Memory effects in non-interacting mesoscopic transport

TL;DR

This paper investigates how the history of bias switching affects the final state in a quantum dot system, revealing that bound states retain memory of the switching process while continuum states do not.

Contribution

It demonstrates that in non-interacting mesoscopic transport, bound states exhibit memory effects depending on the switching history, unlike continuum states.

Findings

Final bound state expectation depends on switching history.

Steady-state continuum contributions are memoryless.

Memory effects are specific to bound states in the system.

Abstract

Consider a quantum dot coupled to two semi-infinite one-dimensional leads at thermal equilibrium. We turn on adiabatically a bias between the leads such that there exists exactly one discrete eigenvalue both at the beginning and at the end of the switching procedure. It is shown that the expectation on the final bound state strongly depends on the history of the switching procedure. On the contrary, the contribution to the final steady-state corresponding to the continuous spectrum has no memory, and only depends on the initial and final values of the bias.