Related papers: Many-body Stark resonances by the complex absorbin…
We characterize the resonances of Stark Hamiltonians by the complex absorbing potential method. Namely, we prove that the Stark resonances are the limit points of complex eigenvalues of the Stark Hamiltonian with a quadratic complex…
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…
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 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 consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
We developed a method to calculate positions and widths of three-body resonances. The method combines the hyperspherical adiabatic approach, slow variable discretization method (Tolstikhin et al., J. Phys. B: At. Mol. Opt. Phys. 29, L389…
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 present a theory of resonances for a class of non-autonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of…
It is demonstrated that the complex scaling method can be used in practical calculations to localize three-body resonances. Our model example emphasizes the fact that in three-body systems several essentially different asymptotic behaviors…
The complex scaling method permits calculations of few-body resonances with the correct asymptotic behaviour using a simple box boundary condition at a sufficiently large distance. This is also valid for systems involving more than one…
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…
The method of calculation of the resonance characteristics is developed for the metastable states of the Coulomb three-body (CTB) system with two disintegration channels. The energy dependence of K-matrix in the resonance region is…
The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…
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…
A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…
We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other…
The coherent stochastic resonance is observed and studied with multi-step periodic signal in continuous medium having two absorbing boundaries. The general features of this process are exihibited. The universal features at the resonance…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians $H$ with complex energy eigenvalues are considered. The method of evaluation of quantities $\sigma_n$ known as the singular values of $H$ is proposed. Its basic…