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Quantum Rep., Volume 5, Issue 1 (March 2023) – 21 articles

Cover Story (view full-size image): In this work, we show the complexity measures (Cramér–Rao, Fisher–Shannon; LMC–Rényi) for the quantum states of the multi-dimensional hydrogenic system from first principles. Then, we apply them to the highly excited Rydberg states, which are promising elements used to store and manipulate quantum information due to their extraordinary properties (large dipole polarizability, long-range dipolar interactions, etc.). The hydrogenic system plays a fundamental role in multi-dimensional quantum physics, since it encompasses many three-dimensional hydrogenic atoms and low- and high-dimensional objects in condensed matter, quantum cosmology and quantum computation, including quantum wells, wires and dots, semiconductor excitons, qubits, exotic atoms, antimatter atoms, etc. View this paper
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14 pages, 271 KiB  
Article
Centering the Born Rule
by Isaac Wilhelm
Quantum Rep. 2023, 5(1), 311-324; https://doi.org/10.3390/quantum5010021 - 21 Mar 2023
Viewed by 1276
Abstract
The centered Everett interpretation solves a problem that various approaches to quantum theory face. In this paper, I continue developing the theory underlying that solution. In particular, I defend the centered Everett interpretation against a few objections, and I provide additional motivation for [...] Read more.
The centered Everett interpretation solves a problem that various approaches to quantum theory face. In this paper, I continue developing the theory underlying that solution. In particular, I defend the centered Everett interpretation against a few objections, and I provide additional motivation for some of its key features. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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17 pages, 407 KiB  
Article
Asymptotic Quantization of a Particle on a Sphere
by José L. Romero and Andrei B. Klimov
Quantum Rep. 2023, 5(1), 294-310; https://doi.org/10.3390/quantum5010020 - 21 Mar 2023
Viewed by 1735
Abstract
Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space TS2 in the limit of large average angular momentum. The cotangent bundle [...] Read more.
Quantum systems whose states are tightly distributed among several invariant subspaces (variable spin systems) can be described in terms of distributions in a four-dimensional phase-space TS2 in the limit of large average angular momentum. The cotangent bundle TS2 is also the classical manifold for systems with E(3) symmetry group with appropriately fixed Casimir operators. This allows us to employ the asymptotic form of the star-product proper for variable (integer) spin systems to develop a deformation quantization scheme for a particle moving on the two-dimensional sphere, whose observables are elements of e(3) algebra and the corresponding phase-space is TS2. We show that the standard commutation relations of the e(3) algebra are recovered from the corresponding classical Poisson brackets and the explicit expressions for the eigenvalues and eigenfunctions of some quantized classical observables (such as the angular momentum operators and their squares) are obtained. Full article
(This article belongs to the Special Issue Continuous and Discrete Phase-Space Methods and Their Applications)
12 pages, 2968 KiB  
Article
Molecular Structure of M(N13) Compounds with 12-Membered Nitrogen-Containing Cycle and Axial Nitrogen Atom (M = Mn, Fe): Quantum-Chemical Design by DFT Method
by Oleg V. Mikhailov and Denis V. Chachkov
Quantum Rep. 2023, 5(1), 282-293; https://doi.org/10.3390/quantum5010019 - 15 Mar 2023
Cited by 2 | Viewed by 1281
Abstract
Based on the results of a quantum chemical calculation using the DFT method in the B3PW91/TZVP, OPBE/TZVP, M06/TZVP, and M062/Def2TZVP levels, the possibility of the existence of M(N13) chemical compounds (M = Mn, Fe) that are unknown for these elements has [...] Read more.
