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Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 17122

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Special Issue Editors

Prof. Dr. Ofir E. Alon

E-Mail Website
Guest Editor

1. Department of Mathematics, University of Haifa, Haifa 3498838, Israel
2. Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
Interests: AMO physics; Bose–Einstein condensates; many-body theory; out-of-equilibrium dynamics; fragmentation; variances; MCTDHB; solvable models; computational physics; multiconfigurational methods

Dr. Axel U. J. Lode

E-Mail Website
Guest Editor

Institute of Physics, Albert-Ludwig University of Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
Interests: Bose–Einstein condensation; single-shot images; correlation functions; ultracold atoms; time-dependent Schrödinger equation; MCTDH-X; many-body systems; computational methods; applied mathematics

Special Issue Information

Dear Colleagues,

The Schrödinger equation is central to quantum mechanics and a cornerstone for the description of many fascinating phenomena in AMO, chemical, condensed-matter, and nuclear physics. Quantum many-body dynamics attract an enormous amount of interest in physics, chemistry, and mathematics alike.

The purpose of this Special Issue is to amalgamate contributions from researchers actively working on solutions, applications, and theoretical methodologies for the time-dependent Schrödinger equation for few- and many-particle systems.

We thus solicit contributions including, though not restricted to:

wavefunction-based methods such as configuration interaction, exact diagonalization, multiconfigurational time-dependent Hartree methods, or coupled cluster theory;
exactly-solvable models;
numerical methods;
mathematically rigorous results;
connections between mean-field and many-body descriptions.

We kindly invite you to contribute manuscripts about the theories, models, or methods themselves or, alternatively, their applications, e.g., to quantum correlations and fluctuations in ultracold atoms and Bose–Einstein condensates or correlated electron-dynamics triggered by light–matter interactions.

Prof. Ofir E. Alon
Dr. Axel U. J. Lode
Guest Editors

Manuscript Submission Information

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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. Entropy is an international peer-reviewed open access monthly 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 2600 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

time-dependent Schrödinger equation
wavefunction-based methods
ultracold quantum gases
laser–matter interactions
solvable models
mathematically rigorous results
many-body theory and its applications in physics, chemistry, and mathematics
configuration interaction
exact diagonalization
coupled cluster
systems of identical particles
MCTDH methods
numerical algorithms and computational methods for the many-body problem

Published Papers (7 papers)

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Research

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17 pages, 4816 KiB

Open AccessArticle

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum, Fragmentation, and the Variance of Entropy

by Axel U. J. Lode, Sunayana Dutta and Camille Lévêque

Entropy 2021, 23(4), 392; https://doi.org/10.3390/e23040392 - 25 Mar 2021

Cited by 2 | Viewed by 2147

Abstract

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

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21 pages, 2541 KiB

Open AccessFeature PaperArticle

Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties

by Maxim Pyzh, Kevin Keiler, Simeon I. Mistakidis and Peter Schmelcher

Entropy 2021, 23(3), 290; https://doi.org/10.3390/e23030290 - 26 Feb 2021

Cited by 3 | Viewed by 1621

Abstract

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

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38 pages, 501 KiB

Open AccessArticle

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

by Ofir E. Alon

Entropy 2020, 22(12), 1342; https://doi.org/10.3390/e22121342 - 26 Nov 2020

Cited by 4 | Viewed by 2265

Abstract

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of

N_{1}

interacting bosons of mass

m_{1}

driven by a force of amplitude

f_{L, 1}

and

N_{2}

interacting bosons of mass

m_{2}

driven by [...] Read more.

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of

N_{1}

interacting bosons of mass

m_{1}

driven by a force of amplitude

f_{L, 1}

and

N_{2}

interacting bosons of mass

m_{2}

driven by a force of amplitude

f_{L, 2}

, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are

100 %

condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces

f_{L, 1}

and

f_{L, 2}

. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

16 pages, 454 KiB

Open AccessArticle

Heat Transport in a Spin-Boson Model at Low Temperatures: A Multilayer Multiconfiguration Time-Dependent Hartree Study

by Chou-Hsun Yang and Haobin Wang

Entropy 2020, 22(10), 1099; https://doi.org/10.3390/e22101099 - 29 Sep 2020

Cited by 5 | Viewed by 1847

Abstract

Extending our previous work, quantum dynamic simulations are performed to study low temperature heat transport in a spin-boson model where a two-level subsystem is coupled to two independent harmonic baths. Multilayer multiconfiguration time-dependent Hartree theory is used to numerically evaluate the thermal flux, for which the bath is represented by hundreds to thousands of modes. The simulation results are compared with the approximate Redfield theory approach, and the physics is analyzed versus different physical parameters. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

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13 pages, 1811 KiB

Open AccessArticle

Entropy of a Turbulent Bose-Einstein Condensate

by Lucas Madeira, Arnol Daniel García-Orozco, Francisco Ednilson Alves dos Santos and Vanderlei Salvador Bagnato

Entropy 2020, 22(9), 956; https://doi.org/10.3390/e22090956 - 30 Aug 2020

Cited by 6 | Viewed by 2781

Abstract

Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, which is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

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13 pages, 1332 KiB

Open AccessArticle

Many-Body Dynamics and Decoherence of the XXZ Central Spin Model in External Magnetic Field

by Xu Zhou, Qing-Kun Wan and Xiao-Hui Wang

Entropy 2020, 22(1), 23; https://doi.org/10.3390/e22010023 - 23 Dec 2019

Cited by 4 | Viewed by 2984

Abstract

The many-body dynamics of an electron spin−1/2 qubit coupled to a bath of nuclear spins by hyperfine interactions, as described by the central spin model in two kinds of external field, are studied in this paper. In a completely polarized bath, we use [...] Read more.

X X Z

central spin model in a constant magnetic field and numerically analyze the influence of the disorder strength of the magnetic field on fidelity and entanglement entropy. For a constant magnetic field, the fidelity presents non-attenuating oscillations. The anisotropic parameter

λ

and the magnetic field strength B significantly affect the dynamic behaviour of the central spin. Unlike the periodic oscillation in the constant magnetic field, the decoherence dynamics of the central spin act like a damping oscillation in a disordered field, where the central spin undergoes a relaxation process and eventually reaches a stable state. The relaxation time of this process is affected by the disorder strength and the anisotropic parameter, where a larger anisotropic parameter or disorder strength can speed up the relaxation process. Compared with the constant magnetic field, the disordered field can regulate the decoherence over a large range, independent of the anisotropic parameter. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

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Review

Jump to: Research

33 pages, 884 KiB

Open AccessReview

Order Indices and Entanglement Production in Quantum Systems

by Vyacheslav I. Yukalov

Entropy 2020, 22(5), 565; https://doi.org/10.3390/e22050565 - 18 May 2020

Cited by 5 | Viewed by 2595

Abstract

The review is devoted to two important quantities characterizing many-body systems, order indices and the measure of entanglement production. Order indices describe the type of order distinguishing statistical systems. Contrary to the order parameters characterizing systems in the thermodynamic limit and describing long-range order, the order indices are applicable to finite systems and classify all types of orders, including long-range, mid-range, and short-range orders. The measure of entanglement production quantifies the amount of entanglement produced in a many-partite system by a quantum operation. Despite that the notions of order indices and entanglement production seem to be quite different, there is an intimate relation between them, which is emphasized in the review. Full article

(This article belongs to the Special Issue Quantum Many-Body Dynamics in Physics, Chemistry, and Mathematics)

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