Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0910.5337 · Physical Review Letters

Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems

Hans Peter Stimming, Norbert J. Mauser, Jörg Schmiedmayer, I. E. Mazets

Published Jul 1, 2010• 53 citations
arXivHTMLPDF

Abstract

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.

DOI
10.1103/physrevlett.105.015301

Related papers

Non-perturbative method to compute thermal correlations in one-dimensional systems: A brief overview

Stefan Beck, I. E. Mazets, Thomas Schweigler

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. We start by noticing the equivalence of their description through the transfer matrix formalism and a Fokker-Planck equation for a distribution evolving in space. The corresponding stochastic differential (Itō) equation is very suitable for computer simulations, allowing the calculation of arbitrary correlation functions. As an illustration, we apply our method to the case of two tunnel-coupled quasicondensates of bosonic atoms.

arXiv:1712.01190•Dec 4, 2017•0 citations

Correlations and dynamics of tunnel-coupled one-dimensional Bose gases

Thomas Schweigler

We present a series of experiments performed with two ultracold one-dimensional Bose gases (rubidium atoms) in a double well potential. Employing matter-wave interference, we can measure the spatially resolved phase difference between the two gases and consequently investigate spatial correlations. By investigating whether higher order correlation functions can be factorized into correlations of lower order, we can investigate the interaction properties of the system. For a non-interacting system, all correlation functions with orders greater than two factorize and one observes Gaussian fluctuations. Here, we present the measurement of non-factorizing fourth-order correlation functions, leading to an experimental characterization of the interactions between the collective excitations of the quantum many-body system. The degree of non-factorizibility, i.e., the degree of non-Gaussianity of the phase fluctuations, depends on the tuneable tunneling strength between the wells. Starting from such a non-Gaussian state, we are able to observe the dynamical evolution towards a state with factorizing correlation functions (Gaussian fluctuations). We start in a double well with tunneling and then abruptly decouple the two subsystems. Subsequently, we observe how the initially non-Gaussian phase fluctuations become Gaussian. Moreover, we discuss the dynamical emergence of phase coherence in a double well potential with tunneling. We experimentally investigate the evolution starting from two different initial states. In one case, we split a cloud of atoms into two and trigger global oscillations in their relative phase. The oscillations subsequently damp and phase coherence sets in. In the other case, two independent clouds are suddenly coupled by tunneling. Again, phase coherence emerges between the two subsystems.

arXiv:1908.00422•Aug 1, 2019•18 citations

A study of one-dimensional quantum gases

Andrew G. Sykes

In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

•Mar 1, 2010•0 citations

Time-dependent transition rates for a multilevel quantum system stochastically coupled to a thermal bath

Santiago Velasco, Juan A. White, Antonio Calvo Hernández

Two different approaches (quantum and semiclassical) used to calculate time-dependent transition rates for a multilevel molecular system stochastically interacting with a thermal bath are presented. While the former is based on the use of a relationship between the real and the imaginary parts of the time autocorrelation function (TAF) associated with the interaction Hamiltonian, the latter relies on the replacement of a quantum TAF by the corresponding anticommutator. Two well-known examples for a stochastic interaction Hamiltonian, an Ornstein-Uhlenbeck process and a white-noise process, have been considered. In both cases, explicit expressions for the transition rates in terms of a reduced set of parameters characterizing the bath are obtained. In the Gaussian regime both quantum and semiclassical transition rates show a time-damped oscillatory behavior towards the same steady value. In the white-noise (\ensuremath{\delta}-correlated) regime, while the quantum transition rates are time dependent, the semiclassical rates are not. The high- and the low-temperature limits for the quantum and the semiclassical transition rates are also reported. The semiclassical results reduce to the quantum results only in the high-temperature limit.

Physical Review A•Apr 1, 1989•11 citations

Quantum fluctuations in mesoscopic systems

F Benatti, Federico Carollo, Roberto Floreanini B +1 more

Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.

arXiv:1708.02752•Journal of Physics A Mathematical and Theoretical•Aug 8, 2017•17 citations

Quantum stochastic thermodynamics: A semiclassical theory in phase space

Zhaoyu Fei

A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic Fokker-Planck equation as the dynamics at the mesoscopic level. Here, the noise term characterizing the fluctuation of the flux density accounts for the finite-$N$ effects arising from random collisions between the system and the reservoir. Accordingly, the stationary solution is a quasiequilibrium state in a canonical system. We define stochastic thermodynamic quantities based on the trajectories of the phase-space distribution. The conservation law of energy, the $H$ theorem, and fluctuation theorems are therefore obtained. Our work sets an alternative formalism of quantum stochastic thermodynamics that is independent of the two-point measurement scheme. The numerous projective measurements of quantum systems are replaced by the sampling of the phase-space distribution, offering hope for experimental verifications in the future.

