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3 pages, 189 KiB

Open AccessEditorial

Many Body Quantum Chaos

by Sandro Wimberger

Condens. Matter 2020, 5(2), 41; https://doi.org/10.3390/condmat5020041 - 12 Jun 2020

Cited by 1 | Viewed by 2296

Abstract

This editorial remembers Shmuel Fishman, one of the founding fathers of the research field “quantum chaos”, and puts into context his contributions to the scientific community with respect to the twelve papers that form the special issue. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

Research

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13 pages, 476 KiB

Open AccessArticle

Static Kinks in Chains of Interacting Atoms

by Haggai Landa, Cecilia Cormick and Giovanna Morigi

Condens. Matter 2020, 5(2), 35; https://doi.org/10.3390/condmat5020035 - 13 May 2020

Cited by 5 | Viewed by 2476

Abstract

We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum [...] Read more.

We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent

n \geq 1

. The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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19 pages, 1788 KiB

Open AccessArticle

Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

by Maximilian Nitsch, Benjamin Geiger, Klaus Richter and Juan-Diego Urbina

Condens. Matter 2020, 5(2), 26; https://doi.org/10.3390/condmat5020026 - 04 Apr 2020

Cited by 3 | Viewed by 2572

Abstract

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature [...] Read more.

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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15 pages, 1197 KiB

Open AccessFeature PaperArticle

Quantum-Heat Fluctuation Relations in Three-Level Systems Under Projective Measurements

by Guido Giachetti, Stefano Gherardini, Andrea Trombettoni and Stefano Ruffo

Condens. Matter 2020, 5(1), 17; https://doi.org/10.3390/condmat5010017 - 13 Mar 2020

Cited by 7 | Viewed by 2320

Abstract

We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied [...] Read more.

We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for N-level systems, with

N > 2

. Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor

β_{eff}

that formally plays the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of

β_{eff}

for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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10 pages, 919 KiB

Open AccessArticle

Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

by Eduardo Jonathan Torres-Herrera and Lea F. Santos

Condens. Matter 2020, 5(1), 7; https://doi.org/10.3390/condmat5010007 - 20 Jan 2020

Cited by 6 | Viewed by 2604

Abstract

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss [...] Read more.

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss how properties of the spectrum that are usually associated with chaos can be directly detected from the evolution of the number operator in the one-dimensional, noninteracting Aubry-André model. Both the quantity and the model are studied in experiments with cold atoms. We consider a single-particle and system sizes experimentally reachable. By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. This feature emerges at times that are experimentally accessible. This work is a contribution to a special issue dedicated to Shmuel Fishman. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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17 pages, 880 KiB

Open AccessArticle

Resonant Quantum Kicked Rotor as A Continuous-Time Quantum Walk

by Michele Delvecchio, Francesco Petiziol and Sandro Wimberger

Condens. Matter 2020, 5(1), 4; https://doi.org/10.3390/condmat5010004 - 11 Jan 2020

Cited by 9 | Viewed by 3529

Abstract

We analytically investigate the analogy between a standard continuous-time quantum walk in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions. We verify that the obtained probability distributions are equal for a suitable choice of the kick strength [...] Read more.

We analytically investigate the analogy between a standard continuous-time quantum walk in one dimension and the evolution of the quantum kicked rotor at quantum resonance conditions. We verify that the obtained probability distributions are equal for a suitable choice of the kick strength of the rotor. We further discuss how to engineer the evolution of the walk for dynamically preparing experimentally relevant states. These states are important for future applications of the atom-optics kicked rotor for the realization of ratchets and quantum search. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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21 pages, 880 KiB

Open AccessArticle

On the Husimi Version of the Classical Limit of Quantum Correlation Functions

by Sreeja Loho Choudhury and Frank Großmann

Condens. Matter 2020, 5(1), 3; https://doi.org/10.3390/condmat5010003 - 10 Jan 2020

Cited by 4 | Viewed by 2511

Abstract

We extend the Husimi (coherent state) based version of linearized semiclassical theories for the calculation of correlation functions to the case of survival probabilities. This is a case that could be dealt with before only by use of the Wigner version of linearized [...] Read more.

We extend the Husimi (coherent state) based version of linearized semiclassical theories for the calculation of correlation functions to the case of survival probabilities. This is a case that could be dealt with before only by use of the Wigner version of linearized semiclassical theory. Numerical comparisons of the Husimi and the Wigner case with full quantum results as well as with full semiclassical ones will be given for the revival dynamics in a Morse oscillator with and without coupling to an additional harmonic degree of freedom. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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25 pages, 4096 KiB

Open AccessArticle

Uniform Hyperbolicity of a Scattering Map with Lorentzian Potential

by Hajime Yoshino, Ryota Kogawa and Akira Shudo

Condens. Matter 2020, 5(1), 1; https://doi.org/10.3390/condmat5010001 - 30 Dec 2019

Cited by 1 | Viewed by 2173

Abstract

We show that a two-dimensional area-preserving map with Lorentzian potential is a topological horseshoe and uniformly hyperbolic in a certain parameter region. In particular, we closely examine the so-called sector condition, which is known to be a sufficient condition leading to the uniformly [...] Read more.

