Wave transport in one-dimensional disordered systems with finite-size scatterers

Abstract

We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are n barriers and wells with statistically independent intensities and with a spatial extension l c which may contain an arbitrary number δ/2π of wavelengths, where δ = kl c .We analyze the average Landauer resistance and transmission coefficient of the chain as a function of n and the phase parameter δ. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with n, ii) a regime, to be called II, for δ in the vicinity of π, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for δ very close to π, the formation of a band gap, which becomes ever more conspicuous as n increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with n and δ. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.

Resonant Anderson localization in segmented wires

“…The resonant behavior with one propa- gating mode is qualitatively similar to the behavior in strictly 1D systems discussed in Refs. [15,16]. We stress, however, that we also find similar resonances in higher energy regions, where more modes become propagating.…”

“…1b), a problem that was studied in Refs. [1][2][3][4]. In particular, we have followed the approach of Ref.…”

“…At low energies it was shown in Ref. [2] that the circular bend may be approximated by a 1D square well of depth V 0 = 2 /(2mR 2 ) and width 2a = 2Rθ, wherē R = R(R + d) is an average effective radius. In this approximation the scattering matrices are, of course, analytical.…”

“…The electrical transport properties of bend semiconductor nanowires attracted much interest some years ago [1][2][3][4]. In particular, phenomena such as the formation of localized states and the scattering behavior of circular bends were considered.…”

Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well

“…Particles moving along potential wells or potential barriers are paradigmatic systems in classical mechanics, quantum mechanics, and electrodynamics; for recent studies see Refs. [1][2][3][4][5][6][7][8]. This class of systems can be described by the use of different procedures that may range from quantum approaches, where the Schrödinger equation is solved, to classical-chaos investigations, where chaotic seas are characterized by Lyapunov exponents, passing through the description of phase transitions with the variation of control parameters, among other approaches [9][10][11][12][13][14].…”