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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 27 for “"resolvent"”.
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Liouville resolvent methods applied to highly correlated systems
… on the application of the Liouville Operator Resolvent technique (LRM) to two hamiltonians used to model highly correlated systems: Falicov-Kimball and Anderson Lattice. We calculate specific heats, magnetic susceptibilities, thermal averages of physical operators, and energy bands. We …
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Stability, LES, and Resolvent Analysis of Thermally Non-uniform Supersonic Jet Noise
… on instability, large eddy simulations, and resolvent modes. The first study is a computational investigation of the role of thermal non-uniformity on the development of instability modes in the shear-layer of a supersonic $M= 1.5$, $Re=850,000$ jet. Cold fluid is injected at the axis of a …
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Reducing noise from supersonic jets using linear feedback control informed by resolvent analysis
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-05-01
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Resolvent-based framework for jet noise reduction of a low bypass ratio coannular nozzle
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-08-01
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An application of the Liouville resolvent method to the study of fermion-boson couplings
The Liouville resolvent method is an unconventional technique used for finding a Green function for a Hamiltonian. Implementation of the method entails the calculation of commutators of a second-quantized Hamiltonian operator with particular generalized stepping operators that are elements of a …
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Krein's identity and trace formulas for half-line Schrodinger operators
… at $x=0$. We derive a formula that relates the resolvent operator of $H_{\alpha}$ to the resolvent operator of $H_0$ in terms of the Jost solution corresponding to the underlying differential equation $\mathcal{L}u=zu$. Combining this resolvent formula and properties of the Jost solution, we …
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Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators
… employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary conditions to the corresponding operator with Dirichlet boundary conditions in combination with various operator theoretic facts.
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Extensions of the Cayley-Hamilton Theorem with Applications to Elliptic Operators and Frames.
… closed self-adjoint operators with trace-class resolvent over a separable Hilbert space. Applications of these results include calculating operators resolvents and finding the inverse of a frame operator.</p>
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Microlocal analysis of asymptotically complex hyperbolic manifolds and their conformal contact boundaries
… the second chapter, we study the behavior of the resolvent and wave kernel of the Laplacian on asymptotically complex hyperbolic manifolds. In particular, applying the methods introduced in [Va17] in the real setting, we obtain non-trapping estimates for the resolvent, deriving an effective …
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Constructing and Tabulating Dihedral Function Fields
… with prescribed ramification and fixed quadratic resolvent field, when k0 is a perfect field and not necessarily finite. We give a detailed description of this Kummer theoretic approach when k0, or a quadratic extension thereof, contains the l-th roots of unity. Avoiding the case when k0 is …
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Topics in theory of superconductivity
… superconductor can be expressed in terms of the resolvent of a supersymmetric Hamiltonian corresponding to an effective one-dimensional Schrodinger like equation, resolvent which obeys the so-called Gelfand-Dikii equation. These results are used to formulate general conditions under which the …
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Functional analytic treatment of linear transport equations in kinetic theory and neutron transport theory
… cases a modified version of the Larsen-Habetler resolvent integration technique is applied to obtain full-range and half-range expansions. For the neutron transport equation the method applied is seen to have notational advantages over previous approaches. In the case of the temperature-density …
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Correlations in the one-dimensional Hubbard model
… model are studied by application of the L-resolvent method. The calculations are well beyond one-particle mean field approximation. All correlations involving two neighboring sites are included exactly and higher order correlations are approximated. The effects of varying temperature, band …
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On the asymptotic behaviour of deterministic and stochastic volterra integro-differential equations
… case, necessary and sufficient conditions on the resolvent, kernel and noise are determined o ensure this rate of convergence. In the almost sure case, the same conditions re found to be sufficient; furthermore, it is shown that the conditions on the resolvent and he kernel are necessary. A …
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Swan Modules and Elliptic Functions
… results. The arithmetic nature of elliptic resolvents, the elliptic analogue of the Gauss sum conductor formula and the strength of the elliptic group law being a Lubin-Tate formal group law enabled Taylor to show that the ring of algebraic integers is free over the associated order, if and …
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Judd operator methods in superspace: application to the thermal single particle Green function for the Hubbard dimer
… may be expressed as matrix elements of the resolvent of the Liouville operator, in an abstract Hilbert space. This abstract Hilbert space (the "superspace") contains elements f, g, etc. which are products of an odd number of fermion creation and/or annihilation operators. These operators may …
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A computational electromagnetic framework for waveguide quantum electrodynamics
… of the system are solved in connection with the resolvent formalism of quantum scattering theory. The work presented here represent the first attempts in this important topic of study. This thesis accomplishes the full solution of the problem of a two-level atom coupled to arbitrary lossless …
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Smoothing estimates for non commutative spaces
… estimate on semigroup $T_t$ and general resolvent formula on the generator $A$ of the semigroup (i.e. $Ax= \lim_{t\rightarrow 0} \frac{T_t x - x}{t}$). And we prove a borderline case of noncommutaive Sobolev inequality, namely the noncommutative Trudinger Moser's inequality. The focus of …
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Singularly nonautonomous semilinear evolution equations with almost sectorial operators
… the family A(t) comes from a deficiency in its resolvent estimate. For this semilinear problem in the abstract setting we study local well-posedness, regularity of the solution and the asymptotic dynamics of the problem. To illustrate the ideas developed for the abstract initial value problem, …
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