiation in Interaction of Cosmic String with Point Charge
Universe 2021, 7(7), 206; https://doi.org/10.3390/universe7070206 - 23 Jun 2021
Cited by 2 | Viewed by 1187
Abstract
We consider the scalar bremsstrahlung of the spinless relativistic particle, which interacts with infinitely thin cosmic string by linearized gravity. With the iterational scheme, based on the Perturbaion Theory with respect to the Newtonian constant, we compute the radiation amplitude and the emitted [...] Read more.
We consider the scalar bremsstrahlung of the spinless relativistic particle, which interacts with infinitely thin cosmic string by linearized gravity. With the iterational scheme, based on the Perturbaion Theory with respect to the Newtonian constant, we compute the radiation amplitude and the emitted energy due to collision. The general phenomenon of mutual cancellation of the leading terms on the local and non-local amplitude, known in the ultrarelativistic regime for several types of collision, also takes place here. Remarkably, this cancellation (destructive interference) is complete, and takes place for any particle’s velocity. We compute the spectral and angular distributions of the emitted waves. Particular attention is paid to the ultrarelativistic case. Due to the radiation emission, a string may lose its energy and decrease the tension; it may affect all field effects, including the vacuum polarization and the Casimir effect, in terms of physical problems with the real cosmic strings. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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21 pages, 369 KiB  
Article
Green Functions Scattering in the Casimir Effect
Universe 2021, 7(6), 195; https://doi.org/10.3390/universe7060195 - 09 Jun 2021
Cited by 8 | Viewed by 2072
Abstract
We propose Green functions scattering method to obtain the Casimir–Polder potential between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure between two dielectric half-spaces separated by a vacuum slit is derived within the same method. The method is [...] Read more.
We propose Green functions scattering method to obtain the Casimir–Polder potential between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure between two dielectric half-spaces separated by a vacuum slit is derived within the same method. The method is also applied to known conducting systems including graphene which are overviewed. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
16 pages, 2372 KiB  
Article
Shaping Dynamical Casimir Photons
Universe 2021, 7(6), 189; https://doi.org/10.3390/universe7060189 - 06 Jun 2021
Cited by 3 | Viewed by 2023
Abstract
Temporal modulation of the quantum vacuum through fast motion of a neutral body or fast changes of its optical properties is known to promote virtual into real photons, the so-called dynamical Casimir effect. Empowering modulation protocols with spatial control could enable the shaping [...] Read more.
Temporal modulation of the quantum vacuum through fast motion of a neutral body or fast changes of its optical properties is known to promote virtual into real photons, the so-called dynamical Casimir effect. Empowering modulation protocols with spatial control could enable the shaping of spectral, spatial, spin, and entanglement properties of the emitted photon pairs. Space–time quantum metasurfaces have been proposed as a platform to realize this physics via modulation of their optical properties. Here, we report the mechanical analog of this phenomenon by considering systems in which the lattice structure undergoes modulation in space and in time. We develop a microscopic theory that applies both to moving mirrors with a modulated surface profile and atomic array meta-mirrors with perturbed lattice configuration. Spatiotemporal modulation enables motion-induced generation of co- and cross-polarized photon pairs that feature frequency-linear momentum entanglement as well as vortex photon pairs featuring frequency-angular momentum entanglement. The proposed space–time dynamical Casimir effect can be interpreted as induced dynamical asymmetry in the quantum vacuum. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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20 pages, 4064 KiB  
Article
Optical Forces on an Oscillating Dipole Near VO2 Phase Transition
Universe 2021, 7(6), 159; https://doi.org/10.3390/universe7060159 - 22 May 2021
Cited by 1 | Viewed by 1785
Abstract
We investigate optical forces on oscillating dipoles close to a phase change vanadium dioxide (VO2) film, which exhibits a metal-insulator transition around 340 K and low thermal hysteresis. This configuration emulates the interaction between an illuminated nanosphere and an interface and [...] Read more.
