Analytical and numerical study of a curved planar waveguide with combined Dirichlet and Neumann boundary conditions in a uniform magnetic field

Abstract

A model of a thin straight strip with a uniformly curved section and with different uniform boundary conditions on the opposite edges subjected to the homogeneous magnetic field B is theoretically analyzed within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers and superconducting films. In particular, for the inner Dirichlet and outer Neumann boundaries, it is shown that bend-induced enhancement of the superconductivity survives in the magnetic field with the order parameter ⌿͑r͒ being pushed stronger and stronger to the Neumann surface with increasing B and, simultaneously, the area where the nucleation of the superconductivity takes place is spread more and more in the straight arms. Various magnetotransport properties of the film such as interference blockade of the supercurrent flow at some special field-dependent temperatures are also discussed with special attention being paid to the formation and evolution of the vortices, which appear as a result of the bend-induced interaction between the different subbands; it is shown, in particular, that the number of vortices decreases with the field and some of them transform into the antivortices. A proof of the very close analogy between two kinds of strips, ͑1͒ pure Dirichlet condition on both edges and ͑2͒ inner Dirichlet and outer Neumann requirements, derived earlier for B = 0 is extended to the case of nonzero fields.

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

“…The linear dependence of the latter function at large distance between the third particle and the bound pair leads to asymptotic expression (13) for the first-channel function in the expansion (2). On the other hand, the expression ( 13) is consistent with the asymptotic solution of the first-channel equation in (10), in which the long-range terms P 11 (ρ) and −1/(4ρ 2 ) cancel each other at large ρ.…”

“…Dynamics of few particles confined in low dimensions is of interest in connection with numerous investigations ranging from atoms in ultra-cold gases [1, 2,3,4,5,6,7] to nonostructures [8,9,10]. Experiments with ultra-cold gases in the one-dimensional (1D) and quasi-1D traps have been recently performed [1,11,12,13], amid the rapidly growing interest to the investigation of mixtures of ultra-cold gases [14,15,16,17,18,19,20].…”

Tuning the electrical resistivity of semiconductor thin films by nanoscale corrugation

“…It was theoretically suggested [16,17,18,19] that an electron moving in a thin curved layer experiences potential energy whose sign and magnitude depend on the local geometric curvature. Such a curvature-induced potential has been observed to cause many intriguing phenomena [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]: such as bound states of non-interacting electrons in deformed cylinders [40,41,42] and energy band gaps in periodic curved surfaces [43,44,45,46]. Quite recently, surface curvature was found to markedly affect interacting electrons in the quasi-one dimension, resulting in a significant shift in the Tomonaga-Luttinger exponent of thin hollow cylinders subject to periodic surface deformation [47].…”

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

“…We remark that the linearised GL equation (9) which is the main subject of the present study correctly captures the physical phenomena in the uniform magnetic field B and temperature T ranges close to the transition to the normal state when the order parameter Ψ(r) is small and, accordingly, the cubic term in (10) can be safely neglected [31]. The influence of the cubic term can be strongly suppressed also by the choice of the metal or alloy [65] since the GL parameter β contains material-dependent density of states at the Fermi energy N (0), coherence length ξ(0), critical temperature T c and the mean free path l [31]. In addition, it can be shown that equations derived below for the linear case follow also from the complete nonlinear GL theory [52,53].…”