
Rezonanční srážky elektronů s molekulami
Formánek, Martin ; Houfek, Karel (advisor) ; Kolorenč, Přemysl (referee)
In the present work we study different approaches for solving the nuclear dy namics of resonant electron molecule collisions. Namely, we review two methods addressing this phenomenon which are a local complex potential (LCP) approxi mation and a nonlocal resonance model (NRM). We briefly discuss a numerical implementation of these methods. We show how to derive model parameters for both of them from fixednuclei scattering calculations and we implement them in the time independent picture of quantum mechanics. We compare their vibrational excitation cross sections for the diatomic molecule CO. Then we generalize the non local resonance model for systems with more nuclear degrees of freedom. Output of our work is a computer code producing the vibrational excitation cross sections for systems with two degrees of freedom. We aim to use this code for studying a threshold behavior of the lowenergy electron collisions with the CO2 molecule and therefore we review a current state of understanding for this phenomenon. Mea nwhile we test the functionality of the code by comparing results with those of the LCP approximation on a simple 2D model system.


Solution of integral equations for separable interactions
Hvizdoš, Dávid ; Horáček, Jiří (advisor) ; Kolorenč, Přemysl (referee)
Title: Solution of integral equations for separable interactions Author: Dávid Hvizdoš Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Jiří Horáček, DrSc., Institute of Theoretical Physics Abstract: This work deals with the most fundamental types of integral equations (Fredholm and Volterra). Their occurrence in quantum mechanics is illustrated and the process that leads to the socalled regular and Jost solution is presented. Further their solutions in the case of separable interactions are studied. Analytical solutions on model separable potentials are sought. Analytical extensions of these solutions to the complex energy plane are provided and the properties of these functions are examined. The method of analytical continuation in the coupling constant based on the extension of the coupling constant as a function of is introduced. For some examples of separable potentials the Taylor expansion of the function and from it the inverse series √ are calculated. These series are then used to determine the resonance parameters of the potential and the accuracy of these calculations is discussed. Key words: integral equations, scattering theory, resonances, separable potential


1D model of laserassisted potential scattering
Tesař, Tomáš ; Mašín, Zdeněk (advisor) ; Kolorenč, Přemysl (referee)
The aim of this thesis is to investigate the effect of strong ultrashort electric fields on scattering of a particle by a short range potential, using a simple onedimensional model. The interaction potential has the form of a simple potential step. The transmission amplitude is calculated using Fourier analysis of the scattered wavefunction. The scat tered wavefunction is obtained by solving numerically the timedependent Schrödinger equation combining the finite difference spatial representation with the Crank Nicholson method to approximate the evolution operator. We validate and test the method on the analytically solvable problem of scattering by a potential barrier without the presence of the external field. Finally, we apply the method to calculation of laser assisted trans mission through the potential barrier and find that transmission through the barrier can be strongly enhanced or suppressed depending on the choice of the field parameters. We provide elementary clues on interpretation of our findings. 1


Twoelectron model of interatomic Coulombic decay
Šenk, Jan ; Kolorenč, Přemysl (advisor) ; Čížek, Martin (referee)
In this thesis we construct and examine a twoelectron model of interatomic Coulom bic decay (ICD). We base this model on an unperturbed hamiltonian with closedform stationary solutions with a potential consisting of two finite square wells. The Coulombic interaction mediating the decay between the electrons is incorporated via timedependent perturbation theory. We then examine the dependence of the decay widths on the inter well distance, the depth of the right well and the energy of the ICD electron. The model correctly describes the interwell dependence for high energy ICD electrons. 1


Study of time evolution of metastable states in quantum mechanics
Gedeonová, Hedvika ; Kolorenč, Přemysl (advisor) ; Čížek, Martin (referee)
In this thesis, the metastable states are studied. The work focuses on a theoretical model of one or two metastable states decaying into a continuum of states which is bounded from below. We examine the time evolution of such systems and how it is affected by the energy of the metastable state(s) and by the position of the poles of the scattering matrix in the complex plane. We also look closely at the spectral line shape. Numerical integration of a system of differential equations is used for solving the problem of the time evolution and spectral line shape while FreshbachFano projection operator formalism is used for finding the position of the poles. The results are compared with first order perturbation theory and with semianalytical formula obtained from adiabatic elimination of the continuum. The last part of the thesis is dedicated to an application of the model on neonheliumneon cluster. 1