We investigate optical forces on oscillating dipoles close to a phase change vanadium dioxide (VO2) film, which exhibits a metal-insulator transition around 340 K and low thermal hysteresis. This configuration emulates the interaction between an illuminated nanosphere and an interface and we employ a classical description to capture its important aspects. We consider both electric and magnetic dipoles for two different configurations, namely with the dipole moments parallel and perpendicular to the VO2 film. By using Bruggeman theory to describe the effective optical response of the material, we show that the thermal hysteresis present in the VO2 transition clearly shows up in the behavior of optical forces. In the near-field regime, the force on both dipoles can change from attractive to repulsive just by heating (or cooling) the film for a selected frequency range. We also verified that the optical forces are comparable to the Casimir-Polder force in a similar system, revealing the possibility of modulating or even changing the sign of the resultant force on an illuminated nano-object due to the presence of a thermochromic material. We hope that this work contributes to set the grounds for alternative approaches to control light-matter interactions using phase-change materials. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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19 pages, 440 KiB  
Article
Motion-Induced Radiation Due to an Atom in the Presence of a Graphene Plane
Universe 2021, 7(5), 158; https://doi.org/10.3390/universe7050158 - 20 May 2021
Cited by 8 | Viewed by 1408
Abstract
We study the motion-induced radiation due to the non-relativistic motion of an atom, coupled to the vacuum electromagnetic field by an electric dipole term, in the presence of a static graphene plate. After computing the probability of emission for an accelerated atom in [...] Read more.
We study the motion-induced radiation due to the non-relativistic motion of an atom, coupled to the vacuum electromagnetic field by an electric dipole term, in the presence of a static graphene plate. After computing the probability of emission for an accelerated atom in empty space, we evaluate the corrections due to the presence of the plate. We show that the effect of the plate is to increase the probability of emission when the atom is near the plate and oscillates along a direction perpendicular to it. On the contrary, for parallel oscillations, there is a suppression. We also evaluate the quantum friction on an atom moving at constant velocity parallel to the plate. We show that there is a threshold for quantum friction: friction occurs only when the velocity of the atom is larger than the Fermi velocity of the electrons in graphene. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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20 pages, 825 KiB  
Article
The Casimir Interaction between Spheres Immersed in Electrolytes
Universe 2021, 7(5), 156; https://doi.org/10.3390/universe7050156 - 18 May 2021
Cited by 12 | Viewed by 1936
Abstract
We investigate the Casimir interaction between two dielectric spheres immersed in an electrolyte solution. Since ionized solutions typically correspond to a plasma frequency much smaller than kBT/ħ at room temperature, only the contribution of the zeroth Matsubara frequency is [...] Read more.
We investigate the Casimir interaction between two dielectric spheres immersed in an electrolyte solution. Since ionized solutions typically correspond to a plasma frequency much smaller than kBT/ħ at room temperature, only the contribution of the zeroth Matsubara frequency is affected by ionic screening. We follow the electrostatic fluctuational approach and derive the zero-frequency contribution from the linear Poisson-Boltzmann (Debye-Hückel) equation for the geometry of two spherical surfaces of arbitrary radii. We show that a contribution from monopole fluctuations, which is reminiscent of the Kirkwood-Shumaker interaction, arises from the exclusion of ionic charge in the volume occupied by the spheres. Alongside the contribution from dipole fluctuations, such monopolar term provides the leading-order Casimir energy for very small spheres. Finally, we also investigate the large sphere limit and the conditions for validity of the proximity force (Derjaguin) approximation. Altogether, our results represent the first step towards a full scattering approach to the screening of the Casimir interaction between spheres that takes into account the nonlocal response of the electrolyte solution. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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8 pages, 222 KiB  
Communication
Axion Electrodynamics and the Axionic Casimir Effect
Universe 2021, 7(5), 133; https://doi.org/10.3390/universe7050133 - 05 May 2021
Cited by 8 | Viewed by 1606
Abstract
A general scheme for axion electrodynamics is given, in which a surrounding medium of constant permittivity and permeability is assumed. Then, as an application, we provide simple numerical estimates for the electromagnetic current density produced by the electrically neutral time-dependent axions [...] Read more.
