Boson and Fermion Brownian Motion

A theoretical parallel between the classical Brownian motion and quantum mechanics is explored. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive behavior. In the case of simultaneous action of the two stochastic sources, the quantum Brownian motion takes place, which is theoretically described as well.

We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.

A unified canonical operator formalism for quantum stochastic differential equations, including the quantum stochastic Liouville equation and the quantum Langevin equation both of the It\^o and the Stratonovich types, is presented within the framework of Non-Equilibrium Thermo Field Dynamics (NETFD). It is performed by introducing an appropriate martingale operator in the Schr\"odinger and the Heisenberg representations with fermionic and bosonic Brownian motions. In order to...

Dynamical aspects of quantum Brownian motion in a low temperature environment are investigated. We give a systematic calculation of quantum entanglement among two Brownian oscillators without invoking Born-Markov approximation widely used for the study of open systems. Our approach is suitable to probe short time dynamics at cold temperatures where many experiments on quantum information processing are performed.

A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order quantum effects is derived.

We review in a pedagogic manner the topic of quantum Brownian motion, with an emphasis on its thermodynamic aspects. For the sake of completeness, we begin with the classical treatment of one-dimensional Brownian motion, discussing correlation functions and fluctuation-dissipation relations. The equation-of-motion approach, based on the Langevin equation, is mostly followed throughout the paper. A microscopic derivation of the generalized Langevin equation is outlined, based ...

A Brownian particle in an ideal quantum gas is considered. The mean square displacement (MSD) is derived. The Bose-Einstein or Fermi-Dirac distribution, other than the Maxwell-Boltzmann distribution, provides a different stochastic force compared with the classical Brownian motion. The MSD, which depends on the thermal wavelength and the density of medium particles, reflects the quantum effect on the Brownian particle explicitly. The result shows that the MSD in an ideal Bose...

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle ent...

Einstein's kinetic theory of the Brownian motion, based upon light water molecules continuously bombarding a heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. Since the discovery of quantum mechanics it has been a challenge to verify the emergence of diffusion from the Schr\"odinger equation. The first step in this program is to verify the linear Boltzmann equation as a certain scaling limit of a Schr\"odinger equation with random potential. I...

We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the process allows us to specify and to construct the dilation of the quantum dynamical maps, including conditional quantum expectations. The quantum phase space Brownian motion possesses many properties similar to that of the classical Brownian mo...