1,324 research outputs found
Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
We investigate the dependence of the largest Lyapunov exponent of a
-particle self-gravitating ring model at equilibrium with respect to the
number of particles and its dependence on energy. This model has a continuous
phase-transition from a ferromagnetic to homogeneous phase, and we numerically
confirm with large scale simulations the existence of a critical exponent
associated to the largest Lyapunov exponent, although at variance with the
theoretical estimate. The existence of chaos in the magnetized state evidenced
by a positive Lyapunov exponent, even in the thermodynamic limit, is explained
by the resonant coupling of individual particle oscillations to the diffusive
motion of the center of mass of the system due to the thermal excitation of a
classical Goldstone mode. The transition from "weak" to "strong" chaos occurs
at the onset of the diffusive motion of the center of mass of the
non-homogeneous equilibrium state, as expected. We also discuss thoroughly for
the model the validity and limits of a geometrical approach for their
analytical estimate.Comment: 21 pages, 14 figure
Ergodicity in a two-dimensional self gravitating many body system
We study the ergodic properties of a two-dimensional self-gravitating system
using molecular dynamics simulations. We apply three different tests for
ergodicity: a direct method comparing the time average of a particle momentum
and position to the respective ensemble average, sojourn times statistics and
the dynamical functional method. For comparison purposes they are also applied
to a short-range interacting system and to the Hamiltonian mean-field model.
Our results show that a two-dimensional self-gravitating system takes a very
long time to establish ergodicity. If a Kac factor is used in the potential
energy, such that the total energy is extensive, then this time is independent
of particle number, and diverges with without a Kac factor
Thermofield qubits, generalized expectations and quantum information protocols
Thermofield dynamics (TFD) approach is a real time quantum field method for
dealing with finite temperature quantum states in a purified version of usual
density operator formalism at finite temperature. In the domain of quantum
information, TFD represents a quite promising direction for dealing with qubits
under thermal influence and can also be associated to Gaussian states. Here, we
propose a generalized TFD mean expectation for the case of thermofield qubits
considering the action of gate operators. We propose quantum teleportation
protocols involving thermofield states, considering thermal-to-thermal and
thermal-to-non-thermal transfering cases. In particular, we discuss the case in
which Alice and Bob are at different temperatures. Action of gate operators on
the result of the Mandel parameter for thermofields and on Gibbs-like density
operators are also discussed. The no-cloning and non-broadcasting theorems in
TFD are also considered and cases of superposed thermofield states and maps
connecting thermofield vacua at different temperatures are also addressed and
associated to metastable and non-equilibrium scenarios.Comment: 9 pages, 0 figure
On the entropy of classical systems with long-range interaction
We discuss the form of the entropy for classical hamiltonian systems with
long-range interaction using the Vlasov equation which describes the dynamics
of a -particle in the limit . The stationary states of the
hamiltonian system are subject to infinite conserved quantities due to the
Vlasov dynamics. We show that the stationary states correspond to an extremum
of the Boltzmann-Gibbs entropy, and their stability is obtained from the
condition that this extremum is a maximum. As a consequence the entropy is a
function of an infinite set of Lagrange multipliers that depend on the initial
condition. We also discuss in this context the meaning of ensemble
inequivalence and the temperature
Long velocity tails in plasmas and gravitational systems
Long tails in the velocity distribution are observed in plasmas and
gravitational systems. Some experiments and observations in
far-from-equilibrium conditions show that these tails behave as 1/v^(5/2). We
show here that such heavy tails are due to a universal mechanism related to the
fluctuations of the total force field. Owing to the divergence in 1/r^2 of the
binary interaction force, these fluctuations can be very large and their
probability density exhibits a similar long tail. They induce large velocity
fluctuations leading to the 1/v^(5/2) tail. We extract the mechanism causing
these properties from the BBGKY hierarchy representation of Statistical
Mechanics. This leads to a modification of the Vlasov equation by an additional
term. The novel term involves a fractional power 3/4 of the Laplacian in
velocity space and a fractional iterated time integral. Solving the new kinetic
equation for a uniform system, we retrieve the observed 1/v^(5/2) tail for the
velocity distribution. These results are confirmed by molecular dynamics
simulations
A convergent kinetic equation for gravitational and Coulomb systems
It is well known that due to its divergence at large impact parameters, the
