Material Type  

 학위논문

 

0017164019

Date and Time of Latest Transaction  

20250211152822

ISBN  

9798384463771

DDC  

540

Author  

Wang, Haina.

Title/Author  

Inverse and Forward Problems of Statistical Mechanics: Classical and Quantum Systems.

Publish Info  

[S.l.] : Princeton University., 2024

Publish Info  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Material Info  

416 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-04, Section: B.

General Note  

Advisor: Torquato, Salvatore.

학위논문주기  

Thesis (Ph.D.)--Princeton University, 2024.

Abstracts/Etc  

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.

Subject Added Entry-Topical Term  

Chemistry.

Subject Added Entry-Topical Term  

Statistics.

Subject Added Entry-Topical Term  

Mechanics.

Index Term-Uncontrolled  

Statistical mechanics

Index Term-Uncontrolled  

Quantum fermi gases

Index Term-Uncontrolled  

Quantum-mechanical simulations

Added Entry-Corporate Name  

Princeton University Chemistry

Host Item Entry  

Dissertations Abstracts International. 86-04B.

Electronic Location and Access  

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Control Number  

joongbu:654114