arXiv:2303.05935•Physical Review A•Dec 7, 2023•2 citations
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.
We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. We start by noticing the equivalence of their description through the transfer matrix formalism and a Fokker-Planck equation for a distribution evolving in space. The corresponding stochastic differential (Itō) equation is very suitable for computer simulations, allowing the calculation of arbitrary correlation functions. As an illustration, we apply our method to the case of two tunnel-coupled quasicondensates of bosonic atoms.
We present a series of experiments performed with two ultracold one-dimensional Bose gases (rubidium atoms) in a double well potential. Employing matter-wave interference, we can measure the spatially resolved phase difference between the two gases and consequently investigate spatial correlations. By investigating whether higher order correlation functions can be factorized into correlations of lower order, we can investigate the interaction properties of the system. For a non-interacting system, all correlation functions with orders greater than two factorize and one observes Gaussian fluctuations. Here, we present the measurement of non-factorizing fourth-order correlation functions, leading to an experimental characterization of the interactions between the collective excitations of the quantum many-body system. The degree of non-factorizibility, i.e., the degree of non-Gaussianity of the phase fluctuations, depends on the tuneable tunneling strength between the wells. Starting from such a non-Gaussian state, we are able to observe the dynamical evolution towards a state with factorizing correlation functions (Gaussian fluctuations). We start in a double well with tunneling and then abruptly decouple the two subsystems. Subsequently, we observe how the initially non-Gaussian phase fluctuations become Gaussian. Moreover, we discuss the dynamical emergence of phase coherence in a double well potential with tunneling. We experimentally investigate the evolution starting from two different initial states. In one case, we split a cloud of atoms into two and trigger global oscillations in their relative phase. The oscillations subsequently damp and phase coherence sets in. In the other case, two independent clouds are suddenly coupled by tunneling. Again, phase coherence emerges between the two subsystems.
In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.
Two different approaches (quantum and semiclassical) used to calculate time-dependent transition rates for a multilevel molecular system stochastically interacting with a thermal bath are presented. While the former is based on the use of a relationship between the real and the imaginary parts of the time autocorrelation function (TAF) associated with the interaction Hamiltonian, the latter relies on the replacement of a quantum TAF by the corresponding anticommutator. Two well-known examples for a stochastic interaction Hamiltonian, an Ornstein-Uhlenbeck process and a white-noise process, have been considered. In both cases, explicit expressions for the transition rates in terms of a reduced set of parameters characterizing the bath are obtained. In the Gaussian regime both quantum and semiclassical transition rates show a time-damped oscillatory behavior towards the same steady value. In the white-noise (\ensuremath{\delta}-correlated) regime, while the quantum transition rates are time dependent, the semiclassical rates are not. The high- and the low-temperature limits for the quantum and the semiclassical transition rates are also reported. The semiclassical results reduce to the quantum results only in the high-temperature limit.
Abstract Recent experimental results point to the existence of coherent quantum phenomena in systems made of a large number of particles, despite the fact that for many-body systems the presence of decoherence is hardly negligible and emerging classicality is expected. This behaviour hinges on collective observables, named quantum fluctuations , that retain a quantum character even in the thermodynamic limit: they provide useful tools for studying properties of many-body systems at the mesoscopic level, in-between the quantum microscopic scale and the classical macroscopic one. We herein present the general theory of quantum fluctuations in mesoscopic systems, and study their dynamics in a quantum open system setting, taking into account the unavoidable effects of dissipation and noise induced by the external environment. As in the case of microscopic systems, decoherence is not always the only dominating effect at the mesoscopic scale: certain types of environment can provide means for entangling collective fluctuations through a purely noisy mechanism.
A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic Fokker-Planck equation as the dynamics at the mesoscopic level. Here, the noise term characterizing the fluctuation of the flux density accounts for the finite-NNN effects arising from random collisions between the system and the reservoir. Accordingly, the stationary solution is a quasiequilibrium state in a canonical system. We define stochastic thermodynamic quantities based on the trajectories of the phase-space distribution. The conservation law of energy, the HHH theorem, and fluctuation theorems are therefore obtained. Our work sets an alternative formalism of quantum stochastic thermodynamics that is independent of the two-point measurement scheme. The numerous projective measurements of quantum systems are replaced by the sampling of the phase-space distribution, offering hope for experimental verifications in the future.