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Teorie agregátů fotosyntetických molekul: spektroskopie, struktura, přenosové jevy
Lalinský, Ján ; Mančal, Tomáš (advisor) ; Šanda, František (referee)
Title: Theory of aggregates of photosynthetic molecules: spectroscopy, structure, transport phenomena Author: Ján Lalinský Institute: Institute of Physics of Charles University Supervisor of the master thesis: RNDr. Tomáš Mančal, PhD., Institute of Physics of Charles University Abstract. A theory of absorption of light in an isotropic solution of molecules was formulated on the basis of electromagnetic theory of par- ticles with attention to relativistic nature of their interaction and its im- pact on the spectrum of circular dichroism. Calculations of the absorption spectra of simple systems were performed to demonstrate the properties of the mathematical model. Also calculations of the absorption spectra of the models of the bacteriochlorophyll dimer which were proposed as possible basic unit in the lamellar model of the interior of a chlorosome were performed. The experimental spectra of solution of non-aggregated bacteriochlorophyll were used to fit the parameters of the mathematical model of the molecule and for these parameters the spectra of the pro- posed models of a dimer were calculated. It has been found that the new non-electrostatic terms in the description of the mutual interaction of the parts of the molecule are negligible for calculations of ordinary absorption spectrum, but they have...
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Srovnání poruchových a neporuchových přístupů k teorii optické spektroskopie
Malý, Pavel ; Mančal, Tomáš (advisor) ; Pšenčík, Jakub (referee)
This thesis focuses on the comparison of perturbative and non-perturba-tive calculation of the third order polarization in two dimensional (2D) optical spec- troscopy. A two-level molecule and a coupled dimer are chosen as simple systems for which the 2D spectrum is calculated using explicit equations of motion for the reduced density matrix and integrating the response functions. The two approaches are compared qualitatively and quantitatively using obtained re- sults. The main difference found is the presence of higher order polarization contributions in non-perturbatively calculated spectrum. 1
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Přenos koherencí při relaxaci excitační energie v molekulárních agregátech
Olšina, Jan ; Mančal, Tomáš (advisor)
We study the time dependence of the density operator of molecular aggregates in contact with thermal bath, to find a proper approximation for the description of a coherence transfer influence on this evolution. It is based on results of the computer program, written by the author of the work. The program uses three methods of evaluation - the solution of the convolution Quantum Master Equation, and solution of the derived Redfield equations in Markov and subsequent Secular approximations. The temperature dependence and dependence on other parameters of the model are discussed on the basis of the obtained numerical results performed on an example of a trimer. The influence of coherence transfer on time-evolution superoperator of the trimer is discussed as well. The reasons why the Markov approximation fails for a wide spectrum of parameters are given. It is concluded that it is not suitable for the description of coherence transfer effects.
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Analytical Solutions of Two-Dimensional Schrödinger Equation
Tichý, Vladimír ; Skála, Lubomír (advisor) ; Šťovíček, Pavel (referee) ; Mančal, Tomáš (referee)
The goal of the dissertation is to find new method of solving two-dimensional Schrödinger equation in such cases, when the separation of the variables is not applicable. The results are applied to the two-dimensional Schrödinger equation with the potentials of the form of the quartic polynomial, of the sextic polynomial and of the quartic Morse potential. For these cases, the analytical formulae for the ground state wave functions and the corresponding energies have been found. For the specific class of the potentials of the form of the quartic polynomial, analytical formula for one of the excited states and for the corresponding energy have been found.
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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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Nelineární optická spektroskopie molekulárních komplexů
Linhart, Jan ; Mančal, Tomáš (advisor) ; Pšenčík, Jakub (referee)
Práce se zabývá teorií nelineární spektroskopie a projevy kvantové koherentní dynamiky v nelineární spektroskopii. Poskytuje stručný přehled spektroskopických metod se zaměřením na metodu pump-probe. Dále rozví- jíme teorii nelineární odezvy, přičemž vycházíme z obecného N-wave mixing experimentu, a dospíváme ke tvaru odezvové funkce třetího řádu vyjádřené pomocí Liouvillových drah. Pro vybrané modelové systémy sledujeme koher- entní efekty, které se projevují v 2D a pump-probe spektrech, a provádíme jejich porovnání. D·raz je kladen na objasnění jev· relaxace a excitonové koherence mezi dvěma excitovanými stavy molekulárního dimeru. 1
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Coherence transfer during relaxation in molecular aggregates
Olšina, Jan ; Mančal, Tomáš (advisor) ; Skála, Lubomír (referee)
We study the time dependence of the density operator of molecular aggregates in contact with thermal bath, to find a proper approximation for the description of a coherence transfer influence on this evolution. It is based on results of the computer program, written by the author of the work. The program uses three methods of evaluation - the solution of the convolution Quantum Master Equation, and solution of the derived Redfield equations in Markov and subsequent Secular approximations. The temperature dependence and dependence on other parameters of the model are discussed on the basis of the obtained numerical results performed on an example of a trimer. The influence of coherence transfer on time-evolution superoperator of the trimer is discussed as well. The reasons why the Markov approximation fails for a wide spectrum of parameters are given. It is concluded that it is not suitable for the description of coherence transfer effects.
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