1,721,221 research outputs found
Equilibrium and nonequilibrium properties of systems with long-range interactions
No full text05.20.-y Classical statistical mechanics, 05.70.Fh Phase transitions: general studies, 05.45.-a Nonlinear dynamics and chaos,
Clustering and relaxation in long range Hamiltonian dynamics
No full textWe study the dynamics of a fully coupled network of N classical rotators, which can also be viewed as a mean-field XY Heisenberg (HMF) model, in the attractive (ferromagnetic) and repulsive (antiferromagnetic) cases. The exact free energy and the spectral properties of a Vlasov-Poisson equation give hints on the values of dynamical observables and on time relaxation properties. At high energy (high temperature T) the system relaxes to Maxwellian equilibrium with vanishing magnetization, but the relaxation time to the equilibrium momentum distribution diverges with N as NT2 in the ferromagnetic case and as NT3/2 in the antiferromagnetic case. The N dependence of the relaxation time is suggested by an analogy of the HMF model with gravitational and charged sheets dynamics in one dimension, and is verified in numerical simulations. Below the critical temperature the ferromagnetic HMF model shows a collective phenomenon where the rotators form a drifting cluster; we argue that the drifting speed vanishes as N--1/2 but increases as one approaches the critical point (a manifestation of critical slowing down). For the antiferromagnetic HMF model a two-cluster drifting state with zero magnetization forms spontaneously at very small temperatures; at larger temperatures an initial density modulation produces this state, which relaxes very slowly. This suggests the possibility of exciting magnetized states in a mean-held antiferromagnetic system
Nonadiabatic Landau-Zener Tunneling in Waveguide Arrays with a Step in the Refractive Index
No full textLandau-Zener tunnelling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This can be achieved using two coupled waveguide arrays with different refractive indices. The step in the refractive index causes wave ``acceleration" and thus induces strongly non adiabatic Landau-Zener tunnelling. Theoretically, the analysis is performed by considering a Schroedinger equation in a periodic potential with a step. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters
An account of the statistical and dynamical properties of systems with long-range interactions
No full textWe shortly review recent progress in the field of long-range interactions, analyzed from the viewpoint of statistical mechanics and of dynamical systems theory
Energy cascade and Burgers turbulence in the Fermi-Pasta-Ulam-Tsingou chain
Full text linkThe dynamics of initial long-wavelength excitations of the Fermi-Pasta-Ulam-Tsingou chain has been the subject of intense investigations since the pioneering work of Fermi and collaborators. We have recently found a regime where the spectrum of the Fourier modes decays with a power law and we have interpreted this regime
as a transient turbulence associated with the Burgers equation. In this paper we present the full derivation of the latter equation from the lattice dynamics using an infinite-dimensional Hamiltonian perturbation theory. This
theory allows us to relate the time evolution of the Fourier spectrum E_k of the Burgers equation to that of the Fermi-Pasta-Ulam-Tsingou (FPUT) chain. As a consequence, we derive analytically both the shock time and
the power law −8/3 of the spectrum at this time. Using the shock time as a unit, we follow numerically the time evolution of the spectrum and observe the persistence of the power −2 over an extensive time window. The exponent −2 has been widely discussed in the literature on the Burgers equation. The analysis of the Burgers
equation in Fourier space also gives information on the time evolution of the energy of each single mode which, at short time, is also a power law depending on the kth wavenumber E_k ~ t^{2k−2}. This approach to the FPUT
dynamics opens the way to a wider study of scaling regimes arising from more general initial conditions
Finite-size effects in a population of interacting oscillators
No full textWe consider a large population of globally coupled noisy phase oscillators. In the thermodynamic limit N-->infinity this system exhibits a nonequilibrium phase transition, at which a macroscopic mean field appears. It is shown that for large but finite system size N the system can be described by the noisy Stuart-Landau equation, yielding scaling behavior of statistical characteristics of the macroscopic mean field with N. The predictions of the theory are checked numerically. [S1063-651X(99)03802-7]
The world of long-range interactions: A bird’s eye view
No full textIn recent years, studies of long-range interacting (LRI) systems have taken center 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. © 2017 World Scientific Publishing Company
Statistical mechanics and dynamics of long-range interacting systems
No full textWe review the field of long-range interactions (from a series of lectures given by Stefano Ruffo to the Porto Ercole School of kinetic theory)
Phase transitions of quasistationary states in the Hamiltonian Mean Field model
Full text linkThe out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
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