Boson and Fermion Brownian Motion

In the frames of classical mechanics the generalized Langevin equation is derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a solid. A time-acting temperature operator is introduced for the quantum Klein-Kramers and Smoluchowski equations, accounting for the effect of the quantum thermal bath oscillators. The model of Brownian emitters is theoretically studied and the relevant evolutionary equations for the probability density are derived. The Schr...

This paper is devoted to generalize some previous results presented in Gaioli et al., Int. J. Theor. Phys. 36, 2167 (1997). We evaluate the autocorrelation function of the stochastic acceleration and study the asymptotic evolution of the mean occupation number of a harmonic oscillator playing the role of a Brownian particle. We also analyze some deviations from the Bose population at low temperatures and compare it with the deviations from the exponential decay law of an unst...

We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but the classical equations of motion with two additional terms and the one of them can be regarded as the the quantum potential. By choosing a parameter space, various important states are obtained. Further, the equations contain other interesting phenomena such as general dynamics of diffusi...

Quantum Brownian motion of a rod-like particle is investigated in the frame work of system plus reservoir model. The quantum mechanical and classical limit for both translational and rotational motions are discussed. Correlation functions, fluctuation-dissipation relations and mean squared values of translational and rotational motions are obtained.

"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually considered, one is driven by a one-dimensional Brownian motion and the other is driven by a counting process. In this article, we present a way to obtain more advanced models which use jump-diffusion stochastic differential equations. Such mode...

The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a system-reservoir nonlinear coupling model we present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Markovian Langevin description and an associated Fokker-Planck equation in position space in the overdamped limit. We examine the thermodynamic con...

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibr...

We present a stochastic approach for the description of the quantum dynamics of open system in a fermionic environment (bath). The full quantum evolution as provided by the Schrodinger equation is reformulated exactly as a probabilistic average over the so-called dressed quantum trajectories. The latter are defined as follows. The fermionic environment can be represented as a fermi sea whose "surface" is covered by the ripples of quantum fluctuations. If we consider these flu...

Brownian motors, i.e. devices able to produce useful work out of thermal forces with the help of other unbiased forces, provide an ideal benchmark for the investigation of quantum dissipative systems, for two reasons. First, the interaction with a dissipative environment plays an essential role in the performance of Brownian motors. Second, dissipative tunneling enriches the dynamics of quantum Brownian motors with respect to their classical counterpart, inducing features suc...