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Title: Real time visualization of quantum walk

Time evolution of quantum particles like electrons is described by time-dependent Schrödinger equation (TDSE). The TDSE is regarded as the diffusion equation of electrons with imaginary diffusion coefficients. And the TDSE is solved by quantum walk (QW) which is regarded as a quantum version of a classical random walk. The diffusion equation is solved in discretized space/time as in the case of classical random walk with additional unitary transformation of internal degree of freedom typical for quantum particles. We call the QW for solution of the TDSE a Schrödinger walk (SW). For observation of one quantum particle evolution under a given potential in atto-second scale, we attempt a successive computation and visualization of the SW. Using Pure Data programming, we observe the correct behavior of a probability distribution under the given potential in real time for observers of atto-second scale.
Authors:
; ;  [1]
  1. Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tenpaku-cho, Toyohashi, 441-8580 Aichi (Japan)
Publication Date:
OSTI Identifier:
22266053
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1585; Journal Issue: 1; Conference: IRAGO conference 2013, Aichi (Japan), 24-25 Oct 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; DEGREES OF FREEDOM; DIFFUSION; DIFFUSION EQUATIONS; GRAPH THEORY; MATHEMATICAL SOLUTIONS; PARTICLES; PROBABILITY; TIME DEPENDENCE