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:1101.6003 · New Journal of Physics

The role of quantum fluctuations in a system with strong fields

Kevin Dusling

Published Mar 16, 2011• 2 citations
arXivHTMLPDF

Abstract

In this paper, we study how quantum fluctuations modify the quantum evolution of an initially classical field theory. We consider a scalar ϕ 4 theory coupled to an external source as a toy model for the color glass condensate description of the early time dynamics of heavy-ion collisions. We demonstrate that quantum fluctuations considerably modify the time evolution driving the system to evolve in accordance with ideal hydrodynamics. We attempt to understand the mechanism behind this relaxation to ideal hydrodynamics by using modified initial spectra and studying the particle content of the theory.

DOI
10.1088/1367-2630/13/3/035011

Related papers

Quantum chaos in the perfect fluid: spectrum of initial fluctuations in the little bang

Kevin Dusling, Thomas Epelbaum, François Gelis +1 more

We outline how unstable quantum fluctuations decohere classical fields in heavy ion collisions, leading to an equation of state and hydrodynamics. Explicit numerical realization of this framework in a scalar $ϕ^4$ theory demonstrates that anomalously low values of $η/s$ can be generated.

arXiv:1210.6053•Oct 22, 2012•1 citation

Nonequilibrium Field Theory Description of the Bose-Einstein Condensate

Daniel Gustavo Barci, Eduardo Souza Fraga, Rudnei O. Ramos

We study the detailed out-of-equilibrium time evolution of a homogeneous Bose-Einstein condensate (BEC). We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the BEC. The interaction between fluctuations proves to be crucial in the mechanism of instability generation. We show the existence of two regimes in k space, with a crossover for k(2)/2m approximately 2 lambda|phi(0)|(2), where lambda is the coupling constant and |phi(0)|(2) is the condensate density. We deduce and solve a set of coupled equations that completely determines the nonequilibrium dynamics of the condensate density.

arXiv:cond-mat/9909279•Physical Review Letters•Jul 17, 2000•14 citations

Aspects of Non-Equilibrium Dynamics in Quantum Field Theory

Manfredini, E.

This work is devoted to the study of relaxation--dissipation processes in systems described by Quantum Field Theory. In the first part, I focus on the phi^4 scalar quantum field theory in finite volume in the large N limit. I find that the zero-mode quantum fluctuations cannot grow macroscopically large starting from microscopic initial conditions, while the long-wavelength fluctuations do scale with the linear size of the system, signalling dynamical infrared properties quite different from the equilibrium ones. I also introduce a non-gaussian Hartree-Fock approximation (tdHF) and I derive the mean-field coupled time-dependent Schroedinger equations for the modes of the scalar field. The dynamical evolution of a uniform condensate is studied in a further controlled gaussian approximation, for N=1. Results similar to the large N case show an internal inconsistency of this approximation. I also study the dynamics of the system in infinite volume in the broken symmetry phase. The data show that the fixed points of the evolution cover at most the classically metastable part of the static effective potential. I finally study the dynamical evolution for the O(N+1) nonlinear sigma model in 1+1 dimensions in the large N limit. I first of all verify that the large coupling limit of the O(N+1) phi^4 model, which renders the model non linear, commutes with the large N limit, so that the O(infty) nonlinear sigma model is uniquely defined. I then study the evolution of several observables, like the spectrum of produced particles, finding no evidence for parametric resonance. I conclude with some remarks on the ``state of art'' in gauge theories and some comments about the open issues in the subject.

arXiv:hep-ph/0101202•Jan 18, 2001•4 citations

Time evolution of gluon coherent state and its von Neumann entropy in heavy-ion collisions

Hideaki Iida, Teiji Kunihiro, Akira Ohnishi A +1 more

We propose a new prescription for evaluating a von Neumann entropy in the initial stage of high-energy heavy-ion collisions utilizing the time evolution of classical Yang-Mills (CYM) field: The von Neumann entropy is computed for the quantum coherent states constructed so as to give the classical gluon fields as the expectation values. The entropy is to be liberated when the complete decoherence is achieved. As a demonstration, the time evolution of the CYM dynamics is solved with an initial condition which mimics the Glasma state, though in a non-expanding geometry; the Glasma state is characterized by the longitudinal color-electric and -magnetic fields with gluon fields' fluctuations around it. We find that the initial longitudinal fluctuations of the fields play essential roles for the entropy production in two ways: First, the field fluctuations at $t=0$ themselves act as a source of the von Neumann entropy prepared before the time evolution. Second, the initial fluctuations triggers field instabilities, and hence the larger the strength of them, the more the entropy production at later time.

arXiv:1410.7309•Oct 27, 2014•0 citations

Entanglement of scales as a possible mechanism for decoherence and thermalization in relativistic heavy ion collisions

S. V. Akkelin, Yu. M. Sinyukov

Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical mechanisms work in the case of the scalar field model. We obtain the evolution equation for the Wigner function of a long-wavelength subsystem that describes its decoherence, isotropization, and approach to thermal equilibrium induced by interaction with short-wavelength modes. Our analysis supports the idea that decoherence, quantum-to-classical transition, and thermalization in isolated quantum systems are attributed to the experimental context, and are related to a particular procedure of decomposition of the whole quantum system into relevant and irrelevant from an observational viewpoint subsystems.

