Related papers: Finite periodic $\delta-\delta'$ comb
The mergings of energy levels associated with the breaking of PT symmetry in the model of Bender and Boettcher, and in its generalisation to incorporate a centrifugal term, are analysed in detail. Even though conventional WKB techniques…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
The p-d model which well describes the CuO_2 planes of the high-Tc superconductors is studied by means of the Composite Operator Method (COM). The relevant quasi-particle excitations are represented by composite operators. As a result of…
Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum…
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
The dynamics of waves in periodic media is determined by the band structure of the underlying periodic Hamiltonian. Symmetries of the Hamiltonian can give rise to novel properties of the band structure. Here we consider a class of periodic…
A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of…
This work presents a numerical study of the Dirichlet problem for the fractional Laplacian $(-\Delta)^s$ with $s\in(0,1)$ using Finite Element methods with non-standard bases. Classical approaches based on piece-wise linear basis yield…
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger…
A recently proposed strongly correlated electron system associated with the Temperley-Lieb algebra is solved by means of the coordinate Bethe ansatz for periodic and closed boundary conditions.
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…
A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong (Fano-Anderson model), is considered. The particle is initially…
A systematic formalism for quantum electrodynamics in a classical uniform magnetic field is discussed. The first order radiative correction to the ground state energy of an electron is calculated. This then leads to the anomalous magnetic…
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…
We consider a two-orbital impurity system with intra and inter-level Coulomb repulsion that is coupled to a single conduction channel. This situation can generically occur in multilevel quantum dots or in systems of coupled quantum dots.…
Symmetries of the periodic Toda lattice are expresssed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Jacobi matrices. Using these symmetries, the phase space of the lattice…
Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider the application of these methods in obtaining the spectrum from the…