Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems

Journal of Computational Physics

Volumn 209, Issue 2, 2005, Pages 559-581

  Dauger, D E ^a,b   Decyk, V K ^b   Dawson, J M ^b  

^a Dauger Research Inc ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Feynman; Grid method; Interacting; Lagrangian; Parallel computation; Particle based; Path integral; Plasma PIC; Quantum particle in cell; Semiclassical; Stationary phase; Time evolving; WKB

Indexed keywords

PLASMA SIMULATION; QUANTUM OPTICS;

FEYNMAN; GRID METHODS; INTERACTING; LAGRANGIAN; PARALLEL COMPUTATION; PARTICLE IN CELL; PARTICLE-BASED; PATH INTEGRAL; PLASMA PIC; QUANTUM PARTICLE-IN-CELL; QUANTUM PARTICLES; SEMICLASSICAL; STATIONARY PHASE; TIME EVOLVING; WKB;

COMPUTATION THEORY;

EID: 21444457592     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.03.028     Document Type: Article

References (59)

1. R.B. Gerber V. Buch M.A. Ratner Simplified time-dependent self consistent field approximation for intramolecular dynamics Chem. Phys. Lett. 91 1982 173
2. U. Peskin M. Steinberg A temperature-dependent Schrödinger equation based on a time-dependent self consistent field approximation J. Chem. Phys. 109 1998 704
3. K.M. Christoffel P. Brumer Quantum and classical dynamics in the stadium billiard Phys. Rev. A 33 1986 1309
4. E.J. Heller Frozen Gaussians: A very simple semiclassical approximation J. Chem. Phys. 75 1981 2923
5. N. Makri Time-dependent self-consistent field approximation with explicit 2-body correlations Chem. Phys. Lett. 169 1990 541
6. L. de Broglie Recherches sur la théorie des Quanta Ann. d. Phys. 3 10 1925 22 (Thèses Paris 1924)
7. J.H. Van Vleck The correspondence principle in the statistical interpretation of quantum mechanics Proc. Natl. Acad. Sci. USA 14 1928 178
8. Commonly known today as "WKB", the method, as it was originally presented, was designed specifically for solving Schrödinger's equation of wave mechanics. It is in such common use today that citations to the original references are difficult to find. The original three papers are: G. Wentzel Eine Verallgemeinerung der Quantenbedingungen für Zwecke der Wellenmechanik Z. Phys. 38 1926 518
9. H.A. Kramers Wellenmechanik und halbzahlige Quantisierung Z. Phys. 39 1926 828
10. L. Brillouin La mècanique ondulatoire de Schrödinger; une mèthode gènèrale de rèsolution par approximations successives C.R. Acad. Sci. 183 1926 24
11. E. Schrödinger Quantiseirung als Eigenwertproblem Ann. d. Phys. 79 1926 361
12. E. Schrödinger Ann. d. Phys. 79 1926 489
13. E. Schrödinger Ann. d. Phys. 80 1926 437
14. E. Schrödinger Ann. d. Phys. 81 1926 109
15. P.M. Dirac Phys. Z. Sowjetunion 3 1933 1
16. R.P. Feynman Rev. Mod. Phys. 20 1948 367-387
17. R.P. Feynman A.R. Hibbs Quantum Mechanics and Path Integrals 1965 McGraw-Hill New York
18. M.C. Gutzwiller Phase-integral approximation in momentum space and the bound states of an atom J. Math. Phys. 8 1967 1979
19. E. Heller J. Chem. Phys. 94 1991 2723
20. S. Tomsovic E. Heller Phys. Rev. Lett. 67 6 1991 664
21. E. Heller S. Tomsovic Postmodern quantum mechanics Phys. Today 46 7 1993 38 and references therein
22. S. Tomsovic E. Heller Phys. Rev. Lett. 70 1993 1405
23. S. Tomsovic E.J. Heller Long-time semiclassical dynamics of chaos: The stadium billiard Phys. Rev. E 47 1993 282
24. V.P. Maslov M.V. Fedoriuk Semiclassical Approximations in Quantum Mechanics 1981 Reidel Dordrecht (English translation)
25. L.S. Schulman Techniques and Applications of Path Integration 1981 Wiley New York and references therein
26. M.A. Sepúlveda S. Tomsovic E. Heller Phys. Rev. Lett. 69 1992 402
27. M.C. Gutzwiller Chaos in classical and quantum mechanics 1990 Springer-Verlag New York
