Transport properties of quantum-classical systems

Journal of Chemical Physics

Volumn 122, Issue 21, 2005, Pages

  Kim, Hyojoon ^a   Kapral, Raymond ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

HARMONIC OSCILLATORS; QUANTUM TRANSFER PROCESSES; QUANTUM-CLASSICAL SYSTEMS; SPECTRAL DENSITY FUNCTION;

COMPUTER SIMULATION; CORRELATION METHODS; HARMONIC ANALYSIS; KINETIC ENERGY; MATRIX ALGEBRA; OSCILLATORS (ELECTRONIC); POTENTIAL ENERGY; RATE CONSTANTS; TRANSPORT PROPERTIES;

QUANTUM THEORY;

EID: 21244437963     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1925268     Document Type: Article

References (37)

1. R. Kubo, Rep. Prog. Phys. 29, 255 (1966).
2. Methods based on quantum mode-coupling techniques [E. Rabani and D. Reichman, J. Chem. Phys. 0021-9606 10.1063/1.1631436 120, 1458 (2004); A. A. Golosov, D. R. Reichman, and E. Rabani, J. Chem. Phys. 0021-9606 10.1063/1.1535214 118, 457 (2003)] and the initial value representation [M. Thoss, H. Wang, and W. H. Miller, J. Chem. Phys. 114, 47 (2001)] have been used to evaluate quantum correlation functions.
3. Methods based on quantum mode-coupling techniques [E. Rabani and D. Reichman, J. Chem. Phys. 0021-9606 10.1063/1.1631436 120, 1458 (2004); A. A. Golosov, D. R. Reichman, and E. Rabani, J. Chem. Phys. 0021-9606 10.1063/1.1535214 118, 457 (2003)] and the initial value representation [M. Thoss, H. Wang, and W. H. Miller, J. Chem. Phys. 114, 47 (2001)] have been used to evaluate quantum correlation functions.
4. Methods based on quantum mode-coupling techniques [E. Rabani and D. Reichman, J. Chem. Phys. 0021-9606 10.1063/1.1631436 120, 1458 (2004); A. A. Golosov, D. R. Reichman, and E. Rabani, J. Chem. Phys. 0021-9606 10.1063/1.1535214 118, 457 (2003)] and the initial value representation [M. Thoss, H. Wang, and W. H. Miller, J. Chem. Phys. 114, 47 (2001)] have been used to evaluate quantum correlation functions.
5. P. Pechukas, Phys. Rev. 181, 166 (1969).
6. M. F. Herman, Annu. Rev. Phys. Chem. 45, 83 (1994).
7. J. C. Tully, Modern Methods for Multidimensional Dynamics Computations in Chemistry, edited by, D. L. Thompson, (World Scientific, Singapore, 1998), p. 34.
8. R. Kapral and G. Ciccotti, Lect. Notes Phys. 605, 445 (2002).
9. R. Kapral and G. Ciccotti, J. Chem. Phys. 110, 8919 (1999).
10. I. V. Aleksandrov, Z. Naturforsch. A 36A, 902 (1981).
11. V. I. Gerasimenko, Reports of Ukrainian Academy Science 10, 65 (1981); V. I. Gerasimenko, Teor. Mat. Fiz. 150, 7 (1982).
12. V. I. Gerasimenko, Reports of Ukrainian Academy Science 10, 65 (1981); V. I. Gerasimenko, Teor. Mat. Fiz. 150, 7 (1982).
13. C. C. Martens and J.-Y. Fang, J. Chem. Phys. 0021-9606 10.1063/1.473541 106, 4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998).
14. C. C. Martens and J.-Y. Fang, J. Chem. Phys. 0021-9606 10.1063/1.473541 106, 4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998).
15. I. Horenko, C. Salzmann, B. Schmidt, and C. Schütte, J. Chem. Phys. 117, 11075 (2002).
16. Q. Shi and E. Geva, J. Chem. Phys. 121, 3393 (2004).
17. S. Nielsen, R. Kapral, and G. Ciccotti, J. Chem. Phys. 115, 5805 (2001).
18. A. Sergi and R. Kapral, J. Chem. Phys. 121, 7565 (2004).
19. K. Thompson and N. Makri, J. Chem. Phys. 110, 1343 (1999).
20. J. A. Poulson, G. Nyman, and P. J. Rossky, J. Chem. Phys. 119, 12179 (2003).
21. H. Kim and P. J. Rossky, J. Phys. Chem. B 106, 8240 (2002).
22. Q. Shi and E. Geva, J. Chem. Phys. 108, 6109 (2004).
23. S. Bonella and D. F. Coker, LAND-Map, a Linearized Approach to Nonadiabatic Dynamics Using the Mapping Formalism (to be published).
24. Apart from cross-transport coefficients that couple fluxes and forces for different variables, most often we are interested in situations where B̂ = Â, and this condition is trivially satisfied.
25. In general, transport coefficients are defined in terms of flux-flux correlation functions involving projected dynamics for which the infinite time integral is well defined. In practice, projected dynamics is replaced by ordinary dynamics and the transport coefficient is determined from the plateau value of the finite-time integral, assuming that a separation of time scales exists.
26. E. P. Wigner, Phys. Rev. 0031-899X 10.1103/PhysRev.40.749 40, 749 (1932); K. Imre, E. Özizmir, M. Rosenbaum, and P. F. Zwiefel, J. Math. Phys. 0022-2488 5, 1097 (1967); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
27. E. P. Wigner, Phys. Rev. 0031-899X 10.1103/PhysRev.40.749 40, 749 (1932); