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Kvantnokaotični enodelčni sistemi na mreži brez prisotnosti nereda
Ulčakar, Iris (Author), Vidmar, Lev (Mentor) More about this mentor... This link opens in a new window

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Abstract
V magistrskem delu raziskujemo, ali je enodelčni sistem fermionov na mreži v odsotnosti nereda lahko kvantnokaotičen. Obravnavanje kvantnega kaosa na mreži je namreč v raziskavah ponavadi omejeno na interagirajoče mnogodelčne sisteme in enodelčne sisteme z neredom. Ogledamo si, ali neregularne meje dvodimenzionalne mreže zlomijo kvantno integrabilnost sicer trivialnega translacijsko invariantnegamodela prostih fermionov na kvadratni mreži. V teoretičnem uvodu so opisane mere kvantnega kaosa: ujemanje spektralne statistike z napovedmi teorije naključnih matrik, oblika povprečne von Neumannove in 2. Rényijeve prepletenostne entropije mnogodelčnih stanj ter ujemanje oblike matričnih elementov preprostih opazljivk z napovedmi hipoteze termalizacije lastnih stanj. Definirani so diskretni biljardni sistemi - enodelčni sistemi fermionov na dvodimenzionalni mreži z mejo - in opisane njihove splošne lastnosti. Uvedemo tri diskretne biljarde, ki so v zvezni limiti tako klasično- kot kvantnokaotični, in za njih preverimo predstavljene mere za kvantnikaos.

Language:Slovenian
Keywords:kvantni kaos, enodelčni sistemi na mreži, kvantni diskretni biljardi, prepletenostna entropija, statistika energijskih nivojev, hipoteza o termalizaciji lastnih stanj
Work type:Master's thesis/paper (mb22)
Tipology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2021
COBISS.SI-ID:76342275 This link opens in a new window
Views:59
Downloads:6
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Secondary language

Language:English
Title:Quantum chaotic single-particle systems on a lattice without disorder
Abstract:
In this thesis we aim to show that single-body fermionic systems on a lattice can exhibit quantum chaotic behaviour. Up until now, quantum chaos on a lattice was usually studied only for interacting many-body systems and single-body systems with disorder. We investigate whether irregular boundaries of a two-dimensional lattice break the integrability of the translationally invariant free fermion model on a square lattice. In the first part of the thesis we describe the measures of quantum chaos: the agreement of eigenstate statistics with random matrix predictions, the form of the average von Neumann and 2. Rényi entanglement entropy of many-body Hamiltonian eigenstates, and the agreement of the form of the matrix elements of local observables with the eigenstate thermalization hypothesis ansatz. We define discrete billiard systems - single-body fermionic systems on a two-dimensional lattice with a boundary - and describe their generic properties. I introduce three discrete billiards, which are classically chaotic as well as quantum chaotic in their continuous limit, and test the measures of quantum chaos for them.

Keywords:quantum chaos, single-body systems on a lattice, quantum discrete billiards, entanglement entropy, energy spectrum statistics, eigenstate thermalization hypothesis

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