The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Blaise Rollier - One of the best experts on this subject based on the ideXlab platform.
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Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
Journal of High Energy Physics, 2011Co-Authors: Jelle Hartong, Blaise RollierAbstract:We study the complete class of 5-dimensional asymptotically Schroedinger space-times that can be obtained as the TsT transform of a 5-dimensional asymptotically AdS space-time. Based on this we identify a conformal class of Schroedinger boundaries. We use a Fefferman-Graham type expansion to study the on-shell action for this class of asymptotically Schroedinger space-times and we show that its value is TsT invariant. In the second part we focus on black hole space-times and prove that black hole thermodynamics is also TsT invariant. We use this knowledge to argue that thermal global Schroedinger space-time at finite chemical potential undergoes a Hawking-Page type phase transition.
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Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
Journal of High Energy Physics, 2009Co-Authors: Matthias Blau, Jelle Hartong, Blaise RollierAbstract:We study various geometrical aspects of Schroedinger space-times with dynamical exponent z>1 and compare them with the properties of AdS (z=1). The Schroedinger metrics are singular for 1 2, we show that the Schroedinger space-times admit no global timelike Killing vectors.
Jelle Hartong - One of the best experts on this subject based on the ideXlab platform.
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Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
Journal of High Energy Physics, 2011Co-Authors: Jelle Hartong, Blaise RollierAbstract:We study the complete class of 5-dimensional asymptotically Schroedinger space-times that can be obtained as the TsT transform of a 5-dimensional asymptotically AdS space-time. Based on this we identify a conformal class of Schroedinger boundaries. We use a Fefferman-Graham type expansion to study the on-shell action for this class of asymptotically Schroedinger space-times and we show that its value is TsT invariant. In the second part we focus on black hole space-times and prove that black hole thermodynamics is also TsT invariant. We use this knowledge to argue that thermal global Schroedinger space-time at finite chemical potential undergoes a Hawking-Page type phase transition.
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Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
Journal of High Energy Physics, 2009Co-Authors: Matthias Blau, Jelle Hartong, Blaise RollierAbstract:We study various geometrical aspects of Schroedinger space-times with dynamical exponent z>1 and compare them with the properties of AdS (z=1). The Schroedinger metrics are singular for 1 2, we show that the Schroedinger space-times admit no global timelike Killing vectors.
Gerald Teschl - One of the best experts on this subject based on the ideXlab platform.
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Weyl–Titchmarsh Theory for Schrödinger Operators with Strongly Singular Potentials
International Mathematics Research Notices, 2011Co-Authors: Aleksey Kostenko, Alexander Sakhnovich, Gerald TeschlAbstract:We develop Weyl-Titchmarsh theory for Schroedinger operators with strongly singular potentials such as perturbed spherical Schroedinger operators (also known as Bessel operators). It is known that in such situations one can still define a corresponding singular Weyl m-function and it was recently shown that there is also an associated spectral transformation. Here we will give a general criterion when the singular Weyl function can be analytically extended to the upper half plane. We will derive an integral representation for this singular Weyl function and give a criterion when it is a generalized Nevanlinna function. Moreover, we will show how essential supports for the Lebesgue decomposition of the spectral measure can be obtained from the boundary behavior of the singular Weyl function. Finally, we will prove a local Borg-Marchenko type uniqueness result. Our criteria will in particular cover the aforementioned case of perturbed spherical Schroedinger operators.
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weyl titchmarsh theory for Schroedinger operators with strongly singular potentials
arXiv: Spectral Theory, 2010Co-Authors: Aleksey Kostenko, Alexander Sakhnovich, Gerald TeschlAbstract:We develop Weyl-Titchmarsh theory for Schroedinger operators with strongly singular potentials such as perturbed spherical Schroedinger operators (also known as Bessel operators). It is known that in such situations one can still define a corresponding singular Weyl m-function and it was recently shown that there is also an associated spectral transformation. Here we will give a general criterion when the singular Weyl function can be analytically extended to the upper half plane. We will derive an integral representation for this singular Weyl function and give a criterion when it is a generalized Nevanlinna function. Moreover, we will show how essential supports for the Lebesgue decomposition of the spectral measure can be obtained from the boundary behavior of the singular Weyl function. Finally, we will prove a local Borg-Marchenko type uniqueness result. Our criteria will in particular cover the aforementioned case of perturbed spherical Schroedinger operators.
Avy Soffer - One of the best experts on this subject based on the ideXlab platform.
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l p boundedness of the scattering wave operators of Schroedinger dynamics with time dependent potentials and applications
arXiv: Analysis of PDEs, 2020Co-Authors: Avy SofferAbstract:This paper establishes the L^p boundedness of wave operators for linear Schrodinger equations in R3 with time-dependent potentials. The approach to the proof is based on new cancellation lemmas. As a typical application based on this method combined with Strichartz estimates, is the existence and scattering for nonlinear dispersive equations. For example, we prove global existence for a class of Hartree nonlinear Schroedinger equations in L^2(R^3); allowing the presence of solitons.
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A semilinear Schroedinger equation with random potential
arXiv: Analysis of PDEs, 2019Co-Authors: Marius Beceanu, Avy SofferAbstract:We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential enable us to also treat the case of small semi-linear perturbations. In both the linear and the nonlinear instances, we prove that, on average, energy remains bounded and solutions scatter.
M. Ehler - One of the best experts on this subject based on the ideXlab platform.
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Schroedinger Eigenmaps for the Analysis of Biomedical Data
IEEE transactions on pattern analysis and machine intelligence, 2013Co-Authors: W. Czaja, M. EhlerAbstract:We introduce Schroedinger Eigenmaps (SE), a new semi-supervised manifold learning and recovery technique. This method is based on an implementation of graph Schroedinger operators with appropriately constructed barrier potentials as carriers of labeled information. We use our approach for the analysis of standard biomedical datasets and new multispectral retinal images.
