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Semiclassical Quantum Maps of Semi-Hyperbolic Type
Let M be either Rn or possibly a noncompact Riemannian manifold. For an h-differential operator H(x,hDx; h) on L2(M), we consider semiexcited...
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On the Essential Self-Adjointness of Singular Sub-Laplacians
We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular...
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Absolutely Continuous Spectrum for Laplacians on Radial Metric Trees and Periodicity
On an infinite, radial metric tree graph we consider the corresponding Laplacian equipped with self-adjoint vertex conditions from a large class...
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The fourth-order nonlinear Schrödinger limit for quantum Zakharov system
This paper is concerned with the quantum Zakharov system. We prove that when the ionic speed of sound goes to infinity, the solution to the...
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Born–Jordan Pseudodifferential Calculus, Bopp Operators and Deformation Quantization
There has recently been a resurgence of interest in Born–Jordan quantization, which historically preceded Weyl’s prescription. Both mathematicians...
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Dynamics of a Strongly Coupled Polaron
We study the dynamics of large polarons described by the Fröhlich Hamiltonian in the limit of strong coupling. The initial conditions are...
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The Helmholtz Operator on Higher Dimensional Möbius Strips Embedded in \({\mathbb{R}^{4}}\)
In this paper we present explicit formulas for the fundamental solution to the Helmholtz operator on a higher-dimensional analogue of the Möbius...
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Quantum Zakharov model in a bounded domain
We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global...
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Solvable Models of Resonances and Decays
Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a...
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Regularity for Eigenfunctions of Schrödinger Operators
We prove a regularity result in weighted Sobolev (or Babuška–Kondratiev) spaces for the eigenfunctions of certain Schrödinger-type operators. Our...
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On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator
Absolute continuity of the spectrum of a 3D periodic magnetic Dirac operator is proved provided that the magnetic potential A belongs to the space
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Finite Energy Weak Solutions to the Quantum Hydrodynamics System
In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily...
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The Schrödinger Flow in a Compact Manifold: High-frequency Dynamics and Dispersion
We discuss various aspects of the dynamics of the Schrödinger flow on a compact Riemannian manifold that are related to the behavior of highfrequency...
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The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator
Following Wong’s point of view (see [14], by Wong) we give a formula for the heat kernel of the generalized Hermite operator Lλ on...
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Weighted Spectral Gap for Magnetic Schrödinger Operators with a Potential Term
We prove that singular Schrödinger equations with external magnetic field admit a representation with a positive Lagrangian density whenever their...
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Groups of Operators for Evolution Equations of Quantum Many-particle Systems
The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von...
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Remarks about Observables for the Quantum Mechanical Harmonic Oscillator
A comparison algebra \( \mathcal{A} \) for the...
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A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications
Theory and main applications of infinite dimensional oscillatory integrals are discussed, with special attention to the mathematical realization of...