Boltzmann collision integral in the kinetic equation for 3D systems of
particles interacting through a potential must be replaced by a
Balescu-Lenard-like collision term. However, the latter diverges at small
impact parameters. This comes from the fact that only weak interactions are
considered while strong collisions between close particles are neglected in its
derivation. We show that a solution to this dilemma exists in the framework of
the BBGKY formulation of statistical mechanics. It is based on a separate
treatment of the contribution of the strong interactions from that of the weak
interactions. The strong interaction part leads to a new term that involves a
fractional Laplacian operator in velocity space while the weak interaction
component yields the Balescu-Lenard collision term with an explained lower
cut-off at the Landau length. For spatially uniform initial conditions, the
fractional Laplacian contribution leads to a long-tailed velocity distribution
as long as the spatial inhomogeneity remains small. We present results from
molecular dynamics simulations confirming the existence of such long tails.Comment: arXiv admin note: substantial text overlap with arXiv:1605.0598
Non-equilibrium Entropy and Dynamics in a System with Long-Range Interactions
The core-halo approach of Levin et al.\ [Phys.\ Rep.\ {\bf 535}, 1 (2014)]
for the violent relaxation of long-range interacting systems with a waterbag
initial conditions is revisited for the case of the Hamiltonian Mean Field
model. The Gibbs entropy maximization principle is considered with the
constraints of energy conservation and of infinite Casimir invariants of the
Vlasov equation. All parameters in the core-halo distribution function are then
completely determined without resorting to the envelope equation for the
contour of the initial state, which was required in the original approach. We
also show that a different ansatz is possible for the core-halo distribution
with similar or even better results. This work also evidences a link between a
parametric resonance causing the non-equilibrium phase transition in the HMF
model, a purely dynamical property, and a discontinuity of the
(non-equilibrium) entropy of the system
Ensemble Inequivalence and Maxwell Construction in the Self-Gravitating Ring Model
Equilibrium Statistical Mechanics is undoubtedly a cornerstone for the
description of many particle systems. The common interpretation is based on
ensemble theory as put forward by Gibbs, alongside the basic assumptions that
different ensembles are equivalent, i.~e.\ the properties of the system can
equally be obtained in any ensemble with the same results. However, the
simplicity of the argument that provides such equivalence, mathematically
grounded by the existence of Legendre transformation between the ensembles and
the existence of its inverse, may break down for physical systems with long
range interactions. In this paper we study the behavior of a simple toy model
with a long range interaction and show from first principles, by solving
numerically the mechanical equations of motion and Monte Carlo simulations, the
inequivalence of ensembles, and discuss in what situations and how the Maxwell
construction is applicable.Comment: 14 pages, 6 figure
Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
Quasi-Stationary States of long-range interacting systems have been studied
at length over the last fifteen years. It is known that the collisional terms
of the Balescu-Lenard and Landau equations vanish for one-dimensional systems
in homogeneous states, thus requiring a new kinetic equation with a proper
dependence on the number of particles. Here we show that previous scalings
described in the literature are due either to small size effects or the use of
improper variables to describe the dynamics. The correct scaling is
proportional to the square of the number of particles and deduce the kinetic
equation valid for the homogeneous regime and numerical evidence is given for
the Hamiltonian Mean Field and ring models
Microcanonical Monte Carlo Study of One Dimensional Self-Gravitating Lattice Gas Models
In this study we present a Microcanonical Monte Carlo investigation of one
dimensional self-gravitating toy models. We study the effect of hard-core
potentials and compare to those results obtained with softening parameters and
also the effect of the geometry of the models. In order to study the effect of
the geometry and the borders in the system we introduce a model with the
symmetry of motion in a line instead of a circle, which we denominate as
model. The hard-core particle potential introduces the effect of the size of
particles and, consequently, the effect of the density of the system that is
redefined in terms of the packing fraction of the system. The latter plays a
role similar to the softening parameter in the softened particles'
case. In the case of low packing fractions both models with hard-core particles
show a behavior that keeps the intrinsic properties of the three dimensional
gravitational systems such as negative heat capacity. For higher values of the
packing fraction the ring the system behaves as the Hamiltonian Mean Field
model and while for the it is similar to the one-dimensional systems
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