Overview: Brownian Motion and Dephasing due to Dynamical Disorder

The motion of a particle under the influence of a dynamical disorder is described by the DLD model. One motivation is to understand the motion of an electron inside a metal; Another is to understand quantal Brownian motion. The overview is based on a research report for 1996-1998. A generic toy model for quantal Brownian motion that takes into account the disordered nature of an environment (See Fig.1) has been defined and explored [P1P5]. The treatment of diffusion localization and dissipation (DLD) has been unified, the propagator of the reduced probability-density-matrix has been calculated, and its non-classical structure has been explained. One motivation for studying this effective ‘DLD model’, which constitutes a nontrivial generalization of Zwanzig-Caldeira-Leggett (ZCL) model, is the wish to understand the motion of an electron inside a metal, taking into account both the the static disorder configuration and also the Coulomb interaction with the rest of the Fermi sea. An important issue [P3] is the study of decoherence using Wigner’s phase-space representation for the description of the evolving quantum-mechanical state. In case of the ZCL model the propagator of the Wigner function is just a Gaussian kernel. In case of the DLD model the propagator contains a singular term that corresponds to an unscattered component of the wavepacket. Consequently it is possible to distinguish between smearing mechanism and scattering mechanism for decoherence. This distinction is essential in order to get a proper understanding of dephasing. The extension of the latter study [P4] to the low-temperatures regime has been done in collaboration with Y. Imry. The limitations of the semiclassical strategy have been clarified. The work was motivated by a controversy regarding the effect of ‘zero point fluctuations’ [1], following experimental observation by Mohanty, Jariwala and Webb [2]. The study of dephasing has been extended [P3] to various types of transport, which are illustrated by Fig.2. The main goal was to derive results for all these cases using a general formula for dephasing that applies to any temperature. The final result can be written in terms of two functions: the form-factor of the environment and the power spectrum of the motion under consideration. The introduction of adhoc or ambiguous cutoffs into the calculations, as in the works of Chakravarty and Schmid [3] and followers, is not required. Overview: Brownian Motion and Dephasing due to Dynamical Disorder 2