相关论文: Semi-classical analysis of a conjoint crossing of …
We study the asymptotic distribution of the eigenvalues of a one-dimensional two-by-two semiclassical system of coupled Schr\"odinger operators in the presence of two potential wells and with an energy-level crossing. We provide…
The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…
We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schr\"odinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point…
In this article, we analyze the propagation of Wigner measures of a family of solutions to a system of semi-classical pseudodifferential equations presenting eigenvalues crossings on hypersurfaces. We prove the propagation along classical…
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
In this article we study the propagation of Wigner measures linked to solutions of the Schr{\"o}dinger equation with potentials presenting conical singularities and show that they are transported by two different Hamiltonian flows, one over…
Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the…
Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, each focus…
We study the semiclassical distribution of resonances of a $2 \times 2$ matrix Schr\"odinger operator, obtained as a reduction of an Hamiltonian when studying molecular predissociation models under the Born-Oppenheimer approximation. The…
This is the third paper in a series analyzing the asymptotic distribution of the phase shifts in the semiclassical limit. We analyze the distribution of phase shifts, or equivalently, eigenvalues of the scattering matrix, $S_h(E)$, for…
In this work, we study the Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+\eta(t)\sum_{j=1}^J\delta_{x=a_j(t)}\psi$ on $L^2((0,1),C)$ where $\eta:[0,T]\longrightarrow R^+$ and $a_j:[0,T]\longrightarrow (0,1)$, $j=1,...,J$. We show how…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's…
We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying…
The chemical potiential for the ground states of the atomic elements have been calculated within the semiclassical approximation The present work closely follows Schwinger and Englert's semiclassical treatment of atomic structure.
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…
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
In this paper we study the semiclassical limit of the Schr\"odinger equation. Under mild regularity assumptions on the potential $U$ which include Born-Oppenheimer potential energy surfaces in molecular dynamics, we establish asymptotic…
We describe the behaviour of semiclassical electrodynamics under gauge transformations. For this purpose we observe the structure of Schr\"odinger equation and matricial elements under these transformations. We conclude this theory is not…