Energy and particle number fluctuations in superconducting heterostructures

TL;DR

This paper develops a general theoretical framework using the Keldysh formalism to analyze energy fluctuations in mesoscopic superconducting islands, deriving Langevin equations and applying them to specific superconducting-normal metal systems.

Contribution

It introduces a comprehensive approach to describe energy and particle fluctuations in superconducting heterostructures, including derivation of Langevin equations for these fluctuations.

Findings

Derived Langevin equations for energy fluctuations in mesoscopic islands.

Calculated temperature and quasiparticle number statistics in superconducting islands.

Provided a general formalism applicable to various superconducting heterostructures.

Abstract

We consider fluctuations of the energy on a mesoscopic island coupled to two leads. We use the Keldysh effective action formalism to derive the Langevin equation for the energy of the island in a very general setting and show how the Langevin equation for the case of uncorrelated tunneling events is derived from a more general one. As an application of the theory, we consider a superconducting island coupled to two normal metal leads and calculate the statistics of the temperature (in the quasiequilibrium case) and the number of quasiparticle excitations on the island.