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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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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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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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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 Solvable Model for Scattering on a Junction and a Modified Analytic Perturbation Procedure
We consider a one-body spin-less electron spectral problem for a resonance scattering system constructed of a quantum well weakly connected to a...
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Non-existence of a minimizer to the magnetic Hartree-Fock functional
In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result...
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Beyond Bilinear Controllability: Applications to Quantum Control
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order...
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Dispersive bounds for the three-dimensional Schrödinger equation with almost critical potentials
We prove a dispersive estimate for the time-independent Schrödinger operator H = − Δ + V in three dimensions. The potential V ( x ) is assumed to lie in...
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The Time-Dependent Approach to Inverse Scattering
In this talk we present a time-dependent approach for the solution of inverse scattering problems. With our approach we prove uniqueness and we give...