50 research outputs found
Power-law tail distributions and nonergodicity
We establish an explicit correspondence between ergodicity breaking in a
system described by power-law tail distributions and the divergence of the
moments of these distributions.Comment: 4 pages, 1 figure, corrected typo
Gas-plasma compressional wave coupling by momentum transfer
Pressure disturbances in a gas-plasma mixed fluid will result in a hybrid response, with magnetosonic plasma waves coupled to acoustic waves in the neutral gas. In the analytical and numerical treatment presented here, we demonstrate the evolution of the total fluid medium response under a variety of conditions, with the gas-plasma linkage achieved by additional coupling terms in the momentum equations of each species. The significance of this treatment lies in the consideration of density perturbations in such fluids: there is no 'pure' mode response, only a collective one in which elements of the characteristics of each component are present. For example, an initially isotropic gas sound wave can trigger an anisotropic magnetic response in the plasma, with the character of each being blended in the global evolution. Hence sound waves do not remain wholly isotropic, and magnetic responses are less constrained by pure magnetoplasma dynamics
Statistical Properties of Many Particle Eigenfunctions
Wavefunction correlations and density matrices for few or many particles are
derived from the properties of semiclassical energy Green functions. Universal
features of fixed energy (microcanonical) random wavefunction correlation
functions appear which reflect the emergence of the canonical ensemble as the
number of particles approaches infinity. This arises through a little known
asymptotic limit of Bessel functions. Constraints due to symmetries,
boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure
Foundation of Statistical Mechanics under experimentally realistic conditions
We demonstrate the equilibration of isolated macroscopic quantum systems,
prepared in non-equilibrium mixed states with significant population of many
energy levels, and observed by instruments with a reasonably bound working
range compared to the resolution limit. Both properties are fulfilled under
many, if not all, experimentally realistic conditions. At equilibrium, the
predictions and limitations of Statistical Mechanics are recovered.Comment: Accepted in Phys. Rev. Let
Entropy production and equilibration in Yang-Mills quantum mechanics
The Husimi distribution provides for a coarse grained representation of the
phase space distribution of a quantum system, which may be used to track the
growth of entropy of the system. We present a general and systematic method of
solving the Husimi equation of motion for an isolated quantum system, and we
construct a coarse grained Hamiltonian whose expectation value is exactly
conserved. As an application, we numerically solve the Husimi equation of
motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and
calculate the time evolution of the coarse grained entropy of a highly excited
state. We show that the coarse grained entropy saturates to a value that
coincides with the microcanonical entropy corresponding to the energy of the
system.Comment: 23 pages, 23 figure
Canonical thermalization
For quantum systems that are weakly coupled to a much 'bigger' environment,
thermalization of possibly far from equilibrium initial ensembles is
demonstrated: for sufficiently large times, the ensemble is for all practical
purposes indistinguishable from a canonical density operator under conditions
that are satisfied under many, if not all, experimentally realistic conditions
Chaos and Quantum Thermalization
We show that a bounded, isolated quantum system of many particles in a
specific initial state will approach thermal equilibrium if the energy
eigenfunctions which are superposed to form that state obey {\it Berry's
conjecture}. Berry's conjecture is expected to hold only if the corresponding
classical system is chaotic, and essentially states that the energy
eigenfunctions behave as if they were gaussian random variables. We review the
existing evidence, and show that previously neglected effects substantially
strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas
as an explicit example of a many-body system which is known to be classically
chaotic, and show that an energy eigenstate which obeys Berry's conjecture
predicts a Maxwell--Boltzmann, Bose--Einstein, or Fermi--Dirac distribution for
the momentum of each constituent particle, depending on whether the wave
functions are taken to be nonsymmetric, completely symmetric, or completely
antisymmetric functions of the positions of the particles. We call this
phenomenon {\it eigenstate thermalization}. We show that a generic initial
state will approach thermal equilibrium at least as fast as
, where is the uncertainty in the total energy
of the gas. This result holds for an individual initial state; in contrast to
the classical theory, no averaging over an ensemble of initial states is
needed. We argue that these results constitute a new foundation for quantum
statistical mechanics.Comment: 28 pages in Plain TeX plus 2 uuencoded PS figures (included); minor
corrections only, this version will be published in Phys. Rev. E;
UCSB-TH-94-1
Examen critique de la théorie des plasmas basée sur le libre parcours moyen, à la lumière de la méthode fondée sur la fonction de distribution solution de l'équation de Boltzmann
On montre la supériorité incontestable de la méthode des fonctions de distribution sur celle du libre parcours moyen en examinant divers exemples caractéristiques choisis dans la théorie des plasmas et en mettant en relief les déficiences manifestes de la méthode du libre parcours moyen. Au cours de cette étude on reprend, en outre, diverses objections soulevées à propos de résultats antérieurs obtenus par les auteurs
Déduction de la formule de biréfringence ionosphérique d'Appleton à partir de la théorie magnétoionique non maxwellienne. Conditions et domaine de validité
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