Based on the results of a quantum chemical calculation using the DFT method in the B3PW91/TZVP, OPBE/TZVP, M06/TZVP, and M062/Def2TZVP levels, the possibility of the existence of M(N13) chemical compounds (M = Mn, Fe) that are unknown for these elements has been predicted. Data on the structural parameters, the multiplicity of the ground state, APT and NBO analysis, and standard thermodynamic parameters of formation (standard enthalpy ΔfH0, entropy S0, and Gibbs’s energy ΔfG0) for these compounds are presented. Full article
(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)
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15 pages, 335 KiB  
Article
Everett’s Interpretation and Convivial Solipsism
by Hervé Zwirn
Quantum Rep. 2023, 5(1), 267-281; https://doi.org/10.3390/quantum5010018 - 10 Mar 2023
Cited by 2 | Viewed by 1433
Abstract
I show how the quantum paradoxes occurring when we adopt a standard realist framework (or a framework in which the collapse implies a physical change of the state of the system) vanish if we abandon the idea that a measurement is related (directly [...] Read more.
I show how the quantum paradoxes occurring when we adopt a standard realist framework (or a framework in which the collapse implies a physical change of the state of the system) vanish if we abandon the idea that a measurement is related (directly or indirectly) to a physical change of state. In Convivial Solipsism, similarly to Everett’s interpretation, there is no collapse of the wave function. However, contrary to Everett’s interpretation, there is only one world. This also allows us to get rid of any non-locality and to provide a solution to the Wigner’s friend problem and its more recent versions. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
14 pages, 4672 KiB  
Article
Quantum Study of the Optical Conductivity of Composite Films Formed by Bilayer Graphene and Single-Walled Carbon Nanotubes under Axial Stretching
by Michael M. Slepchenkov, Pavel V. Barkov and Olga E. Glukhova
Quantum Rep. 2023, 5(1), 253-266; https://doi.org/10.3390/quantum5010017 - 06 Mar 2023
Viewed by 1412
Abstract
In this article, quantum methods are used to study the optical properties of composite films formed by AB-stacked bilayer graphene and chiral single-walled carbon nanotubes (SWCNT) (12, 6) with a diameter of 1.2 nm. The analysis of optical properties is carried out on [...] Read more.
In this article, quantum methods are used to study the optical properties of composite films formed by AB-stacked bilayer graphene and chiral single-walled carbon nanotubes (SWCNT) (12, 6) with a diameter of 1.2 nm. The analysis of optical properties is carried out on the basis of the results of calculating the diagonal elements of complex optical conductivity tensor in the wavelength range of 0.2–2 μm. Two cases of electromagnetic radiation polarization are considered: along the X axis (along the graphene bilayer) and along the Y axis (along the nanotube axis). The calculations are performed for three topological models (V1, V2, V3) of composite films, which differ in the width of the graphene bilayer and in the value of the shift between graphene layers. It is found that in the case of polarization along the X axis, the profile of the real part of optical conductivity in the region of extremal and middle UV radiation is determined by SWCNT (12, 6), and in the region of near UV and visible radiations, it is determined by bilayer graphene. In the case of polarization along the Y axis, the profile of the real part of optical conductivity in the region of extremal, near UV, and visible radiation is determined by SWCNT (12, 6), and in the region of the mid-UV range, it is determined by bilayer graphene. Regularities in the change in the profile of the surface optical conductivity of bilayer graphene-SWCNT (12,6) composite films under the action of stretching deformation along the Y axis are revealed. For models V1 (width of the graphene nanoribbon is 0.5 nm, the shift between layers is 0.48 nm) and V2 (width of the graphene nanoribbon is 0.71 nm, the shift between layers is 0.27 nm), the shift of the conductivity peaks in the region of extreme UV radiation along the wavelength to the right is shown. For the model V3 (width of the graphene nanoribbon is 0.92 nm, the shift between layers is 0.06 nm), the shift of the conductivity peaks to the right along the wavelength is observed not only in the region of extreme UV radiation, but also in the region of visible radiation. It is assumed that graphene-SWCNT (12,6) composite films with island topology are promising materials for photodetectors in the UV-visible and near-IR ranges. Full article
(This article belongs to the Special Issue Fundamentals and Applications in Quantum Chemistry)
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16 pages, 300 KiB  
Article
Set Theory and Many Worlds
by Paul Tappenden
Quantum Rep. 2023, 5(1), 237-252; https://doi.org/10.3390/quantum5010016 - 02 Mar 2023
Cited by 1 | Viewed by 1668
Abstract
The 2022 Tel Aviv conference on the many-worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders–Wallace–Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always [...] Read more.
