Dissipation and Decoherence in Nanodevices: a Generalized Fermi's Golden Rule

TL;DR

This paper introduces a generalized adiabatic approach that ensures physically consistent, positive-definite density matrices in quantum device modeling, effectively describing dissipation and dephasing processes with a Lindblad evolution.

Contribution

It proposes a more general adiabatic procedure that maintains positivity, reduces to Fermi's golden rule in the semiclassical limit, and accurately models energy dissipation and dephasing.

Findings

Ensures positive-definite density matrices in quantum dissipation models.

Reduces to standard Fermi's golden rule in the semiclassical limit.

Provides a robust Lindblad evolution for electronic quantum devices.

Abstract

We shall revisit the conventional adiabatic or Markov approximation, which --contrary to the semiclassical case-- does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule, and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that include the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum.