Phase transitions in full counting statistics for periodic pumping

TL;DR

This paper explores phase transitions in the full counting statistics of periodic quantum and classical pumps, identifying conditions under which the generating function exhibits different thermodynamic phases and singularities.

Contribution

It introduces a criterion for the analytic phase in quantum pumps with noninteracting fermions and discusses phase transitions in full counting statistics.

Findings

Identification of different thermodynamic phases in time domain

Criterion for the analytic phase in quantum pumping

Examples of phase transitions in classical and quantum systems

Abstract

We discuss the problem of full counting statistics for periodic pumping. The probability generating function is usually defined on a circle of the "physical" values of the counting parameter, with its periodicity corresponding to charge quantization. The extensive part of the generating function can either be an analytic function on this circle or have singularities. These two cases may be interpreted as different thermodynamic phases in time domain. We discuss several examples of phase transitions between these phases for classical and quantum systems. Finally, we prove a criterion for the "analytic" phase in the problem of a quantum pump for noninteracting fermions.