105,404 research outputs found
Marriage record of Dinger, Charles H. and McClung, Eva M.
No full textMarriage license for Charles H. Dinger and Eva M. McClung. H.B. Yluiekie was the officiant
H\"{o}lder Stability in the Inverse Steklov Problem for Radial Schr\"{o}dinger operators and Quantified Resonances
No full textInternational audienceIn this paper, we obtain H\"{o}lder stability estimates for the inverse Steklov problem for Schr\"{o}dinger operators corresponding to a special class of radial potentials on the unit ball. These results provide an improvement on earlier logarithmic stability estimates obtained in [8] in the case of the Schr\"{o}dinger operators related to deformations of the closed unit ball. The main tools involve a formula relating the difference of the Steklov spectra of the Schr\"{o}dinger operators associated to the original and perturbed potential to the Laplace transform of the difference of the corresponding amplitude functions introduced by B. Simon and a key moment stability estimate due to Still. It is noteworthy that with respect to the original Schr\"{o}dinger operator, the type of perturbation being considered for the amplitude function amounts to the introduction of a finite number of negative eigenvalues and of a countable set of negative resonances which are quantified explicitly in terms of the eigenvalues of the Laplace-Beltrami operator on the boundary sphere
H\"{o}lder Stability in the Inverse Steklov Problem for Radial Schr\"{o}dinger operators and Quantified Resonances
No full textInternational audienceIn this paper, we obtain H\"{o}lder stability estimates for the inverse Steklov problem for Schr\"{o}dinger operators corresponding to a special class of radial potentials on the unit ball. These results provide an improvement on earlier logarithmic stability estimates obtained in [8] in the case of the Schr\"{o}dinger operators related to deformations of the closed unit ball. The main tools involve a formula relating the difference of the Steklov spectra of the Schr\"{o}dinger operators associated to the original and perturbed potential to the Laplace transform of the difference of the corresponding amplitude functions introduced by B. Simon and a key moment stability estimate due to Still. It is noteworthy that with respect to the original Schr\"{o}dinger operator, the type of perturbation being considered for the amplitude function amounts to the introduction of a finite number of negative eigenvalues and of a countable set of negative resonances which are quantified explicitly in terms of the eigenvalues of the Laplace-Beltrami operator on the boundary sphere
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Low Regularity Solutions of Korteweg-de Vries and Chern-Simons-Schr\"{o}dinger Equations
No full textThe aim of this thesis is to understand the locall wellposednesstheory for some nonlinear dispersive equations at low regularity. The Korteweg-de Vries equation has sharp wellposedness at if we are concerned about the Lipschitzdependence of solutions on the initial data. For lower regularity,one might still have a weaker form of wellposedness only withcontinuous dependence on data. Here we prove that the smoothsolutions satisfy a-priori local in time bound in terms ofthe size of the initial data for . Together withthe bounds we obtained on the nonlinearity, the result hereensures that the equation is satisfied in the sense ofdistributions even for weak limits.The Chern-Simons-Schr\"{o}dinger equation is a planar gaugedSchr\"{o}dinger equation which has some similarity to thederivative formulation of the Schr\"{o}dinger map problem. We workon to prove local wellposedness in the full subcritical rangeH^s(\mathbb{R}^2), s>0.One important idea in working on these problems is to find asuitable space to characterize the solution. We use spaces introduced by Bourgain, and , spaces introduced by Koch and Tataru. For the Chern-Simons-Schr\"{o}dinger equation, we also need to fix a suitable gauge to make the problem well-posed. The heat gauge is a variation of Coulomb gauge, and it serves as a good candidate for this problem
Regularity Properties and Lipschitz Spaces Adapted to High-Order Schrödinger Operators
No full textLet be the high-order Schrödinger operator (−Δ)2+V2, where V is a non-negative potential satisfying the reverse Hölder inequality (RHq), with q>n/2 and n≥5. In this paper, we prove that when 0<α≤2−n/q, the adapted Lipschitz spaces Λα/4L we considered are equivalent to the Lipschitz space CLα associated to the Schrödinger operator L=−Δ+V. In order to obtain this characterization, we should make use of some of the results associated to (−Δ)2. We also prove the regularity properties of fractional powers (positive and negative) of the operator ℒ, Schrödinger Riesz transforms, Bessel potentials and multipliers of the Laplace transforms type associated to the high-order Schrödinger operators
Global well-posedness of quadratic and subquadratic half wave Schr{\"o}dinger equations
No full textWe consider the following order nonlinear half wave Schr{\"o}dinger
equationson the plane with . This equation
is considered as a toy model motivated by the study of solutions to weakly
dispersive equations. In particular, the global well-posedness of this equation
is a difficult problem due to the anisotropic property of the equation, with
one direction corresponding to the half-wave operator, which is not dispersive.
