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Inverse and Forward Problems of Statistical Mechanics: Classical and Quantum Systems
Inverse and Forward Problems of Statistical Mechanics: Classical and Quantum Systems
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152822
- ISBN
- 9798384463771
- DDC
- 540
- 저자명
- Wang, Haina.
- 서명/저자
- Inverse and Forward Problems of Statistical Mechanics: Classical and Quantum Systems
- 발행사항
- [Sl] : Princeton University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 416 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-04, Section: B.
- 주기사항
- Advisor: Torquato, Salvatore.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2024.
- 초록/해제
- 요약Statistical mechanics connects the microscopic properties of systems of interacting entities (e.g., particles and spins) to their macroscopic properties. The "forward" approach of statistical mechanics aims to determine thermodynamics and kinetic features of a system with known interactions. In the "inverse" approach, one attempts to determine the interactions or configurations that realize a desired "target" microstructure descriptor.For the inverse problems, we first introduce sensitivity metrics that measure the variation in pair statistics associated with any given variation in the corresponding pair potentials. We identify illustrative cases in which distinctly different potential functions give very similar pair statistics, demonstrating the need for more precise inverse techniques. Motivated by this and other challenges, we introduce a new methodology that yields much more precise interactions than previous procedures and is able to treat challenging nonequilibrium pair statistics as well as exotic "hyperuniform" states. This methodology enables one to study nontrivial attributes of systems equilibrated under the optimized effective potentials. We also use the methodology to tackle the realizability problem of pair statistics and identify precise density ranges on which the unit-step function g2 is realizable. Furthermore, we determine classical states that mimic pair statistics of quantum fermi gases, which could facilitate quantum-mechanical simulations. Finally, we study the structural degeneracy problem of whether one can "hear the shape of a crystal", i.e., whether a crystal is uniquely determined, up to isometry, by its radial distribution function. The identification of isospectral crystals enables one to study the degeneracy of the ground-state manifold.
- 일반주제명
- Chemistry
- 일반주제명
- Statistics
- 일반주제명
- Mechanics
- 기타저자
- Princeton University Chemistry
- 기본자료저록
- Dissertations Abstracts International. 86-04B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798384463771
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■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a540
■1001 ▼aWang, Haina.▼0(orcid)0000-0001-7811-4583
■24510▼aInverse and Forward Problems of Statistical Mechanics: Classical and Quantum Systems
■260 ▼a[Sl]▼bPrinceton University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a416 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-04, Section: B.
■500 ▼aAdvisor: Torquato, Salvatore.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2024.
■520 ▼aStatistical mechanics connects the microscopic properties of systems of interacting entities (e.g., particles and spins) to their macroscopic properties. The "forward" approach of statistical mechanics aims to determine thermodynamics and kinetic features of a system with known interactions. In the "inverse" approach, one attempts to determine the interactions or configurations that realize a desired "target" microstructure descriptor.For the inverse problems, we first introduce sensitivity metrics that measure the variation in pair statistics associated with any given variation in the corresponding pair potentials. We identify illustrative cases in which distinctly different potential functions give very similar pair statistics, demonstrating the need for more precise inverse techniques. Motivated by this and other challenges, we introduce a new methodology that yields much more precise interactions than previous procedures and is able to treat challenging nonequilibrium pair statistics as well as exotic "hyperuniform" states. This methodology enables one to study nontrivial attributes of systems equilibrated under the optimized effective potentials. We also use the methodology to tackle the realizability problem of pair statistics and identify precise density ranges on which the unit-step function g2 is realizable. Furthermore, we determine classical states that mimic pair statistics of quantum fermi gases, which could facilitate quantum-mechanical simulations. Finally, we study the structural degeneracy problem of whether one can "hear the shape of a crystal", i.e., whether a crystal is uniquely determined, up to isometry, by its radial distribution function. The identification of isospectral crystals enables one to study the degeneracy of the ground-state manifold.
■590 ▼aSchool code: 0181.
■650 4▼aChemistry
■650 4▼aStatistics
■650 4▼aMechanics
■653 ▼aStatistical mechanics
■653 ▼aQuantum fermi gases
■653 ▼aQuantum-mechanical simulations
■690 ▼a0485
■690 ▼a0346
■690 ▼a0463
■71020▼aPrinceton University▼bChemistry.
■7730 ▼tDissertations Abstracts International▼g86-04B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17164019▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
