Original title: Renormalizace v poruchové teorii více-fotonové ionizace molekul
Translated title: Renormalization in Perturbation Theory of Multi-photon Ionization of Molecules
Authors: Mendl, Adam ; Benda, Jakub (advisor) ; Zamastil, Jaroslav (referee)
Document type: Master’s theses
Year: 2026
Language: eng
Abstract: [eng] [cze]
We study the appearance of divergences in stationary perturbation R matrix theory applied to the calculation of multi-photon above threshold ionization pro- cesses. We remove divergent parts of the amplitude using projection formalisms by renormalized T matrix and discuss problems of this approach. Furthermore, we show that by summing up indistinguishable ionization paths in the velocity gauge at the third order of perturbation theory, divergences can be removed. Moreover, we study the same processes at third order of perturbation theory using time-dependent perturbation theory and illustrate that even the time- dependent perturbation theory diverges. Finally, by using summation of indis- tinguishable processes in time-dependent and stationary perturbation theory in velocity gauge, we obtain comparable finite results for divergent processes. 1 Studujeme vy 'skyt divergencı ́ ve staciona ́rnı ́ poruchove ́ R maticove ́ teorii popisujı ́cı ́ nadprahovou vı ́cefotonovou ionizaci. Pomocı ́ projekc ̌nı ́ch formalismu ̊ zaloz ̌eny ́ch na renormalizovane ́ T matici odstran ̌ujeme divergentnı ́ c ̌a 'sti ampli- tudy a zaby ́va ́me se proble ́my spojeny ́mi s tı ́mto pr ̌ı 'stupem. Da ́le ukazujeme, z ̌e sec ̌tenı ́m principia ́lne ̌ nerozlis ̌itelny ́ch ionizac ̌nı ́ch procesu ̊ v rychlostnı ́ kalibraci lze divergence ve tr ̌etı ́m r ̌a ́du odstranit. Take ́ studujeme procesy tr ̌etı ́ho r ̌a ́du pomocı ́ c ̌asove ́ poruchove ́ teorie a ilustrujeme, z ̌e i tento popis vede k diver- gencı ́m. Konec ̌ne ̌ pomocı ́ sec ̌tenı ́ nerozlis ̌itelny ́ch procesu ̊ v c ̌asove ̌ za ́visle ́ a sta- ciona ́rnı ́ poruchove ́ teorii v rychlostnı ́ kalibraci zı 'ska ́va ́me srovnatelne ́ konec ̌ne ́ vy 'sledky pro divergentnı ́ procesy. 1
Keywords: perturbation theory|photoionization|multi-photon transitions|renormalization; poruchová teorie|fotoionizace|vícefotonové přechody|renormalizace

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/209594

Permalink: http://www.nusl.cz/ntk/nusl-780664


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Master’s theses