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Stability of Quantum Many-Body Systems
Stability of Quantum Many-Body Systems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103029
- ISBN
- 9798314899700
- DDC
- 530.1
- 저자명
- Yin, Chao.
- 서명/저자
- Stability of Quantum Many-Body Systems
- 발행사항
- [Sl] : University of Colorado at Boulder, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 279 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-11, Section: B.
- 주기사항
- Advisor: Lucas, Andrew.
- 학위논문주기
- Thesis (Ph.D.)--University of Colorado at Boulder, 2025.
- 초록/해제
- 요약In quantum many-body systems subjected to generic perturbations, eigenstates are typically fragile and prone to strong mixing, leading to rapid thermalization in dynamics to an equilibrium state described by statistical mechanics. However, there exist robust counterexamples that defy this typical expectation, exhibiting novel non-equilibrium phenomena and offering potential applications in (quantum) information processing. This dissertation explores such systems and establishes their stability against perturbations with mathematical rigor.First, by generalizing the exponentially slow tunneling effect in single-particle quantum mechanics, we develop a theory of metastability in quantum many-body systems, demonstrating their nonperturbatively long lifetimes. As a canonical application, we provide the first general and tight bounds on the slow decay of false vacua.Second, it is known that ground states in finite spatial dimensions can resist arbitrary local perturbations through topologically ordered phases of matter. We extend this notion of stability to quantum error-correcting codes in infinite dimensions, specifically quantum low-density parity-check (LDPC) codes. These codes are of significant interest due to their promise of lower fault-tolerance overhead compared to finite-dimensional codes.Lastly, we analyze classical counterparts of LDPC codes and prove that their eigenstates remain localized in the many-body Hilbert space under generic perturbations. This finding presents the first unambiguous example of a robust violation of the eigenstate thermalization hypothesis. To achieve these results, we introduce advanced techniques to control operator locality, leveraging and generalizing methods such as Lieb-Robinson bounds, cluster expansions, and Schrieffer-Wolff transformations. These tools not only underpin our specific findings but may also prove valuable for broader challenges in mathematical physics of quantum many-body systems.
- 일반주제명
- Theoretical physics
- 일반주제명
- Quantum physics
- 일반주제명
- Condensed matter physics
- 키워드
- False vacuum
- 키워드
- Metastability
- 기타저자
- University of Colorado at Boulder Physics
- 기본자료저록
- Dissertations Abstracts International. 86-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798314899700
■035 ▼a(MiAaPQ)AAI31845664
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530.1
■1001 ▼aYin, Chao.▼0(orcid)0000-0003-3379-310X
■24510▼aStability of Quantum Many-Body Systems
■260 ▼a[Sl]▼bUniversity of Colorado at Boulder▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a279 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-11, Section: B.
■500 ▼aAdvisor: Lucas, Andrew.
■5021 ▼aThesis (Ph.D.)--University of Colorado at Boulder, 2025.
■520 ▼aIn quantum many-body systems subjected to generic perturbations, eigenstates are typically fragile and prone to strong mixing, leading to rapid thermalization in dynamics to an equilibrium state described by statistical mechanics. However, there exist robust counterexamples that defy this typical expectation, exhibiting novel non-equilibrium phenomena and offering potential applications in (quantum) information processing. This dissertation explores such systems and establishes their stability against perturbations with mathematical rigor.First, by generalizing the exponentially slow tunneling effect in single-particle quantum mechanics, we develop a theory of metastability in quantum many-body systems, demonstrating their nonperturbatively long lifetimes. As a canonical application, we provide the first general and tight bounds on the slow decay of false vacua.Second, it is known that ground states in finite spatial dimensions can resist arbitrary local perturbations through topologically ordered phases of matter. We extend this notion of stability to quantum error-correcting codes in infinite dimensions, specifically quantum low-density parity-check (LDPC) codes. These codes are of significant interest due to their promise of lower fault-tolerance overhead compared to finite-dimensional codes.Lastly, we analyze classical counterparts of LDPC codes and prove that their eigenstates remain localized in the many-body Hilbert space under generic perturbations. This finding presents the first unambiguous example of a robust violation of the eigenstate thermalization hypothesis. To achieve these results, we introduce advanced techniques to control operator locality, leveraging and generalizing methods such as Lieb-Robinson bounds, cluster expansions, and Schrieffer-Wolff transformations. These tools not only underpin our specific findings but may also prove valuable for broader challenges in mathematical physics of quantum many-body systems.
■590 ▼aSchool code: 0051.
■650 4▼aTheoretical physics
■650 4▼aQuantum physics
■650 4▼aCondensed matter physics
■653 ▼aFalse vacuum
■653 ▼aLow-density parity-check codes
■653 ▼aMany-body localization
■653 ▼aMetastability
■653 ▼aQuantum many-body systems
■653 ▼aTopological order
■690 ▼a0753
■690 ▼a0599
■690 ▼a0611
■71020▼aUniversity of Colorado at Boulder▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g86-11B.
■790 ▼a0051
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356753▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
