Möckel, Michael (2009): Realtime evolution of quenched quantum systems. Dissertation, LMU München: Faculty of Physics 

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Abstract
The study of the interplay between interactioninduced correlations and nonequilibrium initial conditions in manybody systems has recently attracted a lot of attention. New experimental techniques provide high control over manybody systems and systematic access to their nonequilibrium regime. In many systems the nonequilibrium properties of a Fermi liquid can be relevant. A first approach to their understanding is the main content of this thesis. At the beginning, nonequilibrium phenomena, Landau's theory of a Fermi liquid, the Hubbard model, time evolution in quantum mechanics, related experiments, and the flow equation method are reviewed. The key observation of this thesis, namely a characteristic mismatch of expectation values in equilibrium and nonequilibrium, is first illustrated for the squeezed oscillator. For this oneparticle model Hamiltonian the perturbative approach can be compared with the exact solution and it is shown that the mismatch holds even beyond perturbation theory. Afterwards these observations are generalized to a larger class of oneparticle models. Then the nonequilibrium behavior of a Fermi liquid is examined by analyzing the Fermi liquid phase of the Hubbard model in more than one dimension. After a sudden switchon of a weak twoparticle interaction to the noninteracting Fermi gas the relaxation of the manybody system is observed. For this purpose, the flow equation transformation is implemented for the Hubbard Hamiltonian. Then the discussion of the momentum distribution function and of the kinetic energy displays a threestep relaxation behavior of the Fermi liquid from the initial perturbation until thermalization is reached. Firstly, the sudden switch inserts excitation energy into the system which drives the following dynamics. Then a rapid initial buildup of correlations is caused by initial dephasing and leads to the establishment of a quasiparticle picture. By that the system enters into a quasistationary state which can be longlasting for weak interaction. This state shows prethermalization of the kinetic energy which already has relaxed to its final values. However, the momentum distribution still resembles a zero temperature Fermi liquid. Its later relaxation on a second time scale is caused by a residual twoparticle interaction which allows for scattering processes and can be described by a quantum Boltzmann equation. The physical origin of this delayed relaxation can be traced back to an interplay of translational invariance of the Hubbard model and the Pauli principle for fermions; together they restrict the phase space for scattering events. Comparing with similar work I conjecture on the generic nature of the findings made for the quenched Fermi liquid in other manybody systems. Finally I point out to the potential relevance of the delayed relaxation for the observation of further nonequilibrium phenomena, for instance in BCS systems. In order to extend the study of sudden switching to arbitrary switching processes the calculation is repeated using the Keldysh perturbation theory. First evaluations for a linear increase of the interaction strength are given. Extensions of this work are suggested and may motivate further research.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  condensed matter theory; quantum manybody systems; nonequilibrium; Fermi liquid; Hubbard model; squeezed oscillator; renormalization techniques; flow equation method; quantum Boltzmann equation; quantum dynamics; realtime evolution; transient dynamics; mismatch of equilibrium and nonequilibrium expectation values; thermalization 
Subjects:  600 Natural sciences and mathematics 600 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date Accepted:  24. June 2009 
1. Referee:  Kehrein, Stefan 
Persistent Identifier (URN):  urn:nbn:de:bvb:19103950 
MD5 Checksum of the PDFfile:  ad7c4cb3b789858f5d33a0bf88d6de70 
Signature of the printed copy:  0001/UMC 17948 
ID Code:  10395 
Deposited On:  05. Aug 2009 08:18 
Last Modified:  16. Oct 2012 08:30 