Thermodynamics of Mesoscopic Quantum Systems

TL;DR

This thesis investigates heat and particle transport in mesoscopic quantum systems, deriving symmetry relations among transport coefficients using full counting statistics and analyzing generalized flows.

Contribution

It introduces a method to derive relations among transport coefficients for particle, heat, and generalized flows in mesoscopic quantum systems using full counting statistics.

Findings

Derived symmetry relations for transport coefficients

Analyzed generalized flows as superpositions of particle and heat flows

Established conditions for choosing affinities in generalized flows

Abstract

In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its symmetry. The symmetry produces the relations among transport coefficients of the particle and heat flows when we expand these flows with respect to the appropriate affinities. Moreover, we consider the generalized flows which are superpositions of the particle and energy flows. We show that we can choose the appropriate affinities of the generalized flows and derive the relations among their transport coefficients when we expand the generalized flows with respect to their affinities.