Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRelativistic Stark resonances in a simple exactly soluble model for a diatomic molecule
169
0
0.0
(
0
)
Added by
Francois Fillion-Gourdeau
Publication date
2012
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A simple 1-D relativistic model for a diatomic molecule with a double point interaction potential is solved exactly in a constant electric field. The Weyl-Titchmarsh-Kodaira method is used to evaluate the spectral density function, allowing the correct normalization of continuum states. The boundary conditions at the potential wells are evaluated using Colombeaus generalized function theory along with charge conjugation invariance and general properties of self-adjoint extensions for point-like interactions. The resulting spectral density function exhibits resonances for quasibound states which move in the complex energy plane as the model parameters are varied. It is observed that for a monotonically increasing interatomic distance, the ground state resonance can either go deeper into the negative continuum or can give rise to a sequence of avoided crossings, depending on the strength of the potential wells. For sufficiently low electric field strength or small interatomic distance, the behavior of resonances is qualitatively similar to non-relativistic results.
rate research
Read More
We investigate the influence of an electric field on trapped modes arising in a two-dimensional curved quantum waveguide ${bf Omega}$ i.e. bound states of the corresponding Laplace operator $-Delta_{{bf Omega}}$. Here the curvature of the guide is supposed to satisfy some assumptions of analyticity, and decays as $O(|s|^{-varepsilon}), varepsilon > 3$ at infinity. We show that under conditions on the electric field $ bf F$, ${bf H}(F):= -Delta_{{bf Omega}} + {bf F}. {bf x} $ has resonances near the discrete eigenvalues of $-Delta_{{bf Omega}}$.
We extend the class of QM problems which permit for quasi-exact solutions. Specifically, we consider planar motion of two interacting charges in a constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013) addressed the case of the Coulomb interaction between the particles, we explore three other potentials. We do this by reducing the appropriate Hamiltonians to the second-order polynomials in the generators of the representation of $SL(2,C)$ group in the differential form. This allows us to perform partial diagonalisation of the Hamiltonian, and to reduce the search for the first few energies and the corresponding wave functions to an algebraic procedure.
The Schr{o}dinger equation $psi(x)+kappa^2 psi(x)=0$ where $kappa^2=k^2-V(x)$ is rewritten as a more popular form of a second order differential equation through taking a similarity transformation $psi(z)=phi(z)u(z)$ with $z=z(x)$. The Schr{o}dinger invariant $I_{S}(x)$ can be calculated directly by the Schwarzian derivative ${z, x}$ and the invariant $I(z)$ of the differential equation $u_{zz}+f(z)u_{z}+g(z)u=0$. We find an important relation for moving particle as $ abla^2=-I_{S}(x)$ and thus explain the reason why the Schr{o}dinger invariant $I_{S}(x)$ keeps constant. As an illustration, we take the typical Heun differential equation as an object to construct a class of soluble potentials and generalize the previous results through choosing different $rho=z(x)$ as before. We get a more general solution $z(x)$ through integrating $(z)^2=alpha_{1}z^2+beta_{1}z+gamma_{1}$ directly and it includes all possibilities for those parameters. Some particular cases are discussed in detail.
In this paper we study the influence of an electric field on a two dimen-sional waveguide. We show that bound states that occur under a geometrical deformation of the guide turn into resonances when we apply an electric field of small intensity having a nonzero component on the longitudinal direction of the system. MSC-2010 number: 35B34,35P25, 81Q10, 82D77.
We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as boundary degeneracy) does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