A general scheme for axion electrodynamics is given, in which a surrounding medium of constant permittivity and permeability is assumed. Then, as an application, we provide simple numerical estimates for the electromagnetic current density produced by the electrically neutral time-dependent axions a=a(t) in a strong magnetic field. As is known, the assumption a=a(t) is common under astrophysical conditions. In the third part of the paper, we consider the implications by instead assuming an axion amplitude a(z) depending on one coordinate z only. If such an axion field is contained within two large metal plates, one obtains an axion-generated splitting of the eigenmodes for the dispersion relation. These modes yield equal, though opposite, contributions to the pressure on the plates. We calculate the magnitude of the splitting effect in a simple one-dimensional model. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
20 pages, 658 KiB  
Article
Casimir Interaction between a Plane and a Sphere: Correction to the Proximity-Force Approximation at Intermediate Temperatures
Universe 2021, 7(5), 129; https://doi.org/10.3390/universe7050129 - 03 May 2021
Cited by 3 | Viewed by 1720
Abstract
We consider the Casimir interaction energy between a plane and a sphere of radius R at finite temperature T as a function of the distance of closest approach L. Typical experimental conditions are such that the thermal wavelength [...] Read more.
We consider the Casimir interaction energy between a plane and a sphere of radius R at finite temperature T as a function of the distance of closest approach L. Typical experimental conditions are such that the thermal wavelength λT=c/kBT satisfies the condition LλTR. We derive the leading correction to the proximity-force approximation valid for such intermediate temperatures by developing the scattering formula in the plane-wave basis. Our analytical result captures the joint effect of the spherical geometry and temperature and is written as a sum of temperature-dependent logarithmic terms. Surprisingly, two of the logarithmic terms arise from the Matsubara zero-frequency contribution. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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24 pages, 480 KiB  
Article
Vacuum Polarization in a Zero-Width Potential: Self-Adjoint Extension
Universe 2021, 7(5), 127; https://doi.org/10.3390/universe7050127 - 02 May 2021
Cited by 3 | Viewed by 1223
Abstract
The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the [...] Read more.
The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model of pointlike interaction. We use the Perturbation theory in the Fourier space with dimensional regularization of the momentum integrals. In the weak-field approximation, we compute the effects of interest. The “mathematical” approach implies the self-adjoint extension technique. In the Quantum-Field-Theory framework we consider the massless scalar field in a 3-dimensional Euclidean space with an extracted point. With appropriate boundary conditions it is considered an adequate mathematical model for the description of a pointlike source. We compute the renormalized vacuum expectation value ϕ2(x)ren of the field square and the renormalized vacuum averaged of the scalar-field’s energy-momentum tensor Tμν(x)ren. For the physical interpretation of the extension parameter we compare these results with those of perturbative computations. In addition, we present some general formulae for vacuum polarization effects at large distances in the presence of an abstract weak potential with finite-sized compact support. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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14 pages, 3731 KiB  
Article
Nonlinear Actuation of Casimir Oscillators toward Chaos: Comparison of Topological Insulators and Metals
Universe 2021, 7(5), 123; https://doi.org/10.3390/universe7050123 - 29 Apr 2021
Cited by 3 | Viewed by 2807
Abstract
In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are [...] Read more.
In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are currently used in devices. Bifurcation and phase portraits analysis in conservative systems suggest that the strong difference between the conduction states of Bi2Se3 and Au yields sufficiently weaker Casimir force to enhance stable operation. Furthermore, for nonconservative driven systems, the Melnikov function and Poincare portrait analysis probed the occurrence of chaotic behavior leading to increased risk for stiction. It was found that the presence of the TI enhanced stable operation against chaotic behavior over a significantly wider range of operation conditions in comparison to typical metallic conductors. Therefore, the use of TIs can allow sufficient surface conductance to apply electrostatic compensation of residual contact potentials and, at the same time, to yield sufficiently weak Casimir forces favoring long-term stable actuation dynamics against chaotic behavior. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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20 pages, 581 KiB  
Article
No-Slip Boundary Conditions for Electron Hydrodynamics and the Thermal Casimir Pressure
Universe 2021, 7(4), 108; https://doi.org/10.3390/universe7040108 - 20 Apr 2021
Cited by 11 | Viewed by 1818
Abstract
We derive modified reflection coefficients for electromagnetic waves in the THz and far infrared range. The idea is based on hydrodynamic boundary conditions for metallic conduction electrons. The temperature-dependent part of the Casimir pressure between metal plates is evaluated. The results should shed [...] Read more.
