Simulations of quantum transport with quadratic fermionic Hamiltonians
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School of Science |
Master's thesis
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Date
2024-09-13
Department
Major/Subject
Materials Physics and Quantum Technology
Mcode
Degree programme
Master's Programme in Engineering Physics
Language
en
Pages
51
Series
Abstract
In this Master’s thesis, a simulation method for studying quantum transport with quadratic fermionic Hamiltonians is implemented and it is applied for studying the problem of heat transport through a single fermionic mode. The discussion begins with a review of quantum statistical physics and heat transport. Developing on this background, the single fermionic level heat transport problem is introduced and the basic properties of quadratic systems are reviewed. The theoretical basis of the simulation method based on general Bogoliubov transformations is then covered and the method is implemented for the single fermionic level heat transport problem. The validity of the implemented simulation is successfully evaluated by comparing the results to known expressions for steady state heat transport both in the weak coupling regime governed by a Lindblad master equation and the general coupling regime governed by a Landauer type formula. Furthermore, the effects of the density of states and the rotating wave approximation are discussed.Description
Supervisor
Pekola, JukkaThesis advisor
Pekola, JukkaKeywords
statistinen fysiikka, kvanttikuljetus, Bogoliubov muunnos, lämmönsiirto, fermioninen systeemi, simulaatio