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A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator
The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator. The proposed approach combines a...
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Inverse problem for a random Schrödinger equation with unknown source and potential
In this paper, we study an inverse scattering problem associated with the time-harmonic Schrödinger equation where both the potential and the source...
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An Example of Embedded Singular Continuous Spectrum for Discrete Schrödinger Operators
We present an example of a potential such that the corresponding discrete Schrödinger operator has singular continuous spectrum embedded in the...
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Asymptotics for Christoffel functions associated to continuum Schrödinger operators
We prove asymptotics of the Christoffel function, λ L ( ξ ), of a continuum Schrödinger operator for points in the interior of the essential spectrum...
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On the Expansion of Resolvents and the Integrated Density of States for Poisson Distributed Schrödinger Operators
We consider a Schrödinger operator with random potential distributed according to a Poisson process. We show that under a uniform moment bound...
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Spectral Approximation of Generalized Schrödinger Operators via Approximation of Subwords
We prove criteria, purely based on finite subwords of the potential, for spectral inclusion as well as Hausdorff approximation of pseudospectra or...
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Ballistic Transport in Periodic and Random Media
We prove ballistic transport of all orders, that is, $$\Vert...
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Quantitative Green’s function estimates for lattice quasi-periodic Schrödinger operators
In this paper, we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic (QP) Schrödinger operators....
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Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials
We prove a spectral inequality (a specific type of uncertainty relation) for Schrödinger operators with confinement potentials, in particular of...
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Nonlinear Schrödinger Equation with Delay and Its Regularization
AbstractThe properties of an initial-boundary value problem for a nonlinear Schödinger equation including terms with a delay of the time argument in...
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Absence of absolutely continuous spectrum for generic quasi-periodic Schrödinger operators on the real line
We show that a generic quasi-periodic Schrödinger operator in L 2 (ℝ) has purely singular spectrum. That is, for any minimal translation flow on a...
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Solution theory to semilinear stochastic equations of Schrödinger type on curved spaces I: operators with uniformly bounded coefficients
We study the Cauchy problem for Schrödinger type stochastic semilinear partial differential equations with uniformly bounded variable coefficients,...
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Nonlinear Schrödinger Equation and the Hyperbolization Method
Abstract“Nonstandard” equations (like a nonlinear Schrödinger one) that require very small steps in space and time in numerical computations are...
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Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps
This paper aims to investigate stochastic fractional Schrödinger evolution equations with potential and Poisson jumps in Hilbert space. The...
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Fractional Schrödinger Equations with Logarithmic and Critical Nonlinearities
In this paper, we study a class of the fractional Schrödinger equations involving logarithmic and critical nonlinearities. By using the Nehari...