Abstract
We study the equilibrium properties of a single quantum particle interacting with a classical lattice gas. We develop a path-integral formalism in which the quantum particle is represented by a closed, variable-step random walk on the lattice. After demonstrating that a Metropolis algorithm correctly predicts the properties of a free particle, we extend it to investigate the behavior of the quantum particle interacting with the lattice gas. Evidence of weak localization is observed under conditions of quenched disorder, while self-trapping clearly occurs for the fully annealed system. Compared with continuous space systems, convergence of Monte Carlo simulations in this minimum model is orders of magnitude faster in cpu time. Therefore the system behavior can be investigated for a much larger domain of thermodynamic parameters (e.g., density and temperature) in a reasonable time.
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REFERENCES
J. Hernandez, Rev. Mod. Phys. 63:675 (1991); D. Chandler and K. Leung, Annu. Rev. Phys. Chem. 45:557 (1994); G. N. Chuev, Izv. Akad. Nauk., Ser. Fiz. 61:1770 (1997).
For a review of both experimental and theoretical physics of positron annihilation in fluids see I. T. Iakubov and A. G. Khrapak, Prog. Phys. 45:697 (1982).
J. D. McNutt and S. C. Scharma, J. Chem. Phys. 68:130 (1978). S. C. Sharma, R. H. Arganbright, and M. H. Ward, J. Phys. B 20:867 (1987); S. C. Sharma and E. H. Juenguman, Phys. Lett. A 144:47 (1986).
P. Hautojarvi, K. Rytsola, P. Tuovinen, and P. Jauho, Phys. Lett. A 57:175 (1976).
N. Gee and G. R. Freeman, Can. J. Chem. 64:1810 (1986).
A. F. Borghesani and M. Santini, Linking the Gaseous and Condensed Phases of Matter: The Behavior of Slow Electrons, L. G. Christophorou, E. Illenberger, and W. Schmidt, eds. (Plenum, New York, 1994, Vol. 326); Phys. Rev. A 45:8803 (1992).
M. J. Stott and E. Zaremba, Phys. Rev. Lett. 38:1493 (1977).
B. Plenkiewicz, Y. Frongillo, and J. P. Jay-Gerin, Phys. Rev. E 47:419 (1993).
M. H. Cohen and J. Lekner, Phys. Rev. 158:305 (1967).
G. N. Chuev, J. Exp. Th. Phys. 88:807 (1999).
K. Ishi, Prog. Theor. Phys. Supp. 53:77 (1973).
M. Tuomisaari, K. Rytsola, and P. Hautojarvi, J. Phys. B 21:3917 (1988); T. J. Murphy and C. M. Surko, J. Phys. B 23:L727 (1990).
B. N. Miller and T. Reese, Phys. Rev. A 39:4735 (1989).
R. P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972).
G. A. Worrell and B. N. Miller,Phys. Rev. A 46:3380 (1992).
T. L. Reese and B. N. Miller, Phys. Rev. E 47:2581 (1993).
B. J. Berne and D. Thirumali, Ann. Rev. Phys. 37:401 (1986); J. S. Bader, B. J. Nerne, and P. Hanggi, J. Chem. Phys. 106:2372 (1997); J. Cao and B. J. Berne, J. Chem. Phys. 99:2902 (1993).
B. N. Miller, T. L. Reese, and G. A. Worrell, Phys. Rev. E 47:4083 (1993).
A. L. Nichols III, D. Chandler, Y. Singh, and D. M. Richardson, J. Chem. Phys. 81:5109 (1984).
J. Chen and B. N. Miller, Phys. Rev. E 48:3667 (1993).
J. Chen and B. N. Miller, J. Chem. Phys. 100:3013 (1994).
J. Chen and B. N. Miller, Phys. Rev. B 49:615 (1994).
I. Chang, K. Ikeyawa, and M. Kohmoto, Phys. Rev. B 55:12971 (1997); N. W. Ashcroft and D. Mermin, Solid State Physics (Holt, Rinehart, and Winston, 1976).
M. H. Kalos and P. A. Whitlock, Monte Carlo Methods Volume I: Basics (John Wiley, New York, 1986).
R. K. Pathria, Statistical Mechanics, 2nd ed. (Butterworth-Heinemann, 1996).
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Guo, H., Miller, B.N. Monte Carlo Study of Localization on a One-Dimensional Lattice. Journal of Statistical Physics 98, 347–374 (2000). https://doi.org/10.1023/A:1018687124911
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DOI: https://doi.org/10.1023/A:1018687124911