The 2022 Tel Aviv conference on the many-worlds interpretation of quantum mechanics highlighted many differences between theorists. A very significant dichotomy is between Everettian fission (splitting) and Saunders–Wallace–Wilson divergence. For fission, an observer may have multiple futures, whereas for divergence they always have a single future. Divergence was explicitly introduced to resolve the problem of pre-measurement uncertainty for Everettian theory, which is universally believed to be absent for fission. Here I maintain that there is indeed pre-measurement uncertainty prior to fission, so long as objective probability is a property of Everettian branches. This is made possible if the universe is a set and branches are subsets with a probability measure. A universe that is a set of universes that are macroscopically isomorphic and span all possible configurations of local beäbles fulfills that role. If objective probability is a property of branches, then a successful Deutsch–Wallace decision-theoretic argument would justify the Principal Principle and be part of probability theory rather than specific to many-worlds theory. Any macroscopic object in our environment becomes a set of isomorphs with different microscopic configurations, each in an elemental universe (elemental in the set-theoretic sense). This is similar to the many-interacting-worlds theory, but the observer inhabits the set of worlds, not an individual world. An observer has many elemental bodies. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
9 pages, 385 KiB  
Article
The Ontology of the Many-Worlds Theory
by Per Arve
Quantum Rep. 2023, 5(1), 228-236; https://doi.org/10.3390/quantum5010015 - 01 Mar 2023
Viewed by 1406
Abstract
It is shown that the wavefunction describes our observations using the postulate that relates position to the distribution |Ψ|2. This finding implies that a primary ontology is unnecessary. However, what is real is not directly represented by the wavefunction [...] Read more.
It is shown that the wavefunction describes our observations using the postulate that relates position to the distribution |Ψ|2. This finding implies that a primary ontology is unnecessary. However, what is real is not directly represented by the wavefunction but by the gauge invariants. In light of the presented ontology, Spacetime State Realism becomes not a fundamental ontology but derived. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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4 pages, 213 KiB  
Article
The MWI and Distributive Justice
by David Papineau and Thomas Rowe
Quantum Rep. 2023, 5(1), 224-227; https://doi.org/10.3390/quantum5010014 - 28 Feb 2023
Viewed by 1115
Abstract
Everettians generally argue that their view recommends just the same rational choices as orthodoxy. In this note, however, we will show that Everettians should advocate non-standard choices in one specific kind of situation, namely situations where different people have unequal claims to an [...] Read more.
Everettians generally argue that their view recommends just the same rational choices as orthodoxy. In this note, however, we will show that Everettians should advocate non-standard choices in one specific kind of situation, namely situations where different people have unequal claims to an indivisible good. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
26 pages, 469 KiB  
Article
Analytical Solution to DGLAP Integro-Differential Equation in a Simple Toy-Model with a Fixed Gauge Coupling
by Gustavo Álvarez, Gorazd Cvetič, Bernd A. Kniehl, Igor Kondrashuk and Ivan Parra-Ferrada
Quantum Rep. 2023, 5(1), 198-223; https://doi.org/10.3390/quantum5010013 - 27 Feb 2023
Cited by 2 | Viewed by 1759
Abstract
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be [...] Read more.
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not run. This may be N=4 supersymmetric gauge theory with softly broken supersymmetry, other finite supersymmetric gauge theory with a lower level of supersymmetry, or topological Chern–Simons field theories. We maintain only one term in the splitting function of unintegrated gluon distribution and solve DGLAP analytically for this simplified splitting function. The solution is found using the Cauchy integral formula. The solution restricts the form of the unintegrated gluon distribution as a function of momentum transfer and of Bjorken x. Then, we consider an almost realistic splitting function of unintegrated gluon distribution as an input to DGLAP equation and solve it by the same method which we have developed to solve DGLAP equation for the toy-model. We study a result obtained for the realistic gluon distribution and find a singular Bessel-like behavior in the vicinity of the point x=0 and a smooth behavior in the vicinity of the point x=1. Full article
12 pages, 505 KiB  
Article
Consistent Histories and Many Worlds
by Tomasz Bigaj
Quantum Rep. 2023, 5(1), 186-197; https://doi.org/10.3390/quantum5010012 - 23 Feb 2023
Viewed by 1399
Abstract
This paper discusses the fundamental assumptions and background of the consistent histories (CH) approach to quantum mechanics. The focus of the paper is on the concept of frameworks. It is proposed that frameworks should be interpreted objectively as observer-independent realities. Two further options [...] Read more.