We derive modified reflection coefficients for electromagnetic waves in the THz and far infrared range. The idea is based on hydrodynamic boundary conditions for metallic conduction electrons. The temperature-dependent part of the Casimir pressure between metal plates is evaluated. The results should shed light on the “thermal anomaly,” where measurements deviate from the standard fluctuation electrodynamics for conducting metals. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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20 pages, 3534 KiB  
Article
Van der Waals Interactions of Moving Particles with Surfaces of Cylindrical Geometry
Universe 2021, 7(4), 106; https://doi.org/10.3390/universe7040106 - 19 Apr 2021
Cited by 2 | Viewed by 1531
Abstract
General nonrelativistic theory has been developed and the expressions obtained for the tangential (dissipative) and radial (conservative) image forces and van der Waals forces (vdW) acting on charged and neutral particles when they move parallel to the axis of a cylinder with circular [...] Read more.
General nonrelativistic theory has been developed and the expressions obtained for the tangential (dissipative) and radial (conservative) image forces and van der Waals forces (vdW) acting on charged and neutral particles when they move parallel to the axis of a cylinder with circular cross-section, or in the space between coaxial cylinders. Numerical calculations of vdW forces have been performed for metal (Au) and dielectric (Si) materials of cylinders (filaments) and Cs atoms at velocities ~107m/s. A remarkable result is that in the case of metal cylinders (atomic filaments and chains) the dynamic vdW potential can be repulsive for certain values of the velocity–distance parameter and the characteristic atomic frequency. In the case of a Si material, the dynamic vdW potential increases relative to the static one (by modulus) when the velocity–distance parameter Vω0/R changes from zero to ~1.3 and then tends to zero. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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33 pages, 1060 KiB  
Article
Measurement of the Casimir Force between 0.2 and 8 μm: Experimental Procedures and Comparison with Theory
Universe 2021, 7(4), 93; https://doi.org/10.3390/universe7040093 - 07 Apr 2021
Cited by 42 | Viewed by 2377
Abstract
We present results on the determination of the differential Casimir force between an Au-coated sapphire sphere and the top and bottom of Au-coated deep silicon trenches performed by means of the micromechanical torsional oscillator in the range of separations from 0.2 to 8 [...] Read more.
We present results on the determination of the differential Casimir force between an Au-coated sapphire sphere and the top and bottom of Au-coated deep silicon trenches performed by means of the micromechanical torsional oscillator in the range of separations from 0.2 to 8 μm. The random and systematic errors in the measured force signal are determined at the 95% confidence level and combined into the total experimental error. The role of surface roughness and edge effects is investigated and shown to be negligibly small. The distribution of patch potentials is characterized by Kelvin probe microscopy, yielding an estimate of the typical size of patches, the respective r.m.s. voltage and their impact on the measured force. A comparison between the experimental results and theory is performed with no fitting parameters. For this purpose, the Casimir force in the sphere-plate geometry is computed independently on the basis of first principles of quantum electrodynamics using the scattering theory and the gradient expansion. In doing so, the frequency-dependent dielectric permittivity of Au is found from the optical data extrapolated to zero frequency by means of the plasma and Drude models. It is shown that the measurement results exclude the Drude model extrapolation over the region of separations from 0.2 to 4.8 μm, whereas the alternative extrapolation by means of the plasma model is experimentally consistent over the entire measurement range. A discussion of the obtained results is provided. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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27 pages, 430 KiB  
Article
Vacuum Polarization with Zero-Range Potentials on a Hyperplane
Universe 2021, 7(4), 92; https://doi.org/10.3390/universe7040092 - 07 Apr 2021
Cited by 3 | Viewed by 1570
Abstract
The quantum vacuum fluctuations of a neutral scalar field induced by background zero-range potentials concentrated on a flat hyperplane of co-dimension 1 in (d+1)-dimensional Minkowski spacetime are investigated. Perfectly reflecting and semitransparent surfaces are both taken into account, [...] Read more.
