Heat correlations in some nano systems

Abstract

This thesis investigates quantum transport in strongly correlated one-dimensional sys tems. It uses exact analytical tools, including bosonization and refermionization, to ad dress models where interactions can be treated in a non perturbative way. The first chapter provides an overview of mesoscopic condensed matter physics, intro ducing the transition from the Fermi gas to the Luttinger liquid. It discusses both chiral and non-chiral systems and the analytical frameworks used to study them. Physical ob servables such as current density, correlation functions, and noise are clearly defined. The second chapter focuses on thermal transport in a system exhibing the fractional quantum Hall effect (FQHE). The model features two edge states with filling factors ν = 1 (Fermi) and ν = 1/3 (Luttinger). By mapping the system to an analytically tractable ν = 1/2 model, we compute thermal observables such as density, heat current, thermal conductance, and thermal correlation functions. The third chapter explores electrical correlations in a finite-length quantum wire under a longitudinal magnetic field and connected to non-interacting leads. For a special inter action parameter value K = 0.18, the model becomes exactly solvable, allowing detailed analysis of correlations between gapped and gapless modes.