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Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

  • Ilkka Ruokosenmäki (a1) and Tapio T. Rantala (a1)

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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Corresponding author

*Corresponding author. Email addresses: Ilkka.Ruokosenmaki@tut.fi (I. Ruokosenmäki), Tapio.Rantala@tut.fi (T. T. Rantala)

References

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[1]Feynman, R.P. and Hibbs, A.R., Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
[2]Feynman, R.P., Rev. Mod. Phys. 20, 367 (1948).
[3]Duru, I.H. and Kleinert, H., Phys. Lett. 84B, 185 (1979) and Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets. World Scientific Publishing Co. Pte. Ltd. Singapore (2004). The 5th edition.
[4]Schulman, L.S., Techniques and Applications of Path Integration (Wiley, New York, 1981).
[5]Wong, K.-Y., Commun. Comput. Phys. 15, 853 (2014).
[6]Ceperley, D.M., Rev. Mod. Phys. 67, 279 (1995).
[7]Kylänpää, I., PhD Thesis (Tampere University of Technology 2011).
[8]Kylänpää, I. and Rantala, T.T., J. Chem. Phys. 133, 044312 (2010), Kylänpää, I. and Rantala, T.T., J. Chem. Phys. 135, 104310(2011) and Kylänpää, I. and Rantala, T.T., Phys. Rev. A 80, 024504 (2009).
[9]Militzer, and Ceperley, D.M., Phys. Rev. B 63, 066404 (2001).
[10]Weiss, S. and Egger, R., Phys. Rev. B 72, 245301 (2005).
[11]Gull, E.et al., Rev. Mod. Phys. 83, 349 (2011).
[12]Makri, N., Comp. Phys. Comm. 63, 389414.
[13]Makri, N., Chem. Phys. Lett. 193, 435 (1992).
[14]Filinov, V.S., Nucl. Phys. B 271, 717725 (1986).
[15]Wang, H.et al., J. Chem. Phys. 115, 6317(2001).
[16]Makri, N., Ann. Rev. Phys. Chem. 50, 167191 (1999) and Jadhao, V. and Makri, N., J. Chem. Phys. 132, 104110 (2010).
[17]Marchioro, T.L. and Beck, T.L., J. Chem. Phys. 96, 2966 (1992).
[18]Makri, N., Comp. Phys. Comm. 63, 389414 (1991) and Makri, N., J. Math. Phys. 36, 2430–56 (1995).
[19]Lambert, R. and Makri, N., J. Chem. Phys. 137 22A552 and 22A553 (2012).
[20]Makarov, D.E. and Makri, N., Chem. Phys. Lett. 221, 482 (1994).
[21]Kolmogorov, A., G.Ist.Ital.Attuari 4, 83 (1933).
[22]Suzuki, M., Phys. Lett. A 201, 425428 (1995).
[23]Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, H. and Teller, E., J. Chem. Phys. 21, 1087 (1953).
[24]Atkins, P. and Friedman, R., Molecular Quantum Mechanics (Oxford University Press Inc., New York, 2005). The 4th edition.
[25]Schulten, K., “Notes on Quantum Mechanics” (University of Illinois at Urbana Champaign, 2000).

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Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

  • Ilkka Ruokosenmäki (a1) and Tapio T. Rantala (a1)

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