This paper discusses the fundamental assumptions and background of the consistent histories (CH) approach to quantum mechanics. The focus of the paper is on the concept of frameworks. It is proposed that frameworks should be interpreted objectively as observer-independent realities. Two further options are considered: a hidden-variables variant of the CH approach, and a many-worlds version, which considers each individual history belonging to a given family as describing a separate world. The latter interpretation is subsequently compared and contrasted with the standard many-worlds interpretation. Finally, the solution to the measurement problem offered by the many-worlds variant of CH is analyzed and amended. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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30 pages, 2091 KiB  
Article
Local Quantum Theory with Fluids in Space-Time
by Mordecai Waegell
Quantum Rep. 2023, 5(1), 156-185; https://doi.org/10.3390/quantum5010011 - 21 Feb 2023
Cited by 1 | Viewed by 1615
Abstract
In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger’s theory is presented, which reproduces all of the standard empirical predictions of conventional [...] Read more.
In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger’s theory is presented, which reproduces all of the standard empirical predictions of conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant “local hidden variable theory” in space-time, whose existence proves definitively that such theories are possible. This does not conflict with Bell’s theorem because it is a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems’ wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
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18 pages, 4187 KiB  
Article
Patient Data Analysis with the Quantum Clustering Method
by Shradha Deshmukh, Bikash K. Behera and Preeti Mulay
Quantum Rep. 2023, 5(1), 138-155; https://doi.org/10.3390/quantum5010010 - 13 Feb 2023
Cited by 1 | Viewed by 1918
Abstract
Quantum computing is one of the most promising solutions for solving optimization problems in the healthcare world. Quantum computing development aims to light up the execution of a vast and complex set of algorithmic instructions. For its implementation, the machine learning models are [...] Read more.
Quantum computing is one of the most promising solutions for solving optimization problems in the healthcare world. Quantum computing development aims to light up the execution of a vast and complex set of algorithmic instructions. For its implementation, the machine learning models are continuously evolving. Hence, the new challenge is to improve the existing complex and critical machine learning training models. Therefore, the healthcare sector is shifting from a classical to a quantum domain to sustain patient-oriented attention to healthcare patrons. This paper presents a hybrid classical-quantum approach for training the unsupervised data models. In order to achieve good performance and optimization of the machine learning algorithms, a quantum k-means (QK-means) clustering problem was deployed on the IBM quantum simulators, i.e.,the IBM QASM simulator. In the first place, the approach was theoretically studied and then implemented to analyze the experimental results. The approach was further tested using small synthetics and cardiovascular datasets on a qsam simulator to obtain the clustering solution. The future direction connecting the dots is the incremental k-means algorithm with the quantum platform, which would open hitherto unimaginable technological doors. Full article
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22 pages, 447 KiB  
Review
Cramér–Rao, Fisher–Shannon and LMC–Rényi Complexity-like Measures of Multidimensional Hydrogenic Systems with Application to Rydberg States
by Jesús S. Dehesa
Quantum Rep. 2023, 5(1), 116-137; https://doi.org/10.3390/quantum5010009 - 09 Feb 2023
Cited by 2 | Viewed by 1413
Abstract
Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by [...] Read more.
Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by means of the monotone complexity measures of Cramér–Rao, Fisher–Shannon and LMC(Lopez-Ruiz, Mancini, Calbet)–Rényi types. These quantities are shown to be analytically determined from first principles, i.e., explicitly in terms of the space dimensionality D, the nuclear charge and the hyperquantum numbers, which characterize the system’ states. Then, they are applied to several relevant classes of particular states with emphasis on the quasi-spherical and the highly excited Rydberg states, obtaining compact and physically transparent expressions. This is possible because of the use of powerful techniques of approximation theory and orthogonal polynomials, asymptotics and generalized hypergeometric functions. Full article
14 pages, 374 KiB  
Article
The Relation between Wavefunction and 3D Space Implies Many Worlds with Local Beables and Probabilities
by Ovidiu Cristinel Stoica
Quantum Rep. 2023, 5(1), 102-115; https://doi.org/10.3390/quantum5010008 - 08 Feb 2023
Viewed by 1365
Abstract
We show that the quantum wavefunctional can be seen as a set of classical fields on the 3D space aggregated by a measure. We obtain a complete description of the wavefunctional in terms of classical local beables. With this correspondence, classical explanations of [...] Read more.
We show that the quantum wavefunctional can be seen as a set of classical fields on the 3D space aggregated by a measure. We obtain a complete description of the wavefunctional in terms of classical local beables. With this correspondence, classical explanations of the macro level and of probabilities transfer almost directly to the quantum. A key difference is that, in quantum theory, the classical states coexist in parallel, so the probabilities come from self-location uncertainty. We show that these states are distributed according to the Born rule. The coexistence of classical states implies that there are many worlds, even if we assume the collapse postulate. This leads automatically to a new version of the many-worlds interpretation in which the major objections are addressed naturally. We show that background-free quantum gravity provides additional support for this proposal and suggests why branching happens toward the future. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
22 pages, 346 KiB  
Article
Many-Worlds: Why Is It Not the Consensus?
by Valia Allori
Quantum Rep. 2023, 5(1), 80-101; https://doi.org/10.3390/quantum5010007 - 06 Feb 2023
Viewed by 2753
Abstract
In this paper, I argue that the many-worlds theory, even if it is arguably the mathematically most straightforward realist reading of quantum formalism, even if it is arguably local and deterministic, is not universally regarded as the best realist quantum theory because it [...] Read more.
In this paper, I argue that the many-worlds theory, even if it is arguably the mathematically most straightforward realist reading of quantum formalism, even if it is arguably local and deterministic, is not universally regarded as the best realist quantum theory because it provides a type of explanation that is not universally accepted. Since people disagree about what desiderata a satisfactory physical theory should possess, they also disagree about which explanatory schema one should look for in a theory, and this leads different people to different options. Full article
(This article belongs to the Special Issue The Many-Worlds Interpretation of Quantum Mechanics)
2 pages, 164 KiB  
Editorial
Acknowledgment to the Reviewers of Quantum Reports in 2022
by Quantum Reports Editorial Office
Quantum Rep. 2023, 5(1), 78-79; https://doi.org/10.3390/quantum5010006 - 20 Jan 2023
Viewed by 930
Abstract
High-quality academic publishing is built on rigorous peer review [...] Full article
26 pages, 435 KiB  
Article
Simple and Rigorous Proof Method for the Security of Practical Quantum Key Distribution in the Single-Qubit Regime Using Mismatched Basis Measurements
by Michel Boyer, Gilles Brassard, Nicolas Godbout, Rotem Liss and Stéphane Virally
Quantum Rep. 2023, 5(1), 52-77; https://doi.org/10.3390/quantum5010005 - 18 Jan 2023
Cited by 1 | Viewed by 1227
Abstract
Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD implementations typically do not take into account all possible loopholes, [...] Read more.
Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD implementations typically do not take into account all possible loopholes, and practical devices are still not fully characterized for obtaining tight and realistic key rates. We present a simple method of computing secure key rates for any practical implementation of discrete-variable QKD (which can also apply to measurement-device-independent QKD), initially in the single-qubit lossless regime, and we rigorously prove its unconditional security against any possible attack. We hope our method becomes one of the standard tools used for analysing, benchmarking, and standardizing all practical realizations of QKD. Full article
14 pages, 1991 KiB  
Article
Uncertainty Relation and the Thermal Properties of an Isotropic Harmonic Oscillator (IHO) with the Inverse Quadratic (IQ) Potentials and the Pseudo-Harmonic (PH) with the Inverse Quadratic (IQ) Potentials
by Clement A. Onate, Ituen B. Okon, Gian. O. Jude, Michael C. Onyeaju and Akaninyene. D. Antia
Quantum Rep. 2023, 5(1), 38-51; https://doi.org/10.3390/quantum5010004 - 12 Jan 2023
Cited by 1 | Viewed by 1066
Abstract
The solutions for a combination of the isotropic harmonic oscillator plus the inversely quadratic potentials and a combination of the pseudo-harmonic with inversely quadratic potentials has not been reported, though the individual potentials have been given attention. This study focuses on the solutions [...] Read more.
