Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 34 for “"non-Hermitian"”.
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Non-Hermitian Hamiltonians in Field Theory
This thesis is centred around the role of non-Hermitian Hamiltonians in Physics both at the quantum and classical levels. In our investigations of two-level models we demonstrate [1] the phenomenon of fast transitions developed in the PT -symmetric quantum brachistochrone problem may in fact be …
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Detectivity vs. Sensitivity: Non-Hermitian Metasurface Sensor
… plasmonic BIC sensor. Moreover, we induce a non-Hermitian system to control the Q factor by changing the non-radiative loss with little effect on the near field. Using this non-Hermitian structure we can break the trade-off effect
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Non-Hermitian topological states in photonic systems
In this thesis I explore non-Hermitian topological photonics with the aim of describing new phenomena which question our understanding of how far the current classification of topological states extends. This work invigorates the search for topological states in photonic systems with the hope of …
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Non-Hermitian Whispering Gallery Mode Optical Microresonators and Their Applications
… have proven to be an excellent platform to study non-Hermitian physics, due to the ease with which non-Hermiticity can be controlled via gain-loss distribution and modal coupling. Non-Hermitian physics studies open systems such as WGM microresonators with loss and/or gain, described by …
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Non-Hermitian aspects of coherently coupled vertical cavity laser arrays
… in the array, the coupled laser system is non-Hermitian in analogy with non-Hermitian quantum mechanics. The experimentally observed optical mode tuning and beam steering are inherently connected to the non-Hermiticity of the system. Theoretical investigation of the mode tuning mechanism is …
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Non-Hermitian Topology and Directional Amplification in Driven-Dissipative Cavity Arrays
… we first develop a unifying framework based on non-Hermitian topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the …
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The taiji and infinity-loop microresonators: examples of non-hermitian photonic systems
… (MRs) built by passive (no gain) and non-magnetic materials and characterized by both Hermitian and non-Hermitian Hamiltonians. In particular, I have studied three different microresonators: a typical Microring Resonator (MR), a Taiji Microresonator (TJMR), which consists of a …
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Disorder-driven phase transitions in weak, boundary-obstructed, and non-Hermitian topological insulators
… to compute weak, boundary-obstructed, and non-Hermitian topological invariants, establish their stability at weak and strong disorder, and connect these disordered topological invariants to physical signatures. The remainder of the thesis contains an eclectic mix of other work that broadly …
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Crystalline topological phases: Bulk-boundary correspondence, geometric response, entanglement, and non-Hermitian skin effect
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms
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A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Non-Hermitian Perturbation Theory for the Electronic Decay of Excited and Ionized Molecules and Identification of the Electronic Decay Processes in the Auger Decay of Core-Ionized Xenon Fluorides
… in two ways with Wigner-Weisskopf theory and non-degenerate non-Hermitian Rayleigh-Schrödinger perturbation theory employing complex absorbing potentials. A general non-Hermitian multireference perturbation theory is devised, and tested on a model problem, to improve on the accuracy of the two …
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Generalizing smoothed aggregation-based algebraic multigrid
… is that classic SA is only formally defined for Hermitian positive definite problems. For non-Hermitian operators, the operator-induced energy-norm does not exist, which impacts the complementary relationship between relaxation and interpolation. This requires a redesign of SA, such that …
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Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble
… is concerned with eigenvalue statistics of non-Hermitian random matrices in the symplectic symmetry class. It contributes to the questions of how to compute the microscopic scaling limit and whether it is universal.
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Orbital Angular Momentum Microlasers: From The First Demonstration To Ultrafast Tunability
… from instability. In this work, we bring the non-Hermitian physics into the regime of nanophotonics to explore feasible designs of OAM microlasers. Non-Hermitian photonics based on parity-time symmetry successfully expands the design freedom from real material permittivity to a complete …
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Sensitivity analysis and approximation methods for general eigenvalue problems
Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying …
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Parity-time and supersymmetry in optics
… PT symmetry can lead to entirely real spectra in non-Hermitian systems. In optics, PT-symmetric structures involving balanced regions of gain and loss exhibit intriguing properties which are otherwise unattainable in traditional Hermitian systems. We show that selective PT symmetry breaking offers …
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Breaking the Cycle: the Rise and Fall of Conversion Cycle Limited Three-Wave Mixing
… We then show that SHG can replace loss to induce non-Hermitian features such as regions of broken and unbroken PT-symmetric phase demarcated by an exceptional point in three-wave mixing nonlinear interactions. This enables a new paradigm where the behavior associated with the PT-symmetric phase of …
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The structure of hadrons and other potential phases of QCD
… for studying QCD phase structure inspired by non-Hermitian physics, and probe the possibility of new exotic phases near the QCD phase transition.
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Physics and applications of magnetic interactions in topological insulators
… Hamiltonian describing the heterostructure is non-Hermitian with broadening that can obscure the mass gap. We calculate the Hall conductivity of the non-Hermitian effective Hamiltonian and show that it is no longer quantized due to the finite lifetime of quasiparticle states. When the …
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A Riemann-Hilbert Approach to the Kissing Polynomials
… The Kissing Polynomials are a family of non-Hermitian orthogonal polynomials, which are orthogonal with respect to the complex weight function $\exp(i\omega z)$ over the interval $[-1,1]$, where $\omega>0$. Although they have already been used to derive complex quadrature rules, there …
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