Noncyclic and nonadiabatic geometric phase for counting statistics

TL;DR

This paper introduces a geometric-phase interpretation for counting statistics in stochastic processes, extending the concept beyond cyclic and adiabatic evolutions to noncyclic and nonadiabatic cases.

Contribution

It generalizes the geometric phase framework for counting statistics to include noncyclic and nonadiabatic evolutions, broadening its applicability.

Findings

Remaining phase is a geometric phase in noncyclic evolution

Framework applies to nonadiabatic stochastic processes

Enhances understanding of counting statistics in complex systems

Abstract

We propose a general framework of the geometric-phase interpretation for counting statistics. Counting statistics is a scheme to count the number of specific transitions in a stochastic process. The cumulant generating function for the counting statistics can be interpreted as a `phase', and it is generally divided into two parts: the dynamical phase and a remaining one. It has already been shown that for cyclic evolution the remaining phase corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan phase. We here show that the remaining phase also has an interpretation as a geometric phase even in noncyclic and nonadiabatic evolution.