Boson and Fermion Brownian Motion

We derive the quantum thermodynamics of quantum Brownian motion from the exact solution of its reduced density matrix. By exactly traced over all the reservoir states, we solve analytically and exactly the reduced density matrix of the Brownian particle from the total equilibrium thermal state of the system strongly entangling with its reservoir. We find that the reduced Hamiltonian and the reduced partition function of the Brownian particle must be renormalized significantly...

The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian quantum theory is obtained. The conditional transition probability density of the presence of a Browmian particle is obtained with the help of the functional integral. The technique of factorisation of the solution of the Fokker-Planck equat...

Quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. In both the strong and the weak coupling regimes, we obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner...

In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brown...

Quantum systems of interest are typically coupled to several quantum channels (more generally environments). In this paper, we develop an exact stochastic Schr\"{o}dinger equation for an open quantum system coupled to a hybrid environment containing both bosonic and fermionic particles. Such a stochastic differential equation may be obtained directly from a microscopic model through employing a classical complex Gaussian noise and a non-commutative fermionic noise to simulate...

Hu, Paz and Zhang [ B.L. Hu, J.P. Paz and Y. Zhang, Phys. Rev. D {\bf 45} (1992) 2843] have derived an exact master equation for quantum Brownian motion in a general environment via path integral techniques. Their master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In this paper, we give an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evol...

We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the classical case. It is a white noise with a variance proportional to the temperature. The dissipation force is not restrict to be proportional to the velocity and is determined in a way as to guarantee that the stationary state is given by a...

Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we explain how they are derived from purely quantum mechanical models, where the dynamics is represented by a unitary evolution in a Hilbert space, and how they are related to the theory of continual measurements. An essential tool is an isomorphi...

A structure of generator of a quantum dynamical semigroup for the dynamics of a test particle interacting through collisions with the environment is considered, which has been obtained from a microphysical model. The related master-equation is shown to go over to a Fokker-Planck equation for the description of Brownian motion at quantum level in the long wavelength limit. The structure of this Fokker-Planck equation is expressed in this paper in terms of superoperators, givin...

The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term that generates additional position diffusion. He we show that one can obtain a completely positive simple quantum Brownian motion, efficiently solvable, without any extra diffusion. This is achieved by using a stochastic Schroedinger equati...