Quasistationary states in the self-gravitating sheet model

Joyce, Michael; Worrakitpoonpon, Tirawut

doi:10.1103/physreve.84.011139

Cited by 57 publications

(78 citation statements)

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“…On the other hand if dynamics is adiabatic -which is the case for the initial particle distributions that satisfy GVC -then α = 0.4, which is close to the exponent found for non-interacting particles. It will be interesting to explore how universal are these exponents by studying other long range systems, such as magnetically confined plasmas [15] or self-gravitating clusters [16][17][18][19]. The fact that the paramagnetic resonances and chaotic dynamics diminish significantly the entropy production time suggests that for short range interacting systems, for which dynamics is highly non-linear and chaotic, the exponent α → 0, and the entropy production will take place on a microscopic time scale even in the thermodynamic limit.…”

Section: Discussionmentioning

confidence: 99%

Entropy production in systems with long range interactions

Pakter

Levin

2017

J. Stat. Mech.

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On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of thermodynamics. In reality, however, there is no problem since the thermodynamic entropy should be associated with the Boltzmann entropy, which for non-equilibrium systems is different from Gibbs entropy. The Boltzmann entropy accounts for the microstates which are not accessible from a given initial condition, but are compatible with a given macrostate. In a sense the Boltzmann entropy is a coarse grained version of the Gibbs entropy and will not decrease during the dynamical evolution of a macroscopic system. In this paper we will explore the entropy production for systems with long range interactions. Unlike for short range systems, in the thermodynamic limit, the probability density function for these systems decouples into a product of one particle distribution functions and the coarse grained entropy can be calculated explicitly. We find that the characteristic time for the entropy production scales with the number of particles as N α , with α > 0, so that in the thermodynamic limit entropy production takes an infinite amount of time. * pakter@if.ufrgs.br † levin@if.ufrgs.br 2

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Section: Discussionmentioning

confidence: 99%

Entropy production in systems with long range interactions

Pakter

Levin

2017

J. Stat. Mech.

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“…In stages (i) and (ii) the three models predict approximately the same behaviour. Instead, in stage (iii), φ 11 evolves differently: For both MF and full FPE it exhibits a minimum, however reached at different times, which seems to possess the features of a scaling QSS, namely, a sequence of QSS with identical correlations [28]. Its nature could be understood in terms of the onset of collective oscillations which are (almost) decoupled from noise and dissipation.…”

Section: Arxiv:151205243v2 [Quant-ph] 20 Jul 2016mentioning

confidence: 99%

“…3(a) and its inset show the MF predictions as a function of time and indicate that, even though MF reproduces qualitatively the dynamical features, it fails to give the correct time scale by at least one order of magnitude. Further insight is provided by the observable for QSS [28], which we here define as:…”

Section: Arxiv:151205243v2 [Quant-ph] 20 Jul 2016mentioning

confidence: 99%

“…In Ref. [28] it was shown that, in presence of dissipation due to viscous damping or local inelastic collisions, the relaxation dynamics of long-range interacting systems can be cast in terms of so-called scaling QSS, which are solutions of the kinetic mean-field equation and asymptotically tend to a unique QSS [28]. Accordingly, one would expect to observe QSS in cavity systems [19].…”

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confidence: 99%

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Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

2016

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We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a singlemode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems. The quest for a systematic understanding of nonequilibrium phenomena is an open problem in theoretical physics for its importance in the description of dynamics from the microscopic up to astrophysical scales [1-3]. Aspects of these dynamics are studied in the relaxation of systems undergoing temporal changes (quenches) of the control field across a critical point [4][5][6]. Quenches across a non-equilibrium phase transition provide further insight into the interplay between noise and external drives on criticality and thermalization [7,8]. In this context photonic systems play a prominent role, thanks to their versatility [9][10][11][12][13][14][15].Polarizable particles in a high-finesse cavity, like in the setup illustrated in Fig. 1(a), offer a unique system to study relaxation in long-range interacting systems. Here, multiple photon scattering mediates particleparticle interactions whose range scales with the system size in a single-mode cavity [15][16][17][18]. In this limit, atomic ensembles in cavities are expected to share several features with other long-range interacting systems such as gravitational clusters and non-neutral plasmas in two or more dimensions [3,16,19]. The equilibrium thermodynamics of these systems can exhibit ensemble inequivalence [3,20], while quasi-stationary states (QSS) typically characterise the out-of-equilibrium dynamics [3,[21][22][23]. QSS are metastable states in which the system is expected to remain trapped in the thermodynamic limit, they are Vlasov-stable solutions and thus depend on the initial state. So far, however, evidence of QSS has been elusive. It has been conjectured that noise and dissipation can set a time scale that limits the QSS lifetime [24][25][26][27], and possibly gives rise to dynamical phase transitions [25]. In Ref. [28] it was shown that, in pr...

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“…There is also an extensive literature on the statistical mechanics of finite one dimensional self-gravitating systems (see e.g. Joyce & Worrakitpoonpon (2011) and references therein), as well as some studies which use this case to explore issues in cosmological N body simulations: Binney (2004) uses it to probe discreteness effects, and Schulz et al (2012) the issue of universality in cold collapse.…”

Section: Introductionmentioning

confidence: 99%

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

Benhaiem

Joyce

Sicard

2013

Monthly Notices of the Royal Astronomical Society

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One dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three dimensional EdS model, lead for power-law initial conditions to self-similar clustering characterized in the strongly nonlinear regime by power-law behaviour of the two point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalisation of the so-called stable clustering hypothesis in three dimensions, and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the "stable clustering" region from the "universal" region is very well approximated by a "critical" value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of "universality" of non-linear clustering in this context.

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Quasistationary states in the self-gravitating sheet model

Cited by 57 publications

References 30 publications

Entropy production in systems with long range interactions

Entropy production in systems with long range interactions

Dissipation-Assisted Prethermalization in Long-Range Interacting Atomic Ensembles

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

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