Ensemble inequivalence in a mean-field<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>model with ferromagnetic and nematic couplings

Abstract. Atoms in high-finesse optical resonators interact via the photons they multiply scatter into the cavity modes. The dynamics is characterized by dispersive and dissipative optomechanical long-range forces, which are mediated by the cavity photons, and exhibits a steady state for certain parameter regimes. In standingwave cavities the atoms can form stable spatial gratings. Moreover, their asymptotic distribution is a Maxwell-Boltzmann whose effective temperature is controlled by the laser parameters. In this work we show that in a two-mode standing-wave cavity the stationary state possesses the same properties and phases of the Generalized Hamiltonian Mean Field model in the canonical ensemble. This model has three equilibrium phases: a paramagnetic, a nematic, and a ferromagnetic one, which here correspond to different spatial orders of the atomic gas and can be detected by means of the light emitted by the cavities. We further discuss perspectives for investigating in this setup the ensemble inequivalence predicted for the Generalized Hamiltonian Mean Field model. arXiv:1702.07653v1 [quant-ph]

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“…This would allow one to experimentally investigate the ensemble inequivalence that has been predicted for the GHMF [15].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Phases of cold atoms interacting via photon-mediated long-range forces

Keller¹,

Jäger²,

Morigi³

2017

J. Stat. Mech.

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“…For the latter, however, we will adopt an alternative physical interpretation, namely, that of the system of interest in interaction with an external heat bath at temperature T that induces stochastic fluctuations into the dynamics of the system. Thermodynamic ensembles could be inequivalent for LRI systems [9][10][11][12] : a macroscopic physical state that is realizable in one ensemble is not realized in the other. We now discuss this point.…”

mentioning

confidence: 99%

The World of Long-Range Interactions: A Bird’s Eye View

Gupta

Ruffo

2017

Memorial Volume on Abdus Salam's 90th Birthday

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In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as kinetic theory, non-equilibrium statistical mechanics, and large deviation theory, but also due to new and exciting experimental realizations of LRI systems. In the first, introductory, Section 1, we discuss the general features of long-range interactions, emphasizing in particular the main physical phenomenon of non-additivity, which leads to a plethora of distinct effects, both thermodynamic and dynamic, that are not observed with short-range interactions: Ensemble inequivalence, slow relaxation, broken ergodicity. In Section 2, we discuss several physical systems with long-range interactions: mean-field spin systems, self-gravitating systems, Euler equations in two dimensions, Coulomb systems, one-component electron plasma, dipolar systems, free-electron lasers. In Section 3, we discuss the general scenario of dynamical evolution of generic LRI systems. In Section 4, we discuss an illustrative example of LRI systems, the Kardar-Nagel spin system, which involves discrete degrees of freedom, while in Section 5, we discuss a paradigmatic example involving continuous degrees of freedom, the so-called Hamiltonian mean-field (HMF) model. For the former, we demonstrate the effects of ensemble inequivalence and slow relaxation, while for the HMF model, we emphasize in particular the occurrence of the so-called quasistationary states (QSSs) during relaxation towards the Boltzmann-Gibbs equilibrium state. The QSSs are non-equilibrium states with lifetimes that diverge with the system size, so that in the thermodynamic limit, the systems remain trapped in the QSSs, thereby making the latter the effective stationary states. In Section 5, we also discuss an experimental system involving atoms trapped in optical cavities, which may be modelled by the HMF system. In Section 6, we address the issue of ubiquity of the quasistationary behavior by considering a variety of models and dynamics, discussing in each case the conditions to observe QSSs. In Section 7, we investigate the issue of what happens when a long-range system is driven out of thermal equilibrium. Conclusions are drawn in Section 8.

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“…The region around the black dashed circle includes the first-order phase transition [28,29], and is out-of-range of the present investigation. The blue right, the green left, and red lower lines are the critical lines of the Para-Ferro, the Para-Nematic and the Nematic-Ferro phase transitions, respectively.…”

Section: Critical Exponent Matrix γ Cmentioning

confidence: 84%

Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters

Yamaguchi¹,

Sawai²

2017

Phys. Rev. E

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The linear response is investigated in a long-range Hamiltonian system from the view point of dynamics, which is described by the Vlasov equation in the limit of large population. Due to existence of the Casimir invariants of the Vlasov dynamics, an external field does not drive the system to the forced thermal equilibrium in general, and the linear response is suppressed. With the aid of a linear response theory based on the Vlasov dynamics, we compute the suppressed linear response in a system having two order parameters, which introduce the conjugate two external fields and the susceptibility matrix of size two accordingly. Moreover, the two order parameters bring three phases and the three types of second-order phase transitions between two of them. For each type of the phase transitions, all the critical exponents for elements of the susceptibility matrix are computed. The critical exponents reveal that some elements of the matrices do not diverge even at critical points, while the mean-field theory predicts divergences. The linear response theory also suggests appearance of negative off-diagonal elements, in other words, an applied external field decreases the value of an order parameter. These theoretical predictions are confirmed by direct numerical simulations of the Vlasov equation.

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Ensemble inequivalence in a mean-fieldXYmodel with ferromagnetic and nematic couplings

Cited by 11 publications

References 35 publications

Phases of cold atoms interacting via photon-mediated long-range forces

Phases of cold atoms interacting via photon-mediated long-range forces

The World of Long-Range Interactions: A Bird’s Eye View

Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters

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