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Spectral Statistics, Hydrodynamics and Quantum Chaos
Spectral Statistics, Hydrodynamics and Quantum Chaos
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152025
- ISBN
- 9798384423829
- DDC
- 530
- 저자명
- Winer, Michael.
- 서명/저자
- Spectral Statistics, Hydrodynamics and Quantum Chaos
- 발행사항
- [Sl] : University of Maryland, College Park, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 306 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Swingle, Brian;Galitski, Victor.
- 학위논문주기
- Thesis (Ph.D.)--University of Maryland, College Park, 2024.
- 초록/해제
- 요약One of the central problems in many-body physics, both classical and quantum, is the relations between different notions of chaos. Ergodicity, mixing, operator growth, the eigenstate thermalization hypothesis, and spectral chaos are defined in terms of completely different objects in different contexts, don't necessarily co-occur, but still seem to be manifestations of closely related phenomena.In this dissertation, we study the relation between two notions of chaos: thermalization and spectral chaos. We define a quantity called the Total Return Probability (TRP) which measures how a system forgets its initial state after time T, and show that it is closely connected to the Spectral Form Factor (SFF), a measure of chaos deriving from the energy level spectrum of a quantum system.The main thrust of this work concerns hydrodynamic systems- systems where locality prevents charge or energy from spreading quickly, this putting a throttle on thermalization. We show that the detailed spacings of energy levels closely capture the dynamics of these locally conserved charges.We also study spin glasses, a phase of matter where the obstacle to thermalization comes not from locality but from the presence of too many neighbors. Changing one region requires changing nearby regions which requires changing nearby-to-nearby regions, until only catastrophic realignments of the whole system can fully explore phase space. In spin glasses we find our clearest analytic link between thermalization and spectral statistics. We analytically calculate the spectral form factor in the limit of large system size and show it is equal to the TRP.Finally, in the conclusion, we discuss some ideas for the future of both the SFF and the TRP.
- 일반주제명
- Physics
- 일반주제명
- Nuclear physics
- 일반주제명
- Statistical physics
- 일반주제명
- Applied mathematics
- 일반주제명
- Quantum physics
- 일반주제명
- Energy
- 키워드
- Thermalization
- 키워드
- Quantum system
- 기타저자
- University of Maryland, College Park Physics
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211152025
■006m o d
■007cr#unu||||||||
■020 ▼a9798384423829
■035 ▼a(MiAaPQ)AAI31333149
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aWiner, Michael.▼0(orcid)0000-0003-2222-8404
■24510▼aSpectral Statistics, Hydrodynamics and Quantum Chaos
■260 ▼a[Sl]▼bUniversity of Maryland, College Park▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a306 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Swingle, Brian;Galitski, Victor.
■5021 ▼aThesis (Ph.D.)--University of Maryland, College Park, 2024.
■520 ▼aOne of the central problems in many-body physics, both classical and quantum, is the relations between different notions of chaos. Ergodicity, mixing, operator growth, the eigenstate thermalization hypothesis, and spectral chaos are defined in terms of completely different objects in different contexts, don't necessarily co-occur, but still seem to be manifestations of closely related phenomena.In this dissertation, we study the relation between two notions of chaos: thermalization and spectral chaos. We define a quantity called the Total Return Probability (TRP) which measures how a system forgets its initial state after time T, and show that it is closely connected to the Spectral Form Factor (SFF), a measure of chaos deriving from the energy level spectrum of a quantum system.The main thrust of this work concerns hydrodynamic systems- systems where locality prevents charge or energy from spreading quickly, this putting a throttle on thermalization. We show that the detailed spacings of energy levels closely capture the dynamics of these locally conserved charges.We also study spin glasses, a phase of matter where the obstacle to thermalization comes not from locality but from the presence of too many neighbors. Changing one region requires changing nearby regions which requires changing nearby-to-nearby regions, until only catastrophic realignments of the whole system can fully explore phase space. In spin glasses we find our clearest analytic link between thermalization and spectral statistics. We analytically calculate the spectral form factor in the limit of large system size and show it is equal to the TRP.Finally, in the conclusion, we discuss some ideas for the future of both the SFF and the TRP.
■590 ▼aSchool code: 0117.
■650 4▼aPhysics
■650 4▼aNuclear physics
■650 4▼aStatistical physics
■650 4▼aApplied mathematics
■650 4▼aQuantum physics
■650 4▼aEnergy
■653 ▼aSpectral statistics
■653 ▼aTotal Return Probability
■653 ▼aSpectral Form Factor
■653 ▼aThermalization
■653 ▼aQuantum system
■690 ▼a0605
■690 ▼a0599
■690 ▼a0756
■690 ▼a0217
■690 ▼a0364
■690 ▼a0791
■71020▼aUniversity of Maryland, College Park▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0117
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17162553▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
