Breakdown of quantum-to-classical correspondence for diffusion in high temperature thermal environment

TL;DR

This paper reveals a fundamental breakdown of quantum-to-classical correspondence in diffusion processes at high temperatures, showing quantum effects can alter classical predictions in certain models.

Contribution

It demonstrates the quantum breakdown of classical diffusion correspondence in high-temperature environments using a tight binding model with Ohmic dissipation.

Findings

Quantum analysis shows a breakdown of classical diffusion predictions.

Breakdown is second-order in inverse temperature.

Results depend on the specific dissipation scheme used.

Abstract

We re-consider the old problem of Brownian motion in homogeneous high-temperature thermal environment. The semiclassical theory implies that the diffusion coefficient does not depend on whether the thermal fluctuations are correlated in space or disordered. We show that the corresponding quantum analysis exhibits a remarkable breakdown of quantum-to-classical correspondence. Explicit results are found for a tight binding model, within the framework of an Ohmic master equation, where we distinguish between on-site and on-bond dissipators. The breakdown is second-order in the inverse temperature, and therefore, on the quantitative side, involves an inherent ambiguity that is related to the Ohmic approximation scheme.