arXiv:1309.4388•Physical Review C•Mar 20, 2014•9 citations

Quantum dynamics of Φ4 field theory beyond leading order in 1+1 dimensions

Jürgen Baacke, Andreas Heinen

We consider the out-of-equilibrium evolution of a classical condensate field $\ensuremath{\varphi}=〈\ensuremath{\Phi}〉$ and its quantum fluctuations for a ${\ensuremath{\Phi}}^{4}$ model in $1+1$ dimensions with a double well potential. We use the two-particle point-irreducible (2PPI) formalism in the two-loop approximation. We compare our results to those obtained in the Hartree approximation, in the bare vertex approximation, and in the two-particle irreducible next-to-leading order large-$N$ approach, with thermal initial conditions. In the 2PPI scheme, we find that the system tends to the symmetric configuration at late times, as expected in the absence of spontaneous symmetry breaking.

arXiv:hep-ph/0305220•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 23, 2003•11 citations
In this paper, we study how quantum fluctuations modify the quantum evolution of an initially classical field theory. We consider a scalar ϕ 4 theory coupled to an external source as a toy model for the color glass condensate description of the early time dynamics of heavy-ion collisions. We demonstrate that quantum fluctuations considerably modify the time evolution driving the system to evolve in accordance with ideal hydrodynamics. We attempt to understand the mechanism behind this relaxation to ideal hydrodynamics by using modified initial spectra and studying the particle content of the theory.
We outline how unstable quantum fluctuations decohere classical fields in heavy ion collisions, leading to an equation of state and hydrodynamics. Explicit numerical realization of this framework in a scalar ϕ4ϕ^4ϕ4 theory demonstrates that anomalously low values of η/sη/sη/s can be generated.
We study the detailed out-of-equilibrium time evolution of a homogeneous Bose-Einstein condensate (BEC). We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the BEC. The interaction between fluctuations proves to be crucial in the mechanism of instability generation. We show the existence of two regimes in k space, with a crossover for k(2)/2m approximately 2 lambda|phi(0)|(2), where lambda is the coupling constant and |phi(0)|(2) is the condensate density. We deduce and solve a set of coupled equations that completely determines the nonequilibrium dynamics of the condensate density.
This work is devoted to the study of relaxation--dissipation processes in systems described by Quantum Field Theory. In the first part, I focus on the phi^4 scalar quantum field theory in finite volume in the large N limit. I find that the zero-mode quantum fluctuations cannot grow macroscopically large starting from microscopic initial conditions, while the long-wavelength fluctuations do scale with the linear size of the system, signalling dynamical infrared properties quite different from the equilibrium ones. I also introduce a non-gaussian Hartree-Fock approximation (tdHF) and I derive the mean-field coupled time-dependent Schroedinger equations for the modes of the scalar field. The dynamical evolution of a uniform condensate is studied in a further controlled gaussian approximation, for N=1. Results similar to the large N case show an internal inconsistency of this approximation. I also study the dynamics of the system in infinite volume in the broken symmetry phase. The data show that the fixed points of the evolution cover at most the classically metastable part of the static effective potential. I finally study the dynamical evolution for the O(N+1) nonlinear sigma model in 1+1 dimensions in the large N limit. I first of all verify that the large coupling limit of the O(N+1) phi^4 model, which renders the model non linear, commutes with the large N limit, so that the O(infty) nonlinear sigma model is uniquely defined. I then study the evolution of several observables, like the spectrum of produced particles, finding no evidence for parametric resonance. I conclude with some remarks on the ``state of art'' in gauge theories and some comments about the open issues in the subject.
We propose a new prescription for evaluating a von Neumann entropy in the initial stage of high-energy heavy-ion collisions utilizing the time evolution of classical Yang-Mills (CYM) field: The von Neumann entropy is computed for the quantum coherent states constructed so as to give the classical gluon fields as the expectation values. The entropy is to be liberated when the complete decoherence is achieved. As a demonstration, the time evolution of the CYM dynamics is solved with an initial condition which mimics the Glasma state, though in a non-expanding geometry; the Glasma state is characterized by the longitudinal color-electric and -magnetic fields with gluon fields' fluctuations around it. We find that the initial longitudinal fluctuations of the fields play essential roles for the entropy production in two ways: First, the field fluctuations at t=0t=0t=0 themselves act as a source of the von Neumann entropy prepared before the time evolution. Second, the initial fluctuations triggers field instabilities, and hence the larger the strength of them, the more the entropy production at later time.
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical mechanisms work in the case of the scalar field model. We obtain the evolution equation for the Wigner function of a long-wavelength subsystem that describes its decoherence, isotropization, and approach to thermal equilibrium induced by interaction with short-wavelength modes. Our analysis supports the idea that decoherence, quantum-to-classical transition, and thermalization in isolated quantum systems are attributed to the experimental context, and are related to a particular procedure of decomposition of the whole quantum system into relevant and irrelevant from an observational viewpoint subsystems.
We consider the out-of-equilibrium evolution of a classical condensate field $\ensuremath{\varphi}=〈\ensuremath{\Phi}〉$ and its quantum fluctuations for a ${\ensuremath{\Phi}}^{4}$ model in 1+11+11+1 dimensions with a double well potential. We use the two-particle point-irreducible (2PPI) formalism in the two-loop approximation. We compare our results to those obtained in the Hartree approximation, in the bare vertex approximation, and in the two-particle irreducible next-to-leading order large-NNN approach, with thermal initial conditions. In the 2PPI scheme, we find that the system tends to the symmetric configuration at late times, as expected in the absence of spontaneous symmetry breaking.