Related papers: Classical open systems with nonlinear nonlocal dis…
We have studied the finite $N$-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Jpn. {\bf 75} (2006) 033001]. Effects of…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
A large variety of microscopic or mesoscopic models lead to generic results that accommodate naturally within Boltzmann-Gibbs statistical mechanics (based on $S_1\equiv -k \int du p(u) \ln p(u)$). Similarly, other classes of models point…
In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…
Finite $N$-unit Langevin models with additive and multiplicative noises have been studied with the use of the augmented moment method (AMM) previously proposed by the author [H. Hasegawa, Phys. Rev E {\bf 67}, 041903 (2003)]. Original…
We investigate the fluctuating incompressible Navier--Stokes equation driven by spatially correlated thermal noise characterized by a single length scale. This formulation is constructed to preserve thermal equilibrium through the…
This paper is concerned with the long-time dynamics of semilinear wave equation subject to dissipative boundary condition. To do so, we first analyze the set of equilibria, and show it could contain infinitely many elements. Second, we show…
We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the…
The existence of a generalized fluctuation-dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space. Assuming the…
In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site…
This thesis covers various aspects of open systems in classical and quantum mechanics. In the first part, we deal with classical systems. The bath-of-oscillators formalism is used to describe an open system, and the phenomenological…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the…
The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time…
Acceleration of relaxation toward a fixed stationary distribution via violation of detailed balance was reported in the context of a Markov chain Monte Carlo method recently. Inspired by this result, systematic methods to violate detailed…
The synchrony and variability have been discussed of the coupled Langevin model subjected to spatially correlated additive and multiplicative noise. We have employed numerical simulations and the analytical augmented-moment method which is…
The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the…
In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these…
We present a simple derivation of the stochastic equation obeyed by the density function for a system of Langevin processes interacting via a pairwise potential. The resulting equation is considerably different from the phenomenological…
An exact linear response expression is obtained for the heat current in a classical Hamiltonian system coupled to heat baths with time-dependent temperatures. The expression is equally valid at zero and finite frequencies. We present…