Volume 18, Issue 1
Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

Ilkka Ruokosenm¨aki & Tapio T. Rantala

Commun. Comput. Phys., 18 (2015), pp. 91-103.

Published online: 2018-04

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  • Abstract

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.

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@Article{CiCP-18-91, author = {Ilkka Ruokosenm¨aki and Tapio T. Rantala}, title = {Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {1}, pages = {91--103}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180914.161214a}, url = {http://global-sci.org/intro/article_detail/cicp/11019.html} }
TY - JOUR T1 - Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States AU - Ilkka Ruokosenm¨aki & Tapio T. Rantala JO - Communications in Computational Physics VL - 1 SP - 91 EP - 103 PY - 2018 DA - 2018/04 SN - 18 DO - http://dor.org/10.4208/cicp.180914.161214a UR - https://global-sci.org/intro/cicp/11019.html KW - AB -

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.

Ilkka Ruokosenm¨aki & Tapio T. Rantala. (1970). Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States. Communications in Computational Physics. 18 (1). 91-103. doi:10.4208/cicp.180914.161214a
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