Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSubdynamics of fluctuations in an equilibrium classical many-particle system and generalized linear Boltzmann and Landau equations
53
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1 particles of a classical many-body system, are obtained These time-convolution and time-convolutionless GMEs differ from the known GMEs (e.g. Nakajima-Zwanzig GME) by absence of inhomogeneous terms containing correlations between all N particles at the initial moment of time and preventing the closed description of s-particles subsystem evolution. Closed homogeneous GMEs describing the subdynamics of fluctuations are obtained by applying a special projection operator to the Liouville equation governing the dynamics of N-particle system. In the linear approximation in the particles density, the linear Generalized Boltzmann equation accounting for initial correlations and valid at all timescales is obtained This equation for a weak inter-particle interaction converts into the generalized linear Landau equation in which the initial correlations are also accounted for. Connection of these equations to the nonlinear Boltzmann and Landau equations are discussed.
rate research
Read More
A recently developed method for incorporating initial binary correlations into the Kadanoff-Baym equations (KBE) is used to derive a generalized T-matrix approximation for the self-energies. It is shown that the T-matrix obtains additional contributions arising from initial correlations. Using these results and taking the time-diagonal limit of the KBE, a generalized quantum kinetic equation in binary collision approximation is derived. This equation is a far-reaching generalization of Boltzmann-type kinetic equations: it selfconsistently includes memory effects (retardation, off-shell T-matrices) as well as many-particle effects (damping, in-medium T-Matrices) and spin-statistics effects (Pauli-blocking).
We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an infinite time with a period twice as the driving period (synchronized regime) and a regime where the oscillations die after a finite transient (chaotic regime). We emphasize the peculiarity of our result, having been synchronisation observed so far only in driven-dissipative systems. We discuss how our findings can be interpreted as a period-doubling time crystal and we show that synchronisation can appear both for an overall regular and an overall chaotic dynamics.
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual system. Our aim is to discuss and compare these two notions of entropy, along with the associated ensemblist and individualist views of thermal equilibrium. Using the Gibbsian ensembles for the computation of the Gibbs entropy, the two notions yield the same (leading order) values for the entropy of a macroscopic system in thermal equilibrium. The two approaches do not, however, necessarily agree for non-equilibrium systems. For those, we argue that the Boltzmann entropy is the one that corresponds to thermodynamic entropy, in particular in connection with the second law of thermodynamics. Moreover, we describe the quantum analog of the Boltzmann entropy, and we argue that the individualist (Boltzmannian) concept of equilibrium is supported by the recent works on thermalization of closed quantum systems.
Condensation of fluctuations is an interesting phenomenon conceptually distinct from condensation on average. One stricking feature is that, contrary to what happens on average, condensation of fluctuations may occurr even in the absence of interaction. The explanation emerges from the duality between large deviation events in the given system and typical events in a new and appropriately biased system. This surprising phenomenon is investigated in the context of the Gaussian model, chosen as paradigmatical non interacting system, before and after an istantaneous temperature quench. It is shown that the bias induces a mean-field-like effective interaction responsible of the condensation on average. Phase diagrams, covering both the equilibrium and the off-equilibrium regimes, are derived for observables representative of generic behaviors.
Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations are considered. Results of experiments in which dynamical scanning tunneling microscopy is used to evaluate these first-passage properties for steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
