Quantum Kinetic Theory for Spin Fermion Systems

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Title: Quantum Kinetic Theory for Spin Fermion Systems
Author: Mei, Peng
Contributor: University of Helsinki, Faculty of Science, Department of Mathematics and Statistics
Thesis level: Doctoral dissertation (article-based)
Abstract: In this thesis, the main goal is to study the kinetic dynamics based on Hubbard model in dimensions d>2. We analyse rigorously some basic properties of the dynamics in the following scaling limit. As the coupling constant converges to zero, we rescale the time variable to capture the slow dynamics: we let coupling constant go to zero, time to infinity in such a way that the product of square of the coupling constant and time has a finite limit. The main ingredient of the kinetic limit is that, combining some basic ideas of scattering theory (long time scale) and perturbation theory (small coupling parameter), it automatically selects from the microscopic dynamics some dominating terms. This gives rise to a new description of time evolution (given by quantum Boltzmann equation), whose form can already be postulated from the second order perturbative expansion. The limit equation is expected to capture nontrivial information about the original system. Besides the weak coupling dynamics, we also discuss two complementary results in related Fermion systems.Väitöskirja käsittelee matemaattisia malleja monifermionisysteemeille. Erityisesti tavoitteena on kehittää menetelmiä, joilla voidaan paremmin ymmärtää ja analysoida elektronien spinvapausasteiden käytöstä kristallirakenteissa. Tätä ongelmaa lähestytään usein yksinkertaistettujen mallien kautta, joista ehkä kaikken eniten tutkittu on Hubbardin malli. Väitöskirjan keskeinen tulos on johtaa Hubbardin malliin liittyvä Boltzmannin kuljetusyhtälö heikon spinvuorovaikutuksen rajalla, sekä osoittaa, että tämä kuljetusyhtälö on hyvin määritelty yhtälön matemaattisesti poikkeuksellisesta rakenteesta huolimatta.
URI: URN:ISBN:978-952-10-8812-4
Date: 2013-05-20
Subject: mathematics
Rights: This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.

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