A quantum diffusion law

Abstract

We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and temperature, each with its own characteristic rate of spreading. As with earlier analyses, we find logarithmic spreading in the quantum regime, indicating that this behavior is robust. A consistent R(t) must satisfy the key physical requirements of Wightman positivity and passivity, and we prove that ours does so. We also prove in general that these two conditions are equivalent when the FDT holds. Given current technology, our diffusion law can be tested in a laboratory with ultra cold atoms.

Quantum Brownian Motion: Drude and Ohmic Baths as Continuum Limits of the Rubin Model

“…In particular, we discussed the quantum to classical crossover time scales where the mean square displacement changes from a logarithmic to a linear time dependence. The analysis presented in this work provides a microscopic justification for the choice of the position response function used in a recent analysis [24] of quantum Brownian motion based on linear response theory as the starting point.…”

“…We try to understand interesting physical aspects and highlight some of the qualitative differences. In recent years an approach based on linear response and fluctuation-dissipation theorem [23,24] has been used to study Brownian motion at zero temperature. We point out here that this approach is exact for the case of the Rubin model of bath.…”

From Green function to quantum field

“…Among its other consequences, (7) guarantees, via the fluctuationdissipation theorem, the "passivity" condition that one cannot extract work from a system in thermal equilibrium by purely mechanical means (cf. [9]).…”

Measurements and analysis of response function of cold atoms in optical molasses

“…In recent years, diffusion of a Brownian particle in the presence of quantum zero-point fluctuation was analysed in [5,6] starting from the fluctuation-dissipation theorem [1,3]. The fluctuation-dissipation theorem is a linear response theorem according to which the linear response of a system to an external perturbation can be expressed in terms of spontaneous stochastic fluctuations of the system in thermal equilibrium and vice versa.…”

“…The fluctuation-dissipation theorem is a linear response theorem according to which the linear response of a system to an external perturbation can be expressed in terms of spontaneous stochastic fluctuations of the system in thermal equilibrium and vice versa. One of the key inputs in the analysis presented in [6] is the response function characterising the system. The choice of the response function was suggested by the model of a viscous medium.…”