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Teorie elektron-fononové interakce v modelovém otevřeném kvantovém systému
Krčmář, Jindřich ; Mančal, Tomáš (advisor) ; Lipavský, Pavel (referee)
The aim of this work is to investigate projection operator method of deriva- tion of equations of motion for reduced density matrix and apply it to a model open quantum system. We gradually pass from quantum mechanical model of a molecule with one vibrational degree of freedom to an example of open quantum system relevant in the theory of nonlinear spectroscopy. In the thesis we present results of numerical simulations of the time evolution of the open quantum system performed with a program written for this purpose. We are specially concerned with simulations of the solution of the time-convolutionless generalized master equation up to the a second order of the perturbation expan- sion, and we show that under certain conditions it provides an exact solution of the problem. The text also contains derivation of the recurrence relations for the Franck-Condon factors for the most general case of two quantum harmonic oscillators in one space dimension, i. e. transformation matrix between two bases of the L2 (R) space determined by the solutions of the time-independent Schrödinger equation appropriate for these oscillators. 1
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Superconductivity in disordered systems
Šopík, Břetislav ; Lipavský, Pavel (advisor) ; Novotný, Tomáš (referee) ; Munzar, Dominik (referee)
Author: Mgr. Břetislav Šopík Thesis advisor: doc. Pavel Lipavský, CSc. Ph.D. thesis Superconductivity in disordered systems Abstract We study some aspects of the superconductivity in disordered systems - namely the superconductivity in a boron-doped diamond. We also apply theoretical methods originally developed in the field of the disordered systems to the theory of superconductivity. In the case of the boron-doped diamond we focus on the question of the dependence of the critical temperature Tc on boron doping. We discuss the impact of the boron distribution correlations on the Tc as well. First, we evaluate the density of states at the Fermi energy N0 within the dynamical cluster approximation. We discuss the Tc as a function of N0 within the BCS, the McMillan and the Belitz theory. In the case of 100 samples, the simplified Belitz theory gives the best agreement with experimental data. For 111 samples the McMillan theory is sufficient. We also show that the difference of 100 and 111 samples in the N0 dependence of Tc can be explained as given by attractive correlations in the boron distribution. Applying the concept of the coherent potential approximation, we re- move a self-interaction from the Galitskii-Feynman T-matrix approxima- tion. This correction has no effect in the normal state but makes the...
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Interaction of electrons with vibrating molecules: molecular electronic applications
Pshenichnyuk, Ivan ; Čížek, Martin (advisor) ; Lipavský, Pavel (referee) ; Thoss, Michael (referee)
Interaction of electrons with vibrating molecules: molecular electronics applications Ivan A. Pshenichnyuk Submitted for the degree of Doctor of Philosophy October 2010 Abstract Interaction of the electric current, flowing through the molecular junction, with the internal vibrations of the bridging molecule is investigated. Two different theo- retical approaches which allow us to calculate the current and other characteristics of the junction are compared. The first method is based on the scattering theory and Landauer formula, and the second on the Wangsness-Bloch-Redfield master equa- tion technique. A set of original models of the molecular bridge with anharmonic vibrational mode and asymmetric coupling to the leads is formulated. Influence of anharmonic vibrations and different types of symmetry in the junction on the current-voltage dependencies of the bridge are discussed. As an example of the phenomenon, which can only be found beyond the harmonic approximation, we demonstrate the existence of the so called "motor effect", i. e. the strong depen- dence of the average angular momentum of the molecule on the voltage, applied across the junction. The key parameters, responsible for the effect appearance, such as the rotational barrier height and the symmetry in the junction are discussed.
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