Related papers: Continuous Spectra of Generalized Kronig-Penney Mo…
The main purpose of the present paper is to introduce a scattering approach to the study of the Kronig-Penney model in a quadratic channel with $\delta$ interactions, which was discussed in full generality in the first paper of the present…
The delta function potential is a simple model of zero-range contact interaction in one dimension. The Kronig-Penney model is a one-dimensional periodic array of delta functions that models the energy bands in a crystal. Here we investigate…
We present a detailed study of a generalised one-dimensional Kronig-Penney model using $\delta\text{-}\delta'$ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite…
This text is a part of an unfinished project which deals with the generalized point interaction (GPI) in one dimension. We employ two natural parametrizations, which are known but have not attracted much attention, to express the resolvent…
The Kronig-Penney model describes what happens to electron states when a confining potential is repeated indefinitely. This model uses a square well potential; the energies and eigenstates can be obtained analytically for a the single well,…
We consider a complex periodic PT-symmetric potential of the Kronig-Penney type, in order to elucidate the peculiar properties found by Bender et al. for potentials of the form $V=i(\sin x)^{2N+1}$, and in particular the absence of…
A mechanism that produces conical dispersion relations is presented. A Kronig Penney one dimensional array with two different strengths delta function potentials gives rise to both the gap closure and the dispersion relation observed in…
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…
The spectrum of the self-adjoint Schr\"odinger operator associated with the Kronig-Penney model on the half-line has a band-gap structure: its absolutely continuous spectrum consists of intervals (bands) separated by gaps. We show that if…
We investigate the transmission properties of a quantum one-dimensional periodic system of fixed length $L$, with $N$ barriers of constant height $V$ and width $\lambda$, and $N$ wells of width $\delta$. In particular, we study the…
The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the…
We have previously discussed the classical diffusive system of the bounded one-dimensional multitrap using the transfer-matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig-Penney…
This work reports the study of the spectral properties of an open interacting system by solving the Generalized Kadanoff-Baym Ansatz (GKBA) master equation for the single-particle density matrix, namely the time-diagonal lesser Green…
The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of…
An old problem in mathematical physics deals with the structure of the dispersion relation of the Schr\"odinger operator $-\Delta+V(x)$ in $R^n$ with periodic potential near the edges of the spectrum. A well known conjecture says that…
We construct a one-dimensional contact interaction ($\epsilon$ potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the $\epsilon$ potential and the Dirac's $\delta$ function,…
We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy…
We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the…
We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $\gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert…
We introduced some contact potentials that can be written as a linear combination of the Dirac delta and its first derivative, the $\delta$-$\delta'$ interaction. After a simple general presentation in one dimension, we briefly discuss a…