We show that a two-dimensional area-preserving map with Lorentzian potential is a topological horseshoe and uniformly hyperbolic in a certain parameter region. In particular, we closely examine the so-called sector condition, which is known to be a sufficient condition leading to the uniformly hyperbolicity of the system. The map will be suitable for testing the fractal Weyl law as it is ideally chaotic yet free from any discontinuities which necessarily invokes a serious effect in quantum mechanics such as diffraction or nonclassical effects. In addition, the map satisfies a reasonable physical boundary condition at infinity, thus it can be a good model describing the ionization process of atoms and molecules. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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17 pages, 869 KiB

Open AccessArticle

A Quantum Model for the Dynamics of Cold Dark Matter

by Tim Zimmermann, Massimo Pietroni, Javier Madroñero, Luca Amendola and Sandro Wimberger

Condens. Matter 2019, 4(4), 89; https://doi.org/10.3390/condmat4040089 - 13 Nov 2019

Cited by 3 | Viewed by 3407

Abstract

A model for cold dark matter is given by the solution of a coupled Schrödinger–Poisson equation system. We present a numerical scheme for integrating these equations, discussing the problems arising from their nonlinear and nonlocal character. After introducing and testing our numerical approach, [...] Read more.

A model for cold dark matter is given by the solution of a coupled Schrödinger–Poisson equation system. We present a numerical scheme for integrating these equations, discussing the problems arising from their nonlinear and nonlocal character. After introducing and testing our numerical approach, we illustrate key features of the system by numerical examples in

1 + 1

dimensions. In particular, we study the properties of asymptotic states to which the numerical solutions converge for artificial initial conditions. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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10 pages, 367 KiB

Open AccessArticle

Quantum State of the Fermionic Carriers in a Transport Channel Connecting Particle Reservoirs

by Andrey R. Kolovsky and Dmitrii N. Maksimov

Condens. Matter 2019, 4(4), 85; https://doi.org/10.3390/condmat4040085 - 15 Oct 2019

Cited by 5 | Viewed by 1895

Abstract

We analyze the quantum state of fermionic carriers in a transport channel attached to a particle reservoir. The analysis is done from first principles by considering microscopic models of the reservoir and transport channel. In the case of infinite effective temperature of the [...] Read more.

We analyze the quantum state of fermionic carriers in a transport channel attached to a particle reservoir. The analysis is done from first principles by considering microscopic models of the reservoir and transport channel. In the case of infinite effective temperature of the reservoir we demonstrate a full agreement between the results of straightforward numerical simulations of the system dynamics and the solution of the master equation on the single-particle density matrix of the carriers in the channel. This allows us to predict the quantum state of carriers in the case where the transport channel connects two reservoirs with different chemical potentials. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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29 pages, 1708 KiB

Open AccessArticle

Dynamical Thermalization of Interacting Fermionic Atoms in a Sinai Oscillator Trap

by Klaus M. Frahm, Leonardo Ermann and Dima L. Shepelyansky

Condens. Matter 2019, 4(3), 76; https://doi.org/10.3390/condmat4030076 - 08 Aug 2019

Cited by 3 | Viewed by 2506

Abstract

We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that, for a many-body system of cold atoms, the [...] Read more.

We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that, for a many-body system of cold atoms, the interactions, with a strength above a certain quantum chaos border given by the Åberg criterion, lead to the Fermi–Dirac distribution and relaxation of many-body initial states to the thermalized state in the absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links with the Loschmidt–Boltzmann dispute. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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14 pages, 2002 KiB

Open AccessArticle

Many-Body Systems and Quantum Chaos: The Multiparticle Quantum Arnol’d Cat

by Giorgio Mantica

Condens. Matter 2019, 4(3), 72; https://doi.org/10.3390/condmat4030072 - 22 Jul 2019

Cited by 4 | Viewed by 3531

Abstract

A multi-particle extension of the Arnol’d cat Hamiltonian system is presented, which can serve as a fully dynamical model of decoherence. The behavior of the von Neumann entropy of the reduced density matrix is studied, in time and as a function of the [...] Read more.

A multi-particle extension of the Arnol’d cat Hamiltonian system is presented, which can serve as a fully dynamical model of decoherence. The behavior of the von Neumann entropy of the reduced density matrix is studied, in time and as a function of the physical parameters, with special regard to increasing the mass of the cat particle. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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Review

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9 pages, 253 KiB

Open AccessReview

Action Functional for a Particle with Damping

by Federico de Bettin, Alberto Cappellaro and Luca Salasnich

Condens. Matter 2019, 4(3), 81; https://doi.org/10.3390/condmat4030081 - 10 Sep 2019

Cited by 1 | Viewed by 2247

Abstract

In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional [...] Read more.

In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time reversal symmetry. This action functional is exactly the effective action of Caldeira-Leggett model but, in our approach, it is derived without the assumption that the particle is weakly coupled to a bath of infinite harmonic oscillators. Full article

(This article belongs to the Special Issue Many Body Quantum Chaos)

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