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:2506.06618 · Physical review. E

Emergent viscous hydrodynamics from a single quantum particle

Zhi-Li Zhou, Maurício Hippert, Nicki Mullins, Jorge Noronha

Published Dec 15, 2025• 1 citation
arXivHTMLPDF

Abstract

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature T, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant γ, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

DOI
10.1103/f61m-9fqj

Related papers

Quantum decoherence: a study applied to quarkonium-like bound states in strongly interacting matter

Gabriele Coci, Salvatore Plumari, Giuseppe Falci

We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of $J/Ψ$ particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.

hep-phCross-listedarXiv:2607.06137•Jul 8, 2026•0 citations

Quantum dissipation in unbounded systems

Jeremy B. Maddox, Eric R. Bittner

In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie--Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wave function of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to nonclassical equations of motion. Until very recently these schemes have been limited to conservative systems. In this paper, we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme that incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy, we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 25, 2002•37 citations

Quantum Dissipation in Unbounded Systems

Eric R. Bittner, Jeremy B. Maddox

In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wavefunction of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to non-classical equations of motion. Until very recently these schemes have been limited to closed systems. In this paper we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme which incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.

•Sep 1, 2001•0 citations

Navier-Stokes Equations for Nearly Integrable Quantum Gases

Maciej Łebek, Miłosz Panfil

The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the microscopic dynamics of nearly integrable 1D quantum many-body systems. We build upon the recently developed hydrodynamics of integrable models to study the effective Boltzmann equation with collision integral taking into account the non-integrable interactions. We compute the transport coefficients and find that the resulting Navier-Stokes equations have two regimes, which differ in the viscous properties of the fluid. We illustrate the method by computing the transport coefficients for an experimentally relevant case of coupled 1D cold-atomic gases.

arXiv:2404.14292•Physical Review Letters•Jan 3, 2025•10 citations

Quantum Hydrodynamic Analysis of Decoherence

Kyungsun Na, Róbert E. Wyatt

The hydrodynamic formulation of quantum mechanics is used to analyze the mechanism of decoherence for a system interacting with a bath in which the initial system wavefunction is a superposition of spatially separated components. In order to study the decoherence, the various time-evolving hydrodynamic fields are monitored for the two composite systems, each having a single bath mode. In one of these, the system and bath are uncoupled, but in the other they are coupled through an interaction term. For the uncoupled system, a large interference feature develops between the two separated components of the initial superposition. The reduced density matrix for the system initially displays two large off-diagonal peaks and as time proceeds, these peaks broaden but do not disappear. For the coupled system, the interference feature that attempts to form between the two initially separated wavepackets is largely suppressed. Although the quantum force again tends to push fluid elements toward the interference region, this is counteracted by the classical force, which attempts to separate the centers of the two wavepackets into two descending valleys. An essential feature of flux maps for this case is that in the mid-region between the two initial density peaks, an intersecting set of attractors and repellors for flux vectors form and these funnel density away from the central region. As time proceeds, the reduced density matrix for the system shows increasing concentration along the diagonal. The Wigner function for the system shows gradually decaying ripples lying between the two density maxima which themselves are separating with opposite momenta. Finally, at later times, the reduced density matrix for the system is very similar to that obtained from a mixture of independently evolving components.

Physica Scripta•Jan 1, 2003•12 citations

Quantum hydrodynamic analysis of decoherence

Kyungsun Na, Róbert E. Wyatt

The hydrodynamic formulation of quantum mechanics is used to analyze the mechanism of decoherence for a system interacting with a bath in which the initial system wavefunction is a superposition of spatially separated components. In order to study the decoherence, the various time-evolving hydrodynamic fields are monitored for the two composite systems, each having a single bath mode. In one of these, the system and bath are uncoupled, but in the other they are coupled through an interaction term. For the uncoupled system, a large interference feature develops between the two separated components of the initial superposition. The reduced density matrix for the system initially displays two large off-diagonal peaks and as time proceeds, these peaks broaden but do not disappear. For the coupled system, the interference feature that attempts to form between the two initially separated wavepackets is largely suppressed. Although the quantum force again tends to push fluid elements toward the interference region, this is counteracted by the classical force, which attempts to separate the centers of the two wavepackets into two descending valleys. An essential feature of flux maps for this case is that in the mid-region between the two initial density peaks, an intersecting set of attractors and repellors for flux vectors form and these funnel density away from the central region. As time proceeds, the reduced density matrix for the system shows increasing concentration along the diagonal. The Wigner function for the system shows gradually decaying ripples lying between the two density maxima which themselves are separating with opposite momenta. Finally, at later times, the reduced density matrix for the system is very similar to that obtained from a mixture of independently evolving components.

