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Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

Part of: Quantum theory Integral equations, integral transforms

Published online by Cambridge University Press:  03 July 2015

Ilkka Ruokosenmäki  and
Tapio T. Rantala
Ilkka Ruokosenmäki
Affiliation:
Department of Physics, Tampere University of Technology, Finland
Tapio T. Rantala*
Affiliation:
Department of Physics, Tampere University of Technology, Finland
*
*Corresponding author. Email addresses: Ilkka.Ruokosenmaki@tut.fi (I. Ruokosenmäki), Tapio.Rantala@tut.fi (T. T. Rantala)

Abstract

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Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of the Trotter kernel as compared with the exact kernels is tested. Also, a novel approach for finding the ground state and other stationary sates is presented. This is based on the incoherent propagation in real time. For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling. We asses the numerical prerequisites for all of the above.

Keywords

71.15.-m31.15.X-73.21.-bPath integralreal time domainquantum dynamicsincoherent propagationstationary states

MSC classification

Secondary: 81-08: Computational methods 65R20: Integral equations

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 91 - 103
Copyright
Copyright © Global-Science Press 2015 

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