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Applied Sciences
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Computer Simulation of Quantum and Classical Systems
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Computer Simulation of Quantum and Classical Systems

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Applied Physics General".

Deadline for manuscript submissions: closed (25 April 2022) | Viewed by 12446

Special Issue Editors

Dr. Alessandro Sergi

E-Mail Website
Guest Editor
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale Stagno d’Alcontres 31, 98166 Messina, Italy
Interests: quantum-classical hybrid systems; non-Hermitian quantum mechanics; non-Hamiltonian systems; open quantum systems; quantum-biology
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gabriel Hanna

E-Mail Website
Guest Editor
Department of Chemistry, University of Alberta, Edmonton, AB T6G 2R3, Canada
Interests: mixed quantum-classica dynamics; charge transfer reactions; quantum energy transport; metal-organic frameworks

Special Issue Information

Dear Colleagues,

Notwithstanding the promises of quantum computing, classical simulations are still the method of choice for non-perturbative calculations in quantum and classical many-body systems. Classical simulations are closer to our intuition and can provide great insight. Hence, they will remain useful even after the coming of age of quantum computers.

Classical simulations of static and dynamical properties of many-body quantum systems are particularly challenging. For example, Quantum Monte Carlo methods exploit the trade-off between memory requirements and computer time. However, calculations of highly-correlated properties (as found in fermion or fractional statistics) require advanced algorithms for overcoming the infamous sign problem. Classical simulations of quantum dynamics require hybrid Monte Carlo-Molecular Dynamics algorithms that also aim to tame the sign problem. In certain cases, quantum-classical methods can diminish the overall computational complexity but they usually face difficulties in treating the interplay between coherence and dissipation at long times, when nonadiabatic dynamical effects are pronounced.

 There is a very strong connection between simulations of quantum and classical systems. This link is founded on very general grounds: quantum systems are often mapped onto classical models. Hence, the techniques used in simulations of classical systems are also useful for quantum systems and vice versa. Important advancements may be made when simulations of classical systems overcome the problems of multiscale modeling, long-time dynamics, and sampling of rare events. Papers dealing with the above topics are welcome for submission to this Special Issue.

Prof. Dr. Alessandro Sergi
Prof. Dr. Gabriel Hanna
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum Monte Carlo
  • quantum-classical dynamics
  • open quantum systems
  • semi-classical dynamics
  • quantum dynamics
  • molecular dynamics

Published Papers (6 papers)