APS•Mar 1, 2003•0 citations
We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature T, a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant γ, which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.
We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of J/ΨJ/ΨJ/Ψ particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.
In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie--Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wave function of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to nonclassical equations of motion. Until very recently these schemes have been limited to conservative systems. In this paper, we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme that incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy, we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.
In recent years trajectory based methodologies have become increasingly popular for evaluating the time evolution of quantum systems. A revival of the de Broglie Bohm interpretation of quantum mechanics has spawned several such techniques for examining quantum dynamics from a hydrodynamic perspective. Using techniques similar to those found in computational fluid dynamics one can construct the wavefunction of a quantum system at any time from the trajectories of a discrete ensemble of hydrodynamic fluid elements (Bohm particles) which evolve according to non-classical equations of motion. Until very recently these schemes have been limited to closed systems. In this paper we present our methodology for including the effects of a thermal environment into the hydrodynamic formulation of quantum dynamics. We derive hydrodynamic equations of motion from the Caldeira-Leggett master equation for the reduced density matrix and give a brief overview of our computational scheme which incorporates an adaptive Lagrangian mesh. Our applications focus upon the dissipative dynamics of open unbounded quantum systems. Using both the Wigner phase space representation and the linear entropy we probe the breakdown of the Markov approximation of the bath dynamics at low temperatures. We suggest a criteria for rationalizing the validity of the Markov approximation in open unbound systems and discuss decoherence, energy relaxation, and quantum/classical correspondence in the context of the Bohmian paths.
The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the microscopic dynamics of nearly integrable 1D quantum many-body systems. We build upon the recently developed hydrodynamics of integrable models to study the effective Boltzmann equation with collision integral taking into account the non-integrable interactions. We compute the transport coefficients and find that the resulting Navier-Stokes equations have two regimes, which differ in the viscous properties of the fluid. We illustrate the method by computing the transport coefficients for an experimentally relevant case of coupled 1D cold-atomic gases.
The hydrodynamic formulation of quantum mechanics is used to analyze the mechanism of decoherence for a system interacting with a bath in which the initial system wavefunction is a superposition of spatially separated components. In order to study the decoherence, the various time-evolving hydrodynamic fields are monitored for the two composite systems, each having a single bath mode. In one of these, the system and bath are uncoupled, but in the other they are coupled through an interaction term. For the uncoupled system, a large interference feature develops between the two separated components of the initial superposition. The reduced density matrix for the system initially displays two large off-diagonal peaks and as time proceeds, these peaks broaden but do not disappear. For the coupled system, the interference feature that attempts to form between the two initially separated wavepackets is largely suppressed. Although the quantum force again tends to push fluid elements toward the interference region, this is counteracted by the classical force, which attempts to separate the centers of the two wavepackets into two descending valleys. An essential feature of flux maps for this case is that in the mid-region between the two initial density peaks, an intersecting set of attractors and repellors for flux vectors form and these funnel density away from the central region. As time proceeds, the reduced density matrix for the system shows increasing concentration along the diagonal. The Wigner function for the system shows gradually decaying ripples lying between the two density maxima which themselves are separating with opposite momenta. Finally, at later times, the reduced density matrix for the system is very similar to that obtained from a mixture of independently evolving components.
The hydrodynamic formulation of quantum mechanics is used to analyze the mechanism of decoherence for a system interacting with a bath in which the initial system wavefunction is a superposition of spatially separated components. In order to study the decoherence, the various time-evolving hydrodynamic fields are monitored for the two composite systems, each having a single bath mode. In one of these, the system and bath are uncoupled, but in the other they are coupled through an interaction term. For the uncoupled system, a large interference feature develops between the two separated components of the initial superposition. The reduced density matrix for the system initially displays two large off-diagonal peaks and as time proceeds, these peaks broaden but do not disappear. For the coupled system, the interference feature that attempts to form between the two initially separated wavepackets is largely suppressed. Although the quantum force again tends to push fluid elements toward the interference region, this is counteracted by the classical force, which attempts to separate the centers of the two wavepackets into two descending valleys. An essential feature of flux maps for this case is that in the mid-region between the two initial density peaks, an intersecting set of attractors and repellors for flux vectors form and these funnel density away from the central region. As time proceeds, the reduced density matrix for the system shows increasing concentration along the diagonal. The Wigner function for the system shows gradually decaying ripples lying between the two density maxima which themselves are separating with opposite momenta. Finally, at later times, the reduced density matrix for the system is very similar to that obtained from a mixture of independently evolving components.