28. O. Buneman Phys. Rev. 115 1959 503
29. J.M. Dawson, Princeton University Plasma Physics Laboratory, Project Matterhorn Rept., MATT-4, 1959
30. J.M. Dawson, Princeton University Plasma Physics Laboratory, Project Matterhorn Rept., MATT-31, 1960
31. J.M. Dawson Phys. Fluids 5 1962 445
32. J.M. Dawson in: Alder Fernbach Rotenburg (Eds.) Methods in Computational Physics vol. 9 1970 Academic Press New York 1
33. R.W. Hockney Phys. Fluids 9 1966 1826
34. J.W. Cooley J.W. Tukey Math. Comput. 19 1965 297
35. J.M. Dawson, C.G. Hsi, R. Shanny, Princeton University Plasma Physics Laboratory, Project Matterhorn Rept., MATT-719, 1969
36. J.M. Dawson Rev. Mod. Phys. 55 1983 403
37. J.M. Dawson V.K. Decyk R.D. Sydora P. Liewer High-performance computing and plasma physics Phys. Today 46 3 1993 64
38. V.K. Decyk, Parallel processing of particle simulation models, in: M.F. Heyn, W. Kernbichler (Eds.), Proceedings of the International Workshop on Plasma Physics, Pichl, Austria, February 1992, Current Topics in Astrophysical and Fusion Plasma Research, dbu-[Dbu Graz, Austria, 1992], p. 187
39. J.M. Dawson V.K. Decyk Particle modeling of plasmas on super-computers Int. J. Supercomput. Appl. 1 1987 24
40. J.M. Dawson, The numerical Tokamak: A grand challenge for fusion plasma modeling, in: Proceedings of IAEA Technical Committee Meeting on Advances in Simulation and Modeling Thermonuclear Plasmas, Montreal, Que., Canada, vol. 1, 1992
41. J.M. Dawson Computer modeling of plasma: Past, present, future Phys. Plasmas 2 1995 6
42. V.K. Decyk How to write (nearly) portable Fortran programs for parallel computers Comput. Phys. 7 1993 418
43. V.K. Decyk Skeleton PIC Codes for parallel computers Comput. Phys. Commun. 87 1995 87
44. V.K. Decyk D.E. Dauger P.R. Kokelaar How to build an AppleSeed: A parallel Macintosh cluster for numerically intensive computing Phys. Scr. T 84 2000 85-88
45. M.F. Herman E. Kluk H.L. Davis Comparison of the propagation of semiclassical frozen Gaussian wave functions with quantum propagation for a highly excited anharmonic oscillator J. Chem. Phys. 84 1986 326
46. M.S. Child Semiclassical Mechanics with Molecular Applications 1991 Clarendon Press Oxford
47. K.G. Kay Semiclassical propagation for multidimensional systems by an initial value method J. Chem. Phys. 101 3 1994 2250
48. A.R. Walton D.E. Manolopoulos A new semiclassical initial value method for Franck-Condon spectra Mol. Phys. 87 1996 961
49. X. Sum H.B. Wang W.H. Miller Semiclassical theory of electronically nonadiabatic dynamics: Results of a linearized approximation to the initial value representation J. Chem. Phys. 109 1998 7064
50. K. Thompson N. Makri Rigorous forward-backward semiclassical formation of many-body dynamics Phys. Rev. E 59 1999 4729
51. L. Kaplan E.J. Heller Overcoming the wall in semiclassical Baker's map Phys. Rev. Lett. 76 1996 1453
52. G. Campolieti P. Brumer Semiclassical initial value approach for chaotic long-lived dynamics J. Chem. Phys. 109 1998 2999
53. N.T. Maitra E.J. Heller Semiclassical amplitudes: Supercaustics and the whisker map Phys. Rev. A 61 1999 0212107-1
54. M. Brack R.K. Bhaduri Semiclassical Physics 1997 Addison-Wesley New York and references therein
55. E.J. Heller, Proceedings from Les Houchs 1989, in: Chaos and Quantum Physics, North-Holland, Amsterdam, 1989
56. F.P. Simotti E. Vergini M. Saraceno Quantitative study of scars in the boundary section of the stadium billiard Phys. Rev. E 56 1997 3859
57. J.S. Townsend A Modern Approach to Quantum Mechanics 1992 McGraw-Hill New York
58. N.T. Maitra E.J. Heller Phys. Rev. Lett. 78 1997 3035
59. D.H. Zhang E. Pollak Phys. Rev. Lett. 93 2004 140401