Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Quantization of causal diamonds in (2+1)-gravity(2024) Andrade e Silva, Rodrigo; Jacobson, Theodore A; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We develop the non-perturbative reduced phase space quantization of causal diamondsin (2+1)-dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with fixed boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of Diff+(S1)/PSL(2,R). Classically, the states correspond to causal diamonds embedded in AdS3 (or Mink3 if Λ = 0), with fixed corner length, and whose Cauchy surfaces have the topology of a disc. Because the phase space does not have a natural linear structure, a generalization of the standard canonical (coordinate) quantization is required. As the configuration space is a homogeneous space for the Diff+(S1) group, we apply Isham’s group-theoretic quantization scheme. We propose a quantization based on (projective) unitary irreducible representations of the BMS3 group. We find a class of suitable quantum theories labelled by a choice of a coadjoint orbit of the Virasoro group and an irreducible unitary representation of the corresponding little group. The most natural choice, justified by a Casimir matching principle, corresponds to a Hilbert space realized by wavefunctions on Diff+(S1)/PSL(2,R) valued in some unitary irreducible representation of SL(2,R). A surprising result is that the twist of the diamond corner loop is quantized in terms of the ratio of the Planck length to the corner perimeter.Item QUANTUM INFORMATION SCRAMBLING AND PROTECTION IN MANY-BODY SYSTEM(2023) Cheng, Gong; Swingle, Brian; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This work is focused on two main topics in quantum information theory: the scramblingof quantum information and the preservation of quantum information in many-body system. In terms of information scrambling, the main focus of this work is on the Out-of-time-order corre- lator (OTOC), which is used to probe the dynamics of quantum information as it spreads from localized degrees of freedom to those that are distributed throughout the system. On the other hand, the aim of the study of quantum information protection is to construct a system that can preserve quantum information for a sufficiently long time when coupled to a finite-temperature environment. The many-body systems analyzed in this work belong or are related to a class of stronglyinteracting systems known as holographic quantum models. The standard examples in this class are believed to be equivalent to gravitational theory in spacetime that is one-dimensional higher than that the quantum model lives in. Therefore, the results may also provide insights into topics in quantum gravity. The first part of the thesis explores the scrambling dynamics close to a critical point whereconformal symmetry emerges. The second case deals with the scrambling dynamics with con- servation law constraints in holographic quantum field theory. The result also clarifies how con- served charges influence the dynamics in the bulk dual. The third part of the thesis presents a matrix model with a large matrix rank N that belongs to the class of approximate quantum error correction codes. We investigate its thermal stability by coupling it to a thermal bath and demonstrate that it behaves as a self-correcting quantum memory at finite temperature. The coherent memory time scales polynomially with the system size N.Item Thermodynamics of quantum gravitational ensembles(2023) Banihashemi, Batoul; Jacobson, Theodore A; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The discovery of black hole thermodynamics and its extension to cosmological horizonsdemonstrated a deep connection between thermodynamics and the nature of spacetime as a quantum system. It is then of great importance to properly understand the statistical mechanics of gravitational systems with horizon from first principles. While employing a partition function and the gravitational “Euclidean path integral” produces the expected physical result for entropy, a number of fundamental questions about the underlying analysis persist. This dissertation sharpens and resolves some puzzles regarding statistical mechanics of gravitational ensembles and the gravitational path integral, with a focus on cosmological horizons and de Sitter space. The main questions addressed in this dissertation are: how is the entropy of de Sitterspace derived in absence of any boundary on which the statistical ensemble can be properly defined? What is the correct interpretation of the first law of de Sitter horizon, according to which the horizon area shrinks upon adding matter in de Sitter static patch? And finally, can entropy of horizon-bounded systems be derived from a Hamiltonian approach and phase space path integral, without the trickery of the gravitational Euclidean path integral? The first two questions are answered by introducing an artificial boundary in the system on which a gravitational ensemble can be properly defined. Once the ensemble is defined, the semiclassical approximation of the statistical partition function yields the entropy, and the interpretation of the de Sitter first law becomes clear by identifying the system energy as the quasilocal energy defined on the boundary. To tackle the last question, the real-time phase space path integral is utilised in the Hamiltonian formulation which maintains connection to the Hilbert space of the system, and it is found that the horizon entropy is derived from a nearly Lorentzian configuration.