The quantum vacuum fluctuations of a neutral scalar field induced by background zero-range potentials concentrated on a flat hyperplane of co-dimension 1 in (d+1)-dimensional Minkowski spacetime are investigated. Perfectly reflecting and semitransparent surfaces are both taken into account, making reference to the most general local, homogeneous and isotropic boundary conditions compatible with the unitarity of the quantum field theory. The renormalized vacuum polarization is computed for both zero and non-zero mass of the field, implementing a local version of the zeta regularization technique. The asymptotic behaviors of the vacuum polarization for small and large distances from the hyperplane are determined to leading order. It is shown that boundary divergences are softened in the specific case of a pure Dirac delta potential. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
20 pages, 597 KiB  
Article
Casimir Effect for Fermion Condensate in Conical Rings
Universe 2021, 7(3), 73; https://doi.org/10.3390/universe7030073 - 22 Mar 2021
Cited by 4 | Viewed by 2138
Abstract
The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. [...] Read more.
The fermion condensate (FC) is investigated for a (2+1)-dimensional massive fermionic field confined on a truncated cone with an arbitrary planar angle deficit and threaded by a magnetic flux. Different combinations of the boundary conditions are imposed on the edges of the cone. They include the bag boundary condition as a special case. By using the generalized Abel-Plana-type summation formula for the series over the eigenvalues of the radial quantum number, the edge-induced contributions in the FC are explicitly extracted. The FC is an even periodic function of the magnetic flux with the period equal to the flux quantum. Depending on the boundary conditions, the condensate can be either positive or negative. For a massless field the FC in the boundary-free conical geometry vanishes and the nonzero contributions are purely edge-induced effects. This provides a mechanism for time-reversal symmetry breaking in the absence of magnetic fields. Combining the results for the fields corresponding to two inequivalent irreducible representations of the Clifford algebra, the FC is investigated in the parity and time-reversal symmetric fermionic models and applications are discussed for graphitic cones. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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12 pages, 469 KiB  
Article
The Low-Temperature Expansion of the Casimir-Polder Free Energy of an Atom with Graphene
Universe 2021, 7(3), 70; https://doi.org/10.3390/universe7030070 - 16 Mar 2021
Cited by 8 | Viewed by 1459
Abstract
We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential μ and mass gap parameter m. [...] Read more.
We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential μ and mass gap parameter m. The key role plays the dependence of graphene conductivities on the μ and m. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For μ>m, the thermal correction T2, and for μ<m, we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction T5. In the case of exact equality μ=m, the correction T. This point is unstable, and the system falls to the regime with μ>m or μ<m. The analytical calculations are illustrated by numerical evaluations for the Hydrogen atom/graphene system. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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8 pages, 540 KiB  
Communication
Role of Electronic Relaxation Rates in the Casimir Force between High-Tc Superconductors
Universe 2021, 7(3), 69; https://doi.org/10.3390/universe7030069 - 13 Mar 2021
Cited by 3 | Viewed by 1732
Abstract
We revisit the problem of the Casimir force between high-Tc superconductors below and above the critical temperature for the superconducting transition. Ceramic superconductors exhibit a different temperature dependence of the reflectivity when switching from the normal to the superconducting state. We [...] Read more.
We revisit the problem of the Casimir force between high-Tc superconductors below and above the critical temperature for the superconducting transition. Ceramic superconductors exhibit a different temperature dependence of the reflectivity when switching from the normal to the superconducting state. We leverage this unique characteristic with respect to ordinary metals to claim that these kind of materials can prove useful as an alternative system where the long-standing discussion on the role of electronic relaxation can be addressed. Furthermore, we show that the two main damping mechanisms associated with free and mid-infrared electrons dominate at very distinct scales, meaning that they can be considered separately when the Casimir force is measured as a function of slab distance. This facilitates the experimental identification of the role of the two electronic relaxation contributions to the force. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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20 pages, 670 KiB  
Article
Measuring the Casimir Forces with an Adhered Cantilever: Analysis of Roughness and Background Effects
Universe 2021, 7(3), 64; https://doi.org/10.3390/universe7030064 - 10 Mar 2021
Cited by 3 | Viewed by 1584
Abstract
Technological progress has made possible precise measurements of the Casimir forces at distances less than 100 nm. It has enabled stronger constraints on the non-Newtonian forces at short separations and improved control of micromechanical devices. Experimental information on the forces below 30 nm [...] Read more.
