Selected problems in quantum mechanics: towards topological quantum devices and heat engine
| Autor: | Alecce, Antonio |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
FIS/03 Fisica della materia
fluctuation relations topological superconductors Majorana zero modes quantum and metallic dots single electron transistors quantum heat engines Kitaev model quantum thermodynamics quantum heat engines nonequilibrium physics fluctuation relations topological superconductors Kitaev model Majorana zero modes single electron transistors quantum and metallic dots transport Settore FIS/03 - Fisica della Materia Settore FIS/02 - Fisica Teorica Modelli e Metodi Matematici FIS/02 Fisica teorica modelli e metodi matematici quantum thermodynamics transport nonequilibrium physics |
| Popis: | The work presented in this thesis meanly addresses two topics in theoretical physics which are quantum thermodynamics and topological order. In the first case, physicists are trying to build up a theory able to describe quite in general phenomena involving heat and energy exchanges in quantum systems. The second topic, instead, is related to exotic phenomena and states of matter like the quantum Hall effect (QHE) or topological insulators and topological superconductors. In the first part od the thesis we define the quantum dynamics for closed and open systems. This is a key ingredient to address the field of quantum thermodynamics. Then, after an introductory part about the quantum thermodynamic transformations, we move toward the field of nonequilibrium fluctuation relations. We address the problem of irreversibility in classical as well as quantum mechanics. Here we present one of our main result. We characterize the "thermodynamic" irreversible adiabatic evolution of a quantum system starting such branch in a thermal equilibrium state at inverse temperature ßi. We give the amount of thermodynamic entropy growth for the process. As direct application of the preceding result we then address a quantum Otto cycle (QOC) working at finite power. We saw that the increasing of irreversible character of the evolution affects the main figures of merit of the cycle. The second part of the thesis addresses the field of topological order. At first we introduce the concept of topological orders, classes and invariants. Then we introduce the well known Kitaev model for 1 D superconductors. This model predicts Majorana zero mode at the ends of the wire (the 1 D system). MZM are topological states showing great resistance against disorder, local perturbations and any dissipative element. Then we consider a generalized Kitaev model where long range interactions are accounted. We get rich topological phase diagrams showing the presence of several MZM per edge. We study the appearing/disappearing dynamics of the modes according to the time reversal symmetry, that is fundamental in the study of topological phase. The phase diagrams we obtained also show the presence of massive edge modes. In this last case the topological invariants do not well describe any transition. At last we focused on a very limit cases where MZM are obtained at finite length of the wire. Such cases are really interesting since the great advance we can get from the finiteness of the wire in an experimental setup. The last part is about single electron tunneling devices. Here we got a different ability to work as "heat-to-current harvester" for a device using quantum dots respect to an analogue one using metallic dots. These different arguments find their unity by considering recent scientific works in which heat transport is addressed in single electron transistor devices where some element of the circuit shows a topological behaviour. This is a perfect system from hich we can get new transport phenomena. |
| Databáze: | OpenAIRE |
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