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Lozej"},"dc:source":{"@xml:lang":"sl","#text":"visokošolska dela"},"dc:subject":[{"@xml:lang":"sl","#text":"biljard"},{"@xml:lang":"en","#text":"billiard"},{"@xml:lang":"en","#text":"cantorus"},{"@xml:lang":"en","#text":"chaos"},{"@xml:lang":"en","#text":"chaotic eigenstates"},{"@xml:lang":"sl","#text":"disertacije"},{"@xml:lang":"en","#text":"dissertations"},{"@xml:lang":"en","#text":"Hamiltonian systems"},{"@xml:lang":"sl","#text":"Hamiltonski sistemi"},{"@xml:lang":"en","#text":"Husimi functions"},{"@xml:lang":"sl","#text":"Husimijeve funkcije"},{"@xml:lang":"sl","#text":"kantorus"},{"@xml:lang":"sl","#text":"kaos"},{"@xml:lang":"sl","#text":"kaotična lastna stanja"},{"@xml:lang":"sl","#text":"kvantni biljard"},{"@xml:lang":"sl","#text":"kvantni kaos"},{"@xml:lang":"sl","#text":"lepljivost"},{"@xml:lang":"en","#text":"level repulsion"},{"@xml:lang":"en","#text":"level spacing distribution"},{"@xml:lang":"en","#text":"localization"},{"@xml:lang":"sl","#text":"lokalizacija"},{"@xml:lang":"sl","#text":"mešani fazni prostor"},{"@xml:lang":"en","#text":"mixed phase space"},{"@xml:lang":"sl","#text":"odboj med nivoji"},{"@xml:lang":"sl","#text":"porazdelitve razmika med nivoji"},{"@xml:lang":"en","#text":"quantum billiard"},{"@xml:lang":"en","#text":"quantum chaos"},{"@xml:lang":"en","#text":"stickiness"},{"@xml:lang":"sl","#text":"transport"}],"dc:title":{"@xml:lang":"sl","#text":"Transport and localization in classical and quantum billiards| doctoral dissertation|"},"dc:description":[{"@xml:lang":"sl","#text":"In this thesis the classical and quantum dynamics in billiard systems are considered. Extensive numerical studies of the classical transport properties in several examples of billiard families including the ergodic Bunimovich stadium and cut-circle billiards and the mixed-type Robnik and lemon billiards are performed. The analysis of the transport is based on the random model of diffusion which assumes that due the strongly chaotic dynamics the motion of the orbit on the discretized phase space is temporally uncorrelated. The cause of the deviations from the random model dynamics is traced to dynamical trapping due to stickiness. A novel approach to locally quantifying stickiness based on the statistics of the recurrence times is presented and applied to distinguish between exponential decays of recurrence times and other types of decays. This enables the identification of sticky areas in the chaotic components. Detailed maps of their structure for a wide range of parameter values, mapping the evolution of the mixed-phase spaces and revealing some particularly interesting special examples are presented. The recurrence time distributions in sticky areas are found to be well described by a mixture of exponential decays. The transport of particle ensembles in the momentum space of classical billiards is described by using an inhomogeneous diffusion model and the classical transport times are determined. The classical transport times are vital for the analysis of the localization of chaotic eigenstates in quantum billiards. The control parameter that describes the the degree of localization of the chaotic quantum eigenstates is the ratio between the Heisenberg time (Planck's constant divided by the mean level spacing) and the classical transport time. Extensive numerical calculations of the high-lying spectra and eigenstates of the stadium, Robnik and lemon quantum billiards are performed. The spectral statistics are analysed in terms of the standard methods of quantum chaos. The level repulsion exponent of localized eigenstates is found to be a rational function of the control parameter. The degree of localization is determined with respect to localization measures based on the Poincaré-Husimi representation of the eigenstates. The mean localization measure is found to be a rational function of the control parameter and linearly related to the level repulsion exponent. The distributions of the localization measures are analysed and found to be of a universal shape well described by a two parameter empirical distribution in billiards with no apparent stickiness. The nonuniversal system specific features of localization measure distributions are related to the presence of sticky areas in the phase spaces of classical billiards with specific examples shown"},{"@xml:lang":"sl","#text":"V disertaciji je obravnavana klasična in kvantna dinamika v biljardnih sistemih. Narejena je obsežna numerična raziskava klasičnih transportnih lastnosti več družin biljardov vključujoč ergodične Bunimovičeve stadione in odsekane kroge ter Robnikove in limonaste biljarde mešanega tipa. Analiza transporta sloni na naključnem modelu difuzije, ki predpostavlja, da je zaradi močno kaotične dinamike, gibanje orbite v diskretiziranem faznem prostoru časovno nekorelirano. Vzrok odstopanj od naključnega modela je dinamično ujetje orbit v lepljiva območja. Predstavljen je nov način kvantifikacije lokalne lepljivosti temelječ na statistiki časov vračanja, ki omogoča razločevanje med eksponentnim pojemanjem časov vračanja in drugim oblikam pojemanja. To omogoča identifikacijo lepljivih območji znotraj kaotičnih komponent. Predstavljeni so natančni portreti kaotičnih komponent v širokem območju parametrov, ki opisujejo razvoj mešanih faznih prostorov in omogočijo najdbo zanimivih posebnih primerov. Porazdelitve časov vračanja znotraj lepljivih območji so opisane z mešanico eksponentnih distribucij. Transport v impulznem prostoru klasičnih biljardov je opisan s pomočjo modela nehomogene difuzije in določeni klasični transportni časi. Klasični transportni časi so ključni za analizo lokalizacije kaotičnih lastnih stanj kvantnih biljardov. Kontrolni parameter, ki določa stopnjo lokalizacije kaotičnih lastnih stanj, je razmerje med Heisenbergovim časom (Plankova konstanta deljena z povprečnim razmikom med nivoji) in klasičnim transportnim časom. Opravljeni so obsežni numerični izračuni visoko ležečih spektrov in lastnih stanj stadionskih, Robnikovih in limonastih kvantnih biljardov. Statistične lastnosti spektrov so analizirane s standardnimi metodami kvantnega kaosa. Ugotovljeno je, da je eksponent odboja med nivoji lokaliziranih lastnih stanj racionalna funkcija kontrolnega parametra. Stopnja lokalizacije je določena z mer lokalizacij na podlagi Poincaré-Husimijeve reprezentacije lastnih stanj. Ugotovljeno je, da je povprečna mera lokalizacije racionalna funkcija kontrolnega parametra in linearno povezana z eksponentom odboja med nivoji. Analizirane so porazdelitve mer lokalizacij in opaženo je, da so te ob odsotnosti lepljivosti univerzalne oblike dobro opisane z empirično dvoparametrično distribucijo. Neuniverzalne lastnosti porazdelitev mer lokalizacij so povezane z lepljivimi območji v faznih prostorih klasičnih biljardov"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"visokošolska dela"},{"@xml:lang":"en","#text":"theses and dissertations"},{"@rdf:resource":"http://www.wikidata.org/entity/Q1266946"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:DOC-4ZWPID4D","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-4ZWPID4D"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-4ZWPID4D/e457-535f993ee017a--5f440b6cf70a0-b0/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza v Mariboru, Fakulteta za naravoslovje in matematiko"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-4ZWPID4D/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-4ZWPID4D"}}}}