TimeDependent Solution of the Generalized Fano Model
Gedeonová, Hedvika ; Kolorenč, Přemysl (advisor) ; Horáček, Jiří (referee)
In this thesis, the time evolution of Fano model, describing a discrete state embedded in a continuum of states with constant coupling, and generalized ver sion of Fano model for an energy dependent coupling are investigated. For the time evolution of the generalized system, numerical simulation (Gaussian quadra ture and numerical integration of a system of differential equations) is used. The system behaves as Fano model predicts when energydependent coupling tends to a constant one, and the system exponentially decays into the continuum. For a strongly energydependent coupling, the system oscillates between the initial discrete state and the continuum. The thesis provides numerically evaluated time evolution for different parameters of the coupling, brief interpretation of proba bility oscillation phenomenon and study of the transition between oscillatory and nonoscillatory mode. 1


Báze vlnových balíků v popisu rezonančního rozptylu
Lukeš, Petr ; Kolorenč, Přemysl (advisor) ; Houfek, Karel (referee)
Title: Wavepacket basis in the description of the resonance scattering Author: Petr Lukeš Institute: Institute of Theoretical physics Supervisor: RNDr. Přemysl Kolorenč, Ph.D., Institute of Theoretical Physics Abstract: A common approach towards the solution of problems of particle scattering problems is the approximation of the wavefunctions with some set of square integrable functions. A new type of such basis is assessed in this work. The vectors of the basis are obtained by integration of eigenvectors of free Hamiltonian over finite intervals of energies. This basis is called the wave packet basis. This basis is used to compute values of resonance width and resonant energy for two simple cases and the results are compared to benchmark data known from other works. The results serve to evaluate the properties of this basis. Also this work contains a proposal of how could this basis be applied in computations of quantum scattering. Keywords: potential scattering, wavepacket basis, resonance width, resonant energy.


Computing resonance widths using square integrable basis
Votavová, Petra ; Kolorenč, Přemysl (advisor) ; Houfek, Karel (referee)
Four different nonorthogonal basis sets are studied and compared in order to obtain the resonance properties of a model scattering problem. In particular, two types of Gaussian basis sets, one Bspline basis set and one hybrid Gaussian  Bspline basis set. Their ability to represent the scattering continuum is investigated along with their numerical properties. Particular attention is paid to the energy range within which each basis set gives reasonably accurate values of the phase shift and the decay width. The radial Schrödinger equation is solved by the Löwdin's symmetric orthogonalization method and the decay width is extracted by the Stieltjes imaging procedure. The Rmatrix method within the framework of FeshbachFano projection operator formalism with polynomial basis set is utilized as a numerically exact reference method.


Particle interaction with atoms in optical lattice
Vozáb, Filip ; Čížek, Martin (advisor) ; Kolorenč, Přemysl (referee)
The thesis discusses description of associative detachment of electron in the iont interaction with neutral atoms in optical lattice. This is given by combination of the model for interaction of particles in optical lattice, given by periodic potential, and of the model for associative detachment of electron, describe by imaginary component of the potential. In thesis is stated form of Schrödinger's equation for periodic potential, and subsequent solution of such equation in case of general complex and non hermitian Hamiltonian (because of imaginary component of potential). I specifically compute complex energetic levels onedimensional model with numeric method from software package EISPACK for non hermitian Hamiltonian decomposed into finite base. Powered by TCPDF (www.tcpdf.org)


Solution of integral equations for separable interactions
Hvizdoš, Dávid ; Horáček, Jiří (advisor) ; Kolorenč, Přemysl (referee)
Title: Solution of integral equations for separable interactions Author: Dávid Hvizdoš Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Jiří Horáček, DrSc., Institute of Theoretical Physics Abstract: This work deals with the most fundamental types of integral equations (Fredholm and Volterra). Their occurrence in quantum mechanics is illustrated and the process that leads to the socalled regular and Jost solution is presented. Further their solutions in the case of separable interactions are studied. Analytical solutions on model separable potentials are sought. Analytical extensions of these solutions to the complex energy plane are provided and the properties of these functions are examined. The method of analytical continuation in the coupling constant based on the extension of the coupling constant as a function of is introduced. For some examples of separable potentials the Taylor expansion of the function and from it the inverse series √ are calculated. These series are then used to determine the resonance parameters of the potential and the accuracy of these calculations is discussed. Key words: integral equations, scattering theory, resonances, separable potential
