Abstract
This paper will review the techniques which have been used to overcome the problems in applying Monte Carlo to fermion systems. They include the “fixed node approximation”; a projection method often called “transient estimation”; a method, applicable to few-body systems in which the appropriate Green’s functions are cancelled in part; several proposals for optimizing the unknown nodal surface; and removing a set of configurations in such a way as to minimize the effect upon expectations for fermion systems.
The successes achieved and the problems which remain will be outlined.
Supported by the U.S. Department of Energy under Grant AC 02-79ER10353.
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References
McMillan, W.L.: 1965, Phys. Rev. A 138, p.442.
Levesque, D., Khiet, Tu, Schiff, D., and Verlet, L.: Orsay report (1965), unpublished.
Ceperley, D.M. and Kalos, M.H.: “Monte Carlo Methods in Statistical Physics”, edited by K. Binder (Springer, Berlin, 1979) Chap. 4.
Courant, R., Friedrichs, K.D., and Loewy, H.: 1928, Math. Ann. 100, p32.
Metropolis, N. and Ulam, S.: 1949, J. Am. Stat. Ass. 44, p335.
Kalos, M.H.: 1962, Phys. Rev. 128, p1891;
Kalos, M.H.: 1970, Phys. Rev. A 2, p250.
Whitlock, P.A, and Kalos, M.H: Monte Carlo notes (unpublished)
Kalos, M.H., Levesque, D., and Verlet, L.: 1974, Phys. Rev. A 9, p2178.
Whitlock, P.A., Ceperley, D.M., Chester, G.V., and Kalos, M.H.: 1979, Phys. Rev. B 19, p5598.
Kalos, M.H., Lee, M.A., Whitlock, P.A., and Chester, G.V.: 1981, Phys. Rev. B 24, p115.
Pandharipande, V.R., et al.: (1983) Phys. Rev. Letts. 50, pp 1676–1678.
Aziz, R.A., et al.: 1979, J. Chem. Phys. 70, p4330.
Ceperley, D. and Alder, B.: 1980, Phys. Rev. Lett. 45, p566.
Lee, M.A., Schmidt, K.E., Kalos, M.H., and Chester, G.V.: 1981, Phys. Rev. Lett., 46, p728.
Anderson, J.B.: 1975, J. Chem. Phys. 63, p1499.
Moskowitz, J.W., Schmidt, K.E., Lee, M.A., and Kalos, M.H.: 1982, J. Chem. Phys. 77, p349.
Ceperley, D.M.: private communication.
Anderson, J.B.: 1980, J. Chem. Phys. 73, p3897;
Reynolds, P.J., Ceperley, D.M., Alder, B.J., and Lester, W.A.: 1982, J. Chem. Phys., 77, p5593.
Ceperley, D. and Alder, B.J.: 1981, Physica 108B, p875;
Ceperley, D. “A Review of Quantum Monte Carlo Methods and Results for Coulombic Systems”, this volume.
Reatto, L.: 1982, Phys. Rev. B 26, pp 130–136;
Masserini, G.L. and Reatto, L. “Maximum overlap Jastrow Wave Function of the Lennard-Jones Bose Fluid”, this volume.
Arnow, D., “Stochastic Solutions to the Schrodinger Equation for Fermions”, Dissertation, New York University (1981)
Arnow, D., Kalos, M.H., Lee, M.A., and Schmidt, K.E.: 1982, J. Chem. Phys. 77, p1.
Kalos, M.H.: “GFMC and the Many-Fermion Problem”, 1981, Lecture Notes in Physics, 142, Zabolitzky, J.G., et al., Eds, Springer-Verlag, p252.
Burkhard, R.E., and Derigs, U.: “Assignment and Matching Problems”, 1980, in Lecture notes in Economics and Mathematical Systems, Vol. 184, Beckmann, M., and Kunzi, H.P., Eds., Springer-Verlag.
Ceperley, D.M., private communication.
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© 1984 D. Reidel Publishing Company, Dordrecht, Holland
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Kalos, M.H. (1984). Optimization and the Many-Fermion Problem. In: Kalos, M.H. (eds) Monte Carlo Methods in Quantum Problems. NATO ASI Series, vol 125. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6384-9_3
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DOI: https://doi.org/10.1007/978-94-009-6384-9_3
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