In this paper, we prove the global well-posedness of this equation in (), which is the first global well-posedness result of nonlinear half wave
Schr{\"o}dinger equations. With the global well-posedness in the energy space
for the focusing equation and the study on the solitary wave in [1], we
complete the proof of the stability of the set of ground states. Moreover, we
consider the half wave Schr{\"o}dinger equations on
, which can also be called the wave guide
Schr{\"o}dinger equations on . Using a
similar approach in the analysis of the Cauchy problem of half wave
Schr{\"o}dinger equations on , we can also deduce the global
well-posedness of () order wave guide Schr{\"o}dinger equations
in with . With the
global well-posedness in the energy space for the focusing wave guide
Schr{\"o}dinger equations and the study on the ground states in [2], we
complete the proof of the orbital stability of the ground states with small
frequencies
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Schrödinger Operators with Lattice Invariant Potentials
No full textThesis (Ph.D.)--University of Washington, 2025We develop a systematic framework to study the dispersion surfaces of Schrödinger operators H = −∆+V, where the potential V is both periodic with respect to a lattice Λ and respects its symmetries. Our analysis relies on an abstract result, previously proven by Franz Rellich [Rel40] and which we prove using an alternative approach inspired by methods developed by Tosio Kato [Kat95]: if a self-adjoint operator depends analytically on a parameter, then so do its eigenvalues and eigenprojectors in a neighborhood of the real line. Using this and techniques from Floquet-Bloch theory and representation theory, we prove a series of results that can be used to analyze the operator H where the lattice Λ is arbitrary. As an application of this framework, we describe the generic structure of some singularities in the band spectrum of Schrödinger operators invariant under various two- and three-dimensional lattices. Specifically, we study the square, hexagonal, rectangular, simple cubic, body-centered cubic, face-centered cubic, and stacked hexagonal lattices, in the process reproducing results due to [Kel+18] and [FW12], and also proving a conjecture of [GZZ22]
Amplification of optical Schr\"{o}dinger cat states with implementation protocol based on frequency comb
No full textWe proposed and analyzed a scheme to generate large-size Schr\"{o}dinger cat
states based on linear operations of Fock states and squeezed vacuum states and
conditional measurements. By conducting conditional measurements via photon
number detectors, two unbalanced Schr\"{o}dinger kitten states combined by a
beam splitter can be amplified to a large-size cat state with the same parity.
According to simulation results, two Schr\"{o}dinger odd kitten states of
and generated from one-photon-subtracted squeezed
vacuum states of 3 dB, are amplified to an odd cat state of
with a fidelity of . A large-size Schr\"{o}dinger odd cat state with
and is predicted when the input squeezed vacuum states
are increased to 5.91 dB. According to the analysis on the impacts of
experimental imperfections in practice, Schr\"{o}dinger odd cat states of
are available. A feasible configuration based on a quantum frequency
comb is developed to realize the large-size cat state generation scheme we
proposed
Rational solitons of wave resonant-interaction models
No full textIntegrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations
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