Related papers: Analytically solvable quasi-one-dimensional Kronig…
The one-dimensional Kronig-Penney potential in the Schr\"{o}dinger equation, a standard periodic potential in quantum mechanics textbooks known for generating band structures, is solved by using the finite difference method with periodic…
We study the nonlinear Schr\"odinger equation with a periodic delta-function potential. This realizes a nonlinear Kr\"onig-Penney model, with physical applications in the context of trapped Bose-Einstein condensate alkaly gases and in the…
We study the conductance properties of a straight two-dimensional electron waveguide with an s-like scatterer modeled by a single delta-function potential with a finite number of modes. Even such a simple system exhibits interesting…
We solve the two-particle s-wave scattering for an ultracold atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included in terms of Fermi's pseudopotential.…
In the paper the one-dimensional one-center scattering problem with the initial potential $\alpha |x|^{-1}$ on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as…
We use the renormalization group method to study the normal state of quasi-one-dimensional superconductors nearby a spin-density-wave instability. On the basis of one-loop scattering amplitudes for the quasi-one-dimensional electron gas,…
A mechanism to modify the energy band structure is proposed by considering a chain of periodic scatterers forming a linear lattice around which an external cylindrical trapping potential is applied along the chain axis. When this trapping…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
We calculate the self-energy of one-dimensional electron band with the three-dimensional long range Coulomb interaction within the random phase approximation, paying particular attention to the contribution coming from the electron…
We present one-dimensional KKR method with the aim to elucidate its linear features, particularly important in optimizing the numerical algorithms in energy bands computations. The conventional KKR equations based on the multiple scattering…
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,…
A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate…
We revisit the confinement-induced p-wave resonance in quasi-one-dimensional (quasi-1D) atomic gases and study the induced molecules near resonance. We derive the reduced 1D interaction parameters and show that they can well predict the…
We consider a one-body spin-less electron spectral problem for a resonance scattering system constructed of a quantum well weakly connected to a noncompact exterior reservoir, where the electron is free. The simplest kind of the resonance…
A microwave setup for mode-resolved transport measurement in quasi-one-dimensional (quasi-1D) structures is presented. We will demonstrate a technique for direct measurement of the Green's function of the system. With its help we will…
In this paper we consider the 1D Schr\"odinger operator $H$ with periodic point interactions. We show an $L^1-L^\infty$ bound for the time evolution operator $e^{-itH}$ restricted to each energy band with decay order $O(t^{-1/3})$ as $t\to…
We study quantum transport properties of finite periodic quasi-one-dimensional waveguides whose classical dynamics is diffusive. The system we consider is a scattering configuration, composed of a finite periodic chain of $L$ identical…
The goal of this paper is to construct an effective model for studying the asymptotic solution of the scattering problem of three one-dimensional quantum particles with finite (short-range) attractive pair potentials. The asymptotic nature…
We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…
We study the transverse-size effect of a quasi-one-dimensional rectangular waveguide on the single-photon scattering on a two-level system. We calculate the transmission and reflection coefficients for single incident photons using the…