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Prehod med enodelčnim in mnogodelčnim kvantnim kaosom v SYK modelu
ID Pintar, Rok (Author), ID Vidmar, Lev (Mentor) More about this mentor... This link opens in a new window

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Abstract
Raziskovanje kvantnega kaosa in njegovega prehoda v mnogodelčni režim postaja vse bolj poglobljeno področje. V tem magistrskem delu se posvečamo prehodu iz enodelčnega v mnogodelčni kvantni kaos preko regulacije meddelčnih interakcij na primeru Sachdeva-Ye-Kitaeva modela. Ta ima ključno vlogo pri analizi kvantnega kaosa, termalizacije in drugih področjih kvantne fizike. Preučujemo odvisnost moči interakcije v okviru različnih indikatorjev mnogodelčnega kaosa, ki so pogosto uporabljeni v interakcijski kvantni mehaniki. Med njimi so statistika razmikov sosednjih energijskih nivojev, entropija prepletenosti, spektralni oblikovni faktor ter informacijska entropija. Za dosegljive velikosti sistema ti indikatorji nakazujejo gladek prehod iz enodelčnega v mnogodelčni kaos ter kažejo na eksponentno odvisnost kritične vrednosti interakcije glede na velikost sistema. Pri analizi povezanega spektralnega oblikovnega faktorja preučujemo tudi univerzalno področje \textit{prečke} za tako mnogodelčne kot enodelčne sisteme. Za mnogodelčni Thoulessov čas pridobljen iz povezanega spektralnega oblikovnega faktorja opazimo skaliranje $t_{Th}\propto \lambda^{-2.4}$. Na podlagi teh rezultatov smo zaključili, da je mnogodelčni kaos v termodinamski limiti prisoten pri vsaki neničelni interakciji. Obravnavani model se v limiti brez interakcij poenostavi iz mnogodelčnega problema v enodelčnega, kar zmanjša velikost Hilbertovega prostora. Brezinterakcijski model omogoča analizo veliko večjih fizikalnih sistemov preko spektralnega oblikovnega faktorja, ki ga zapišemo z enodelčnimi energijami.

Language:Slovenian
Keywords:kvantni kaos, mnogodelčni kaos, enodelčni kaos, termalizacija kvantnih sistemov, ergodična dinamika, neergodična dinamika, indikatorji kaosa, SYK model, statistika energijskega spektra, struktura lastnih stanj, teorija naključnih matrik
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2023
PID:20.500.12556/RUL-150829 This link opens in a new window
COBISS.SI-ID:164445187 This link opens in a new window
Publication date in RUL:24.09.2023
Views:469
Downloads:128
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Secondary language

Language:English
Title:Transition between one-body and many-body quantum chaos in SYK model
Abstract:
Exploring quantum chaos and its transition into the many-body regime is becoming an increasingly profound area of study. In this thesis, we focus on the transition from single-particle to many-body quantum chaos through the control of interaction strength between particles in the Sachdev-Ye-Kitaev model. This model plays a crucial role in analyzing quantum chaos, thermalization, and other areas of quantum physics. We investigate the dependence of interaction strength through various indicators of many-body chaos commonly utilized in interacting quantum mechanics. Among these are the level spacing ratio, entanglement entropy, spectral form factor, and informational entropy. For accessible system sizes, these indicators suggest a smooth transition from single-particle to many-body chaos, indicating an exponential dependence of the critical interaction value on system size. During the analysis of the connected spectral form factor, we examine the universal \textit{ramp} region for both many-body and single-particle systems. For the many-body Thouless time obtained from the connected spectral form factor, we observe scaling as $t_{Th}\propto \lambda^{-2.4}$. Based on these results, we conclude that many-body chaos emerges in the thermodynamic limit for any nonzero interaction. In the limit of no interactions, the model simplifies from a many-body problem to a single-particle one, reducing the size of the Hilbert space. The non-interacting model enables the analysis of much larger physical systems through the spectral form factor, that we expressed in terms of single-particle energies.

Keywords:quantum chaos, many-body chaos, one-particle chaos, thermalization of quantum systems, ergodic dynamics, non-ergodic dynamics, chaos indicators, SYK model, energy spectrum statistics, structure of eigenstates, random matrix theory

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