Resonances for 1d Stark operators

Resonances for 1d Massless Dirac Operators

We consider the 1D massless Dirac operator on the real line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: 1) asymptotics of counting function, 2) estimates on the resonances and the forbidden domain, 3) the trace formula in terms of re...

Resonances for Matrix Schrödinger Operators

We study the resonances of matrix Schrödinger operators, motivated by the BornOppenheimer approximation. We give a simple criterion for the potential to generate resonances. This criterion also gives the location of the resonances generated.

Higher-order resonances in a Stark decelerator

Fractal stabilization of Wannier-Stark resonances

– The quasienergy spectrum of a Bloch electron affected by dc-ac fields is known to have a fractal structure as function of the so-called electric matching ratio, which is the ratio of the ac field frequency and the Bloch frequency. This paper studies a manifestation of the fractal nature of the spectrum in the system “atom in a standing laser wave”, which is a quantum optical realization of a ...

Dynamical Lower Bounds for 1d Dirac Operators

with Dirichlet boundary conditions, acting on l2(N,C2), resp. L2([0,∞),C2), where c > 0 represents the speed of light, m ≥ 0 the mass of a particle, I2 is the 2× 2 identity matrix and V is a bounded real potential. In the discrete case D is the finite difference operator defined by (Dφ)(n) = φ(n+1)−φ(n), with adjoint (Dφ)(n) = φ(n − 1) − φ(n), and in the continuous case D = D = −i d dx . Model ...