자료유형  

 학위논문

Control Number  

0017164015

International Standard Book Number  

9798342719285

Dewey Decimal Classification Number  

530

Main Entry-Personal Name  

Hulsey, George.

Publication, Distribution, etc. (Imprint  

[S.l.] : University of California, Santa Barbara., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

191 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-05, Section: B.

General Note  

Advisor: Berenstein, David.

Dissertation Note  

Thesis (Ph.D.)--University of California, Santa Barbara, 2024.

Summary, Etc.  

요약The bootstrap program in theoretical physics arose out of attempts to determine the structure of conformal field theories in a constraint-oriented, non-Hamiltonian fashion. In recent years, bootstrap methods have seen a strong resurgence in the numerical analysis of quantum mechanical systems without conformal symmetry. In this thesis, we develop the theory of the bootstrap approach to one-dimensional quantum systems. We show how Schrodinger quantum mechanics can be numerically solved by the method and develop the algebraic theory required to adapt the approach to domains with boundary and to scattering problems. We develop and implement efficient semidefinite programming algorithms to rigorously and numerically determine the energy spectra of confining polynomial potentials in one dimension. We also address the problem of spin chains and demonstrate how bootstrap methods can be used to regress conformal data from numerical approximations of the spin correlation functions. Broadly, this work lays a foundation for the theory and application of bootstrap methods to a wide variety of quantum mechanical systems, and also provides a mathematical background of the method and a thorough review of related work in high-energy theory, condensed matter physics, and mathematical optimization. Future directions for research both in wave mechanics and interacting spin systems are proposed.

Subject Added Entry-Topical Term  

Physics.

Subject Added Entry-Topical Term  

Quantum physics.

Subject Added Entry-Topical Term  

Mechanics.

Subject Added Entry-Topical Term  

Theoretical physics.

Index Term-Uncontrolled  

Bootstrap methods

Index Term-Uncontrolled  

Convex optimization

Index Term-Uncontrolled  

Quantum mechanics

Index Term-Uncontrolled  

Semidefinite programming algorithms

Added Entry-Corporate Name  

University of California, Santa Barbara Physics

Host Item Entry  

Dissertations Abstracts International. 86-05B.

Electronic Location and Access  

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Control Number  

joongbu:654419