Restricted quantum-classical correspondence and counting statistics for a coherent transition

TL;DR

This paper explores the quantum-classical relationship in particle transition statistics, demonstrating how quantum effects influence transport variance through a Landau-Zener crossing in a continuous measurement setting.

Contribution

It introduces a detailed analysis of counting statistics in quantum transitions, highlighting the limitations of classical intuition in a quantum context, especially during adiabatic Landau-Zener processes.

Findings

Quantum counting statistics deviate from classical predictions.

Adiabatic approximation may not accurately capture variance.

Restricted quantum-classical correspondence is demonstrated.

Abstract

The conventional probabilistic point of view implies that if a particle has a probability $p$ to make a transition from one site to another site, then the average transport should be $<Q>=p}$ with a variance $Var(Q)=(1-p)p$. In the quantum mechanical context this observation becomes a non-trivial manifestation of restricted quantum-classical correspondence. We demonstrate this observation by considering the full counting statistics which is associated with a two level coherent transition in the context of a continuous quantum measurement process. In particular we test the possibility of getting a valid result for $Var(Q)$ within the framework of the adiabatic picture, analyzing the simplest non-trivial example of a Landau-Zener crossing.