相关论文: Semiclassical pseudodifferential calculus and the …
In this thesis we consider a magnetic Schr\"odinger inverse problem over a compact domain contained in an infinite cylindrical manifold. We show that, under certain conditions on the electromagnetic potentials, we can recover the magnetic…
Inequalities are derived for sums and quotients of eigenvalues of magnetic Schroedinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.
The two-dimensional Schroedinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields we reduce the spectral problem to the semiclassical analysis of one-dimensional Harper-like…
In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic…
This article is devoted to the spectral analysis of the electro-magnetic Schr\"odinger operator on the Euclidean plane. In the semiclassical limit, we derive a pseudo-differential effective operator that allows us to describe the spectrum…
We examine semiclassical magnetic Schr\"{o}dinger operators with complex electric potentials. Under suitable conditions on the magnetic and electric potentials, we prove a resolvent estimate for spectral parameters in an unbounded parabolic…
We define a Schr\"odinger operator on the half-space with a discontinuous magnetic field having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the infimum of the…
We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neumann map. By applying higher order linearization method, we…
We introduce the fractional magnetic operator involving a magnetic potential and an electric potential. We formulate an inverse problem for the fractional magnetic operator. We determine the electric potential from the exterior partial…
We recover a nonlinear magnetic Schr\"odinger potential from measurement on an arbitrarily small open subset of the boundary on a compact Riemann surface. We assume that the magnetic potential satisfies suitable analytic properties, in…
In our recent papers, we studied semiclassical spectral problems for the Bochner-Schr\"odinger operator on a manifold of bounded geometry. We survey some results of these papers in the setting of the magnetic Schr\"odinger operator in the…
We compute the sum and number of eigenvalues for a certain class of magnetic Schrodinger operators in a domain with boundary. Functions in the domain of the operator satisfy a (magnetic) Robin condition. The calculations are valid in the…
The aim of these notes is to show how the magnetic calculus developed in \cite{MP, IMP1, IMP2, MPR, LMR} permits to give a new information on the nature of the coefficients of the expansion of the trace of a function of the magnetic…
We obtain semiclassical resolvent estimates for the Schr{\"o}dinger operator (ih$\nabla$ + b)^2 + V in R^d , d $\ge$ 3, where h is a semiclassical parameter, V and b are real-valued electric and magnetic potentials independent of h. Under…
We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…
We show that an electric potential and magnetic field can be uniquely determined by partial boundary measurements of the Neumann-to-Dirichlet map of the associated magnetic Schr\"{o}dinger operator. This improves upon previous results of…
In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is…
The paper considers the semiclassical dynamics of electrons on complex Fermi surfaces in the presence of strong magnetic fields. The reconstructions of the general topological structure of such dynamics are accompanied by the appearance of…
For one-dimensional Schroedinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. Our (non-semi-classical) approach results in substantial progress in achieving optimal conditions…
We review recent results on the magnetic pseudo-differential calculus both in symbolic and in $C^*$-algebraic form. We also indicate some applications to spectral analysis of pseudo-differential operators with variable magnetic fields.