The solutions for a combination of the isotropic harmonic oscillator plus the inversely quadratic potentials and a combination of the pseudo-harmonic with inversely quadratic potentials has not been reported, though the individual potentials have been given attention. This study focuses on the solutions of the combination of the potentials, as stated above using the parametric Nikiforov–Uvarov (PNV) as the traditional technique to obtain the energy equations and their corresponding unnormalized radial wave functions. To deduce the application of these potentials, the expectation values, the uncertainty in the position and momentum, and the thermodynamic properties, such as the mean energy, entropy, heat capacity, and the free mean energy, are also calculated via the partition function. The result shows that the spectra for the PHIQ are higher than the spectra for the IHOIQ. It is also shown that the product of the uncertainties obeyed the Heisenberg uncertainty relation/principle. Finally, the thermal properties of the two potentials exhibit similar behaviours. Full article
(This article belongs to the Topic Theoretical, Quantum and Computational Chemistry)
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16 pages, 344 KiB  
Article
Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?
by Martin Bojowald and Artur Tsobanjan
Quantum Rep. 2023, 5(1), 22-37; https://doi.org/10.3390/quantum5010003 - 30 Dec 2022
Viewed by 1373
Abstract
Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very [...] Read more.
Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of “almost-positive” states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame–system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics. Full article
10 pages, 354 KiB  
Article
Blocky Diagonalized Scattering Matrices in Chaotic Scattering with Direct Processes
by Felipe Castañeda-Ramírez and Moisés Martínez-Mares
Quantum Rep. 2023, 5(1), 12-21; https://doi.org/10.3390/quantum5010002 - 21 Dec 2022
Viewed by 1156
Abstract
Scattering matrices that can be diagonalized by a rotation through an angle θ in 2×2 blocks of independent scattering matrices of rank N, are considered. Assuming that the independent scattering matrices are chosen from one of the circular ensembles, or [...] Read more.
Scattering matrices that can be diagonalized by a rotation through an angle θ in 2×2 blocks of independent scattering matrices of rank N, are considered. Assuming that the independent scattering matrices are chosen from one of the circular ensembles, or from the Poisson kernel, the 2N×2N scattering matrix may describe the scattering through chaotic cavities with reduced symmetry in the absence, or presence, of direct processes, respectively. To illustrate the effect of such symmetry, the statistical distribution of the dimensionless conductance through a ballistic chaotic cavity in the presence of direct processes is analyzed for N=1 using analytical calculations. We make a conjecture for N=2 in the absence of direct processes, which is verified by numerical random-matrix theory simulations, and the first two moments are calculated analytically for arbitrary N. Full article
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11 pages, 3809 KiB  
Article
Effect of a Moving Mirror on the Free Fall of a Quantum Particle in a Homogeneous Gravitational Field
by Jawad Allam and Alex Matzkin
Quantum Rep. 2023, 5(1), 1-11; https://doi.org/10.3390/quantum5010001 - 20 Dec 2022
Cited by 1 | Viewed by 1448
Abstract
We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer—a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of [...] Read more.
We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer—a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of a falling particle. We find that some effects, such as the fact that a quantum particle hitting a moving mirror may bounce significantly higher than when the mirror is fixed, are in line with classical intuition. Other effects, such as the change in relative phases or in the current density in spatial regions arbitrarily far from the mirror are specifically quantum. We further discuss how the effects produced by a moving mirror could be observed in link with current experiments, in particular with cold neutrons. Full article
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