Generalized diffusion of quantum Brownian motion

TL;DR

This paper investigates the generalized diffusion behavior of a quantum Brownian particle in an Ohmic bath, revealing oscillatory and discontinuous diffusion patterns across different regimes, with implications for understanding quantum stochastic processes.

Contribution

It introduces a simplified calculation method for quantum diffusion functions and uncovers novel discontinuous and negative diffusion phenomena in quantum Brownian motion.

Findings

Discontinuous diffusion with negative values in the periodic regime.

Oscillatory behavior driven mainly by external response.

Similar behavior observed in the continuum limit.

Abstract

This article discusses the numerical result predicted by the quantum Langevin equation of the generalized diffusion function of a Brownian particle immersed in an Ohmic quantum bath of harmonic oscillators. The time dependence of the standard deviation of the reduced Wiener function of the system, obtained by integrating the whole function in the momentum space, is determined as well. The complexity of the equations leads to resort to a much simpler calculation based in the position correlation function. They are done for the three possible regimes of the system, namely, periodic, aperiodic and overdamped. It is found in the periodic case that the generalized diffusion is a discontinuous function exhibiting negative values during short time periods of time. This counterintuitive result, found theoretically in other systems and waiting for its experimental confirmation, can be perfectly explained in the framework of the quantum Langevin equation. Its oscillatory behavior is primordially due to the response to the external field while its quantum origin contributes only in its magnitude. The results are compared with those of the continuum limit which exhibits similar behavior.