Kinetic theory for quantum nanosystems

TL;DR

This thesis develops a generalized kinetic theory for finite quantum systems, analyzing how kinetic and diffusive processes emerge depending on environment size and interaction strength.

Contribution

It introduces a generalized Redfield theory for finite quantum systems and investigates the critical environment size for kinetic process emergence.

Findings

Verification of the new kinetic theory with the spin-GORM model

Identification of a critical environment size for kinetic processes

Analysis of diffusive transport emergence in finite systems

Abstract

In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat capacity. We then study in detail the spin-GORM model, a model made of a two-level system interacting with a random matrix environment. By doing this, we verify our new theory and find a critical size of the environment over which kinetic processes occur. We finally study the emergence of a diffusive transport process, on a finite tight-binding subsystem interacting with a fast environment, when the size of subsystem exceeds a critical value.