Related papers: Complex absorbing potential method for Stark reson…
The resonances of many-body Stark Hamiltonians are characterized by the complex absorbing potential method. Namely, the resonances are shown to be the limit points of complex discrete eigenvalues of many-body Stark Hamiltonians with…
The Complex Absorbing Potential (CAP) method is widely used to compute resonances in Quantum Chemistry, both for nonrelativistic and relativistic Hamiltonians. In the semiclassical limit $\hbar \to 0$ we consider resonances near the real…
The resonances for the Wigner-von Neumann type Hamiltonian are defined by the periodic complex distortion in the Fourier space. Also, following Zworski, we characterize resonances as the limit points of discrete eigenvalues of the…
We study the Complex Absorbing Potential (CAP) Method in computing quantum resonances of width $c(h) = O(h^N)$, $N\gg1$. We show that up to $h^{-M}\sqrt{c(h)} +\Oh$ error, $M\gg1$, resonances are perturbed eigenvalues of the CAP Hamiltonian…
Effective non-Hermitian Hamiltonians are obtained to describe coherent perfect absorbing and lasing boundary conditions. PT -symmetry of the Hamiltonians enables to design configurations which perfectly absorb at multiple frequencies.…
We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to the case of exponentially decaying potentials. That means that the eigenvalues of $-\Delta + V - i\epsilon x^2$, $|V(x)|\leq C…
We discuss the resonances of Hamiltonians with constant electric field in one dimension in the limit of small field. These resonances occur near the real axis, near zeros of the analytic continuation of a reflection coefficient for…
We study shape resonances of two-dimensional magnetic Stark Hamiltonians in the semiclassical limit. The magnetic field is assumed to be constant and the scalar potential is a perturbation of a linear potential. Under the assumption that…
We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to an abstractly defined class of black box perturbations of the Laplacian in $\mathbb{R}^n$ which can be analytically extended from…
In this note we discuss the complex version of the Higgs oscillator on the hyperbolic space. The eigenvalues and resonances of the complex Higgs oscillator are computed in different examples in the hyperbolic setting. We also propose open…
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the…
In many Hamiltonian systems, propagation of steadily travelling solitons or kinks is prohibited because of resonances with linear excitations. We show that Hamiltonian systems with resonances may admit an infinite number of travelling…
A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple,…
Particle oscillations in absorbing matter are considered. The approach based on the optical potential is shown to be inapplicable in the strong absorption region. Models with Hermitian Hamiltonian are analyzed. They give an increase of the…
We calculate resonances in three-body systems with attractive Coulomb potentials by solving the homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved by using the Coulomb-Sturmian separable…
We investigate theoretically the spatial dependence of the linear absorption spectra of single and coupled semiconductor quantum dots, where the strong three-dimensional quantum confinement leads to an overall enhancement of Coulomb…
A computationally efficient, self-consistent complex scaling approach to calculating characteristics of excitons in an external electric field in quantum wells is introduced. The method allows one to extract the resonance position as well…
We study real resonances and embedded eigenvalues of the Kramers--Fokker--Planck operator with a long-range potential. We prove that thresholds are only possible accumulation points of eigenvalues and that the limiting absorption principle…
Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent…
We consider the Hamiltonian system of scalar wave field and a single nonrelativistic particle coupled in a translation invariant manner. The particle is also subject to a confining external potential. The stationary solutions of the system…