Related papers: Quantitative limiting absorption principle in the …
We consider the large time behavior of solutions to defocusing nonlinear Schrodinger equation in the presence of a time dependent external potential. The main assumption on the potential is that it grows at most quadratically in space,…
We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by suitable diffeomorphisms. Dirichlet Laplacians model quantum…
For the semi-classical limit of the cubic, defocusing nonlinear Schrodinger equation with an external potential, we explain the notion of criticality before a caustic is formed. In the sub-critical and critical cases, we justify the WKB…
We prove optimal pointwise bounds on quasimodes of semiclassical Schrodinger operators with arbitrary smooth real potentials in dimension two. This end-point estimate was left open in the general study of semiclassical Lp bounds conducted…
We prove explicit semiclassical resolvent estimates for an integrable potential on the real line. The proof is a comparatively easy case of the spherical energies method, which has been used to prove similar theorems in higher dimensions…
We establish limiting absorption principles for contractions on a Hilbert space. Our sufficient conditions are based on positive commutator estimates. We discuss the dynamical implications of this principle to the corresponding…
This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schr\"odinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in…
This work establishes new results on spectral theory and time evolution for matrix-valued discrete Schr\"odinger operators on the space of square-summable matrix sequences. The matrix-valued formalism is employed to streamline notation,…
In this paper we prove a subelliptic resolvent estimate for a class of semiclassical non-self-adjoint Schr\"odinger operators with purely imaginary potentials when the spectral parameter is in a parabolic neighborhood of the imaginary axis.
Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and…
In this paper we describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable…
We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and…
We derive lower bounds on the resolvent operator for the linearized steady Boltzmann equation over weighted L1 Banach spaces in velocity, comparable to those derived by Pogan & Zumbrun in an analogous weighted L2 Hilbert space setting.…
We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper…
The current paper is devoted to the scattering theory of a class of continuum Schr\"{o}dinger operators with deterministic sparse potentials. We first establish the limiting absorption principle for both modified free resolvents and…
Cet article est consacre a l'etude des mesures limites associees a la solution de l'equation de Helmholtz avec un terme source se concentrant en un point. Le potentiel est suppose regulier et l'operateur non-captif. La solution de…
In this paper we analyze the classical limit of the Nelson model with cut off, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical…
We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter $h$ tends to $0$. An example of such an operator is the shifted semiclassical Laplacian…
We consider the Schrodinger equation with an external potential and a cubic nonlinearity, in the semiclassical limit. The initial data are sums of WKB states, with smooth phases and smooth, compactly supported initial amplitudes, with…
We show the strong convergence in arbitrary Sobolev norms of solutions of the discrete nonlinear Schr{\"o}dinger on an infinite lattice towards those of the nonlinear Schr{\"o}dinger equation on the whole space. We restrict our attention to…