Technological progress has made possible precise measurements of the Casimir forces at distances less than 100 nm. It has enabled stronger constraints on the non-Newtonian forces at short separations and improved control of micromechanical devices. Experimental information on the forces below 30 nm is sparse and not precise due to pull-in instability and surface roughness. Recently, a method of adhered cantilever was proposed to measure the forces at small distances, which does not suffer from the pull-in instability. Deviation of the cantilever from a classic shape carries information on the forces acting nearby the adhered end. We calculate the force between a flat cantilever and rough Au plate and demonstrate that the effect of roughness dominates when the bodies approach the contact. Short-distance repulsion operating at the contact is included in the analysis. Deviations from the classic shape due to residual stress, inhomogeneous thickness of the cantilever, and finite compliance of the substrate are analysed. It is found that a realistic residual stress gives a negligible contribution to the shape, while the finite compliance and inhomogeneous thickness give measurable contributions that have to be subtracted from the raw data. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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16 pages, 788 KiB  
Article
Light and Airy: A Simple Solution for Relativistic Quantum Acceleration Radiation
Universe 2021, 7(3), 60; https://doi.org/10.3390/universe7030060 - 05 Mar 2021
Cited by 6 | Viewed by 1417
Abstract
We study the quantum radiation of particle production by vacuum from an ultra-relativistic moving mirror (dynamical Casimir effect) solution that allows (possibly for the first time) analytically calculable time evolution of particle creation and an Airy particle spectral distribution. The reality of the [...] Read more.
We study the quantum radiation of particle production by vacuum from an ultra-relativistic moving mirror (dynamical Casimir effect) solution that allows (possibly for the first time) analytically calculable time evolution of particle creation and an Airy particle spectral distribution. The reality of the beta Bogoliubov coefficients is responsible for the simplicity, and the mirror is asymptotically inertial at the speed of light, with finite energy production. We also discuss general relations regarding negative energy flux, the transformation to the 1-D Schrödinger equation, and the incompleteness of entanglement entropy. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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17 pages, 457 KiB  
Article
Vacuum Energy for a Scalar Field with Self-Interaction in (1 + 1) Dimensions
Universe 2021, 7(3), 55; https://doi.org/10.3390/universe7030055 - 03 Mar 2021
Cited by 5 | Viewed by 1409
Abstract
We calculate the vacuum (Casimir) energy for a scalar field with ϕ4 self-interaction in (1 + 1) dimensions non perturbatively, i.e., in all orders of the self-interaction. We consider massive and massless fields in a finite box with Dirichlet boundary conditions and [...] Read more.
We calculate the vacuum (Casimir) energy for a scalar field with ϕ4 self-interaction in (1 + 1) dimensions non perturbatively, i.e., in all orders of the self-interaction. We consider massive and massless fields in a finite box with Dirichlet boundary conditions and on the whole axis as well. For strong coupling, the vacuum energy is negative indicating some instability. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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Review

Jump to: Editorial, Research

39 pages, 3021 KiB  
Review
The Casimir Effect in Topological Matter
Universe 2021, 7(7), 237; https://doi.org/10.3390/universe7070237 - 09 Jul 2021
Cited by 16 | Viewed by 2481
Abstract
We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties [...] Read more.
We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics. Firstly, this is for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and, depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir–Lifshitz force, even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with the Hall conductivity that is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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18 pages, 333 KiB  
Review
Remarks on Some Results Related to the Thermal Casimir Effect in Einstein and Closed Friedmann Universes with a Cosmic String
Universe 2021, 7(7), 232; https://doi.org/10.3390/universe7070232 - 07 Jul 2021
Cited by 2 | Viewed by 1547
Abstract
In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a [...] Read more.
In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic field in these backgrounds, multiplied by a parameter λ=(1/α)1, where α is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, μ, by the expression α=1Gμ. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
21 pages, 466 KiB  
Review
Quantum Vacuum Energy of Self-Similar Configurations
Universe 2021, 7(5), 128; https://doi.org/10.3390/universe7050128 - 03 May 2021
Cited by 3 | Viewed by 1334
Abstract
We offer in this review a description of the vacuum energy of self-similar systems. We describe two views of setting self-similar structures and point out the main differences. A review of the authors’ work on the subject is presented, where they treat the [...] Read more.
