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Title: Perfectly Matched Layers versus discrete transparent boundary conditions in quantum device simulations

Discrete transparent boundary conditions (DTBC) and the Perfectly Matched Layers (PML) method for the realization of open boundary conditions in quantum device simulations are compared, based on the stationary and time-dependent Schrödinger equation. The comparison includes scattering state, wave packet, and transient scattering state simulations in one and two space dimensions. The Schrödinger equation is discretized by a second-order Crank–Nicolson method in case of DTBC. For the discretization with PML, symmetric second-, fourth-, and sixth-order spatial approximations as well as Crank–Nicolson and classical Runge–Kutta time-integration methods are employed. In two space dimensions, a ring-shaped quantum waveguide device is simulated in the stationary and transient regime. As an application, a simulation of the Aharonov–Bohm effect in this device is performed, showing the excitation of bound states localized in the ring region. The numerical experiments show that the results obtained from PML are comparable to those obtained using DTBC, while keeping the high numerical efficiency and flexibility as well as the ease of implementation of the former method. -- Highlights: •In-depth comparison between discrete transparent boundary conditions (DTBC) and PML. •First 2-D transient scattering state simulations using DTBC. •First 2-D transient scattering state simulations of the Aharonov–Bohm effect.
Authors:
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Publication Date:
OSTI Identifier:
22382127
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 275; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AHARONOV-BOHM EFFECT; APPROXIMATIONS; BOUND STATE; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; EXCITATION; FLEXIBILITY; LAYERS; SCATTERING; SCHROEDINGER EQUATION; SYMMETRY; TIME DEPENDENCE; TRANSIENTS; WAVE PACKETS