Resonances for a semi-classical Schrödinger operator near a non-trapping energy level

Semiclassical resonances for a two-level Schrödinger operator with a conical intersection

We study the resonant set of a two-level Schrödinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real half-line. For these ordinary differential systems we locally construct exact WKB solutions, which are connected to global solutions, amongst which are resonant states. The main results are a generalized Bohr...

Tunneling resonances in systems without a classical trapping

In this paper we analyze a free quantum particle in a straight Dirichlet waveguide which has at its axis two Dirichlet barriers of lengths l± separated by a window of length 2a. It is known that if the barriers are semiinfinite, i.e. we have two adjacent waveguides coupled laterally through the boundary window, the system has for any a > 0 a finite number of eigenvalues below the essential spec...

un 2 00 6 Accuracy on eigenvalues for a Schrödinger operator with a degenerate potential in the semi - classical limit

We consider a semi-classical Schrödinger operator −h2∆+ V with a degenerate potential V(x,y) =f(x) g(y) . g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum. We give sharp asymptotic behaviour of low eigenvalues bounded by some power of the parameter h, by improving Born-Oppenheimer approximation.

Quantum and classical resonances for strongly trapping systems

Resonances are one of the most studied objects in physics, and in quantum mechanics they describe states which in addition to a rest energy have a rate of decay. A mathematical example is given by the zeros of the Riemann zeta function which are the resonances of the quantum Hamiltonian given by the Laplacian on the modular surface. The term "resonance" comes from the analogy with "a bell sound...

Semi-classical Approaches to Electric Giant Resonances