We offer in this review a description of the vacuum energy of self-similar systems. We describe two views of setting self-similar structures and point out the main differences. A review of the authors’ work on the subject is presented, where they treat the self-similar system as a many-object problem embedded in a regular smooth manifold. Focused on Dirichlet boundary conditions, we report a systematic way of calculating the Casimir energy of self-similar bodies where the knowledge of the quantum vacuum energy of the single building block element is assumed and in fact already known. A fundamental property that allows us to proceed with our method is the dependence of the energy on a geometrical parameter that makes it possible to establish the scaling property of self-similar systems. Several examples are given. We also describe the situation, shown by other authors, where the embedded space is a fractal space itself, having fractal dimension. A fractal space does not hold properties that are rather common in regular spaces like the tangent space. We refer to other authors who explain how some self-similar configurations “do not have any smooth structures and one cannot define differential operators on them directly”. This gives rise to important differences in the behavior of the vacuum. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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36 pages, 1237 KiB  
Review
Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution
Universe 2021, 7(4), 84; https://doi.org/10.3390/universe7040084 - 01 Apr 2021
Cited by 41 | Viewed by 2278
Abstract
This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, [...] Read more.
This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, we show that the Casimir entropy calculated in the framework of Lifshitz theory violates the Nernst heat theorem when the well-approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature, this situation has been called the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. This review presents a summary of both the main theoretical and experimental findings on this subject. Next, a discussion is provided of the main approaches proposed in the literature to bring the Lifshitz theory into agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions, which consider the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results being in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations of the mass shell. Further advances and trends in this field of research are discussed. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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22 pages, 1401 KiB  
Review
Constraints on Theoretical Predictions beyond the Standard Model from the Casimir Effect and Some Other Tabletop Physics
Universe 2021, 7(3), 47; https://doi.org/10.3390/universe7030047 - 26 Feb 2021
Cited by 8 | Viewed by 1680
Abstract
We review the hypothetical interactions predicted beyond the Standard Model which could be constrained by using the results of tabletop laboratory experiments. These interactions are described by the power-type potentials with different powers, Yukawa potential, other spin-independent potentials, and by the spin-dependent potentials [...] Read more.
We review the hypothetical interactions predicted beyond the Standard Model which could be constrained by using the results of tabletop laboratory experiments. These interactions are described by the power-type potentials with different powers, Yukawa potential, other spin-independent potentials, and by the spin-dependent potentials of different kinds. In all these cases the current constraints on respective hypothetical interactions are considered which follow from the Casimir effect and some other tabletop physics. The exotic particles and constraints on them are discussed in the context of problems of the quantum vacuum, dark energy, and the cosmological constant. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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33 pages, 3981 KiB  
Review
Zeta Functions and the Cosmos—A Basic Brief Review
Universe 2021, 7(1), 5; https://doi.org/10.3390/universe7010005 - 30 Dec 2020
Cited by 5 | Viewed by 3345
Abstract
This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown [...] Read more.
This is a very basic and pedagogical review of the concepts of zeta function and of the associated zeta regularization method, starting from the notions of harmonic series and of divergent sums in general. By way of very simple examples, it is shown how these powerful methods are used for the regularization of physical quantities, such as quantum vacuum fluctuations in various contexts. In special, in Casimir effect setups, with a note on the dynamical Casimir effect, and mainly concerning its application in quantum theories in curved spaces, subsequently used in gravity theories and cosmology. The second part of this work starts with an essential introduction to large scale cosmology, in search of the observational foundations of the Friedmann-Lemaître-Robertson-Walker (FLRW) model, and the cosmological constant issue, with the very hard problems associated with it. In short, a concise summary of all these interrelated subjects and applications, involving zeta functions and the cosmos, and an updated list of the pioneering and more influential works (according to Google Scholar citation counts) published on all these matters to date, are provided. Full article
(This article belongs to the Special Issue The Casimir Effect: From a Laboratory Table to the Universe)
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