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Research

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39 pages, 1055 KiB  
Article
Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths
by Simon Huppert, Thomas Plé, Sara Bonella, Philippe Depondt and Fabio Finocchi
Appl. Sci. 2022, 12(9), 4756; https://doi.org/10.3390/app12094756 - 09 May 2022
Cited by 6 | Viewed by 1936
Abstract
This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in [...] Read more.
This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths. Full article
(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)
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20 pages, 3946 KiB  
Article
Molecular Dynamics of Solids at Constant Pressure and Stress Using Anisotropic Stochastic Cell Rescaling
by Vittorio Del Tatto, Paolo Raiteri, Mattia Bernetti and Giovanni Bussi
Appl. Sci. 2022, 12(3), 1139; https://doi.org/10.3390/app12031139 - 21 Jan 2022
Cited by 1 | Viewed by 2966
Abstract
Molecular dynamics simulations of solids are often performed using anisotropic barostats that allow the shape and volume of the periodic cell to change during the simulation. Most existing schemes are based on a second-order differential equation that might lead to undesired oscillatory behaviors [...] Read more.
Molecular dynamics simulations of solids are often performed using anisotropic barostats that allow the shape and volume of the periodic cell to change during the simulation. Most existing schemes are based on a second-order differential equation that might lead to undesired oscillatory behaviors and should not be used in the equilibration phase. We recently introduced stochastic cell rescaling, a first-order stochastic barostat that can be used for both the equilibration and production phases. Only the isotropic and semi-isotropic variants have been formulated and implemented so far. In this paper, we develop and implement the equations of motion of the fully anisotropic variant and test them on Lennard-Jones solids, ice, gypsum, and gold. The algorithm has a single parameter that controls the relaxation time of the volume, results in the exponential decay of correlation functions, and can be effectively applied to a wide range of systems. Full article
(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)
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21 pages, 3682 KiB  
Article
Classical and Quantum Gases on a Semiregular Mesh
by Davide De Gregorio and Santi Prestipino
Appl. Sci. 2021, 11(21), 10053; https://doi.org/10.3390/app112110053 - 27 Oct 2021
Cited by 2 | Viewed by 1295
Abstract
The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With [...] Read more.
The main objective of a statistical mechanical calculation is drawing the phase diagram of a many-body system. In this respect, discrete systems offer the clear advantage over continuum systems of an easier enumeration of microstates, though at the cost of added abstraction. With this in mind, we examine a system of particles living on the vertices of the (biscribed) pentakis dodecahedron, using different couplings for first and second neighbor particles to induce a competition between icosahedral and dodecahedral orders. After working out the phases of the model at zero temperature, we carry out Metropolis Monte Carlo simulations at finite temperature, highlighting the existence of smooth transitions between distinct “phases”. The sharpest of these crossovers are characterized by hysteretic behavior near zero temperature, which reveals a bottleneck issue for Metropolis dynamics in state space. Next, we introduce the quantum (Bose-Hubbard) counterpart of the previous model and calculate its phase diagram at zero and finite temperatures using the decoupling approximation. We thus uncover, in addition to Mott insulating “solids”, also the existence of supersolid “phases” which progressively shrink as the system is heated up. We argue that a quantum system of the kind described here can be realized with programmable holographic optical tweezers. Full article
(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)
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12 pages, 728 KiB  
Article
Adjustment of Terahertz Properties Assigned to the First Lowest Transition of (D+, X) Excitonic Complex in a Single Spherical Quantum Dot Using Temperature and Pressure
by Noreddine Aghoutane, Laura M. Pérez, Anton Tiutiunnyk, David Laroze, Sotirios Baskoutas, Francis Dujardin, Abdelouahad El Fatimy, Mohamed El-Yadri and El Mustapha Feddi
Appl. Sci. 2021, 11(13), 5969; https://doi.org/10.3390/app11135969 - 27 Jun 2021
Cited by 5 | Viewed by 1998
Abstract
This theoretical study is devoted to the effects of pressure and temperature on the optoelectronic properties assigned to the first lowest transition of the (D+,X) excitonic complex (exciton-ionized donor) inside a single [...] Read more.
This theoretical study is devoted to the effects of pressure and temperature on the optoelectronic properties assigned to the first lowest transition of the (D+,X) excitonic complex (exciton-ionized donor) inside a single AlAs/GaAs/AlAs spherical quantum dot. Calculations are performed within the effective mass approximation theory using the variational method. Optical absorption and refractive index as function of the degree of confinement, pressure, and temperature are investigated. Numerical calculation shows that the pressure favors the electron-hole and electron-ionized donor attractions which leads to an enhancement of the binding energy, while an increasing of the temperature tends to reduce it. Our investigations show also that the resonant peaks of the absorption coefficient and the refractive index are located in the terahertz region and they undergo a shift to higher (lower) therahertz frequencies when the pressure (temperature) increases. The opposite effects caused by temperature and pressure have great practical importance because they offer an alternative approach for the adjustment and the control of the optical frequencies resulting from the transition between the fundamental and the first excited state of exciton bound to an ionized dopant. The comparison of the optical properties of exciton, impurity and (D+,X) facilitates the experimental identification of these transitions which are often close. Our investigation shows that the optical responses of (D+,X) are located between the exciton (high energy region) and donor impurity (low energy region) peaks. The whole of these conclusions may lead to the novel light detector or source of terahertz range. Full article
(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)
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8 pages, 359 KiB  
Article
Superfluid Transition and Specific Heat of the 2D x-y Model: Monte Carlo Simulation
by Phong H. Nguyen and Massimo Boninsegni
Appl. Sci. 2021, 11(11), 4931; https://doi.org/10.3390/app11114931 - 27 May 2021
Cited by 8 | Viewed by 2203
Abstract
We present results of large-scale Monte Carlo simulations of the 2D classical x-y model on the square lattice. We obtain high accuracy results for the superfluid fraction and for the specific heat as a function of temperature, for systems of size [...] Read more.
We present results of large-scale Monte Carlo simulations of the 2D classical x-y model on the square lattice. We obtain high accuracy results for the superfluid fraction and for the specific heat as a function of temperature, for systems of size L×L with L up to 212. Our estimate for the superfluid transition temperature is consistent with those furnished in all previous studies. The specific heat displays a well-defined peak, whose shape and position are independent of the size of the lattice for L>28, within the statistical uncertainties of our calculations. The implications of these results on the interpretation of experiments on adsorbed thin films of 4He are discussed. Full article
(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)
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Review

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11 pages, 527 KiB  
Review
DECIDE: A Deterministic Mixed Quantum-Classical Dynamics Approach
by Zhe Liu, Alessandro Sergi and Gabriel Hanna
Appl. Sci. 2022, 12(14), 7022; https://doi.org/10.3390/app12147022 - 12 Jul 2022
Cited by 1 | Viewed by 1131
Abstract
Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing [...] Read more.
Mixed quantum-classical dynamics provides an efficient way of simulating the dynamics of quantum subsystems coupled to many-body environments. Many processes, including proton-transfer reactions, electron-transfer reactions, and vibrational energy transport, for example, take place in such open systems. The most accurate algorithms for performing mixed quantum-classical simulations require very large ensembles of trajectories to obtain converged expectation values, which is computationally prohibitive for quantum subsystems containing even a few degrees of freedom. The recently developed “Deterministic evolution of coordinates with initial decoupled equations” (DECIDE) method has demonstrated high accuracy and low computational cost for a host of model systems; however, these applications relied on representing the equations of motion in subsystem and adiabatic energy bases. While these representations are convenient for certain systems, the position representation is convenient for many other systems, including systems undergoing proton- and electron-transfer reactions. Thus, in this review, we provide a step-by-step derivation of the DECIDE approach and demonstrate how to cast the DECIDE equations in a quantum harmonic oscillator position basis for a simple one-dimensional (1D) hydrogen bond model. After integrating the DECIDE equations of motion on this basis, we show that the total energy of the system is conserved for this model and calculate various quantities of interest. Limitations of casting the equations in an incomplete basis are also discussed. Full article
(This article belongs to the Special Issue Computer Simulation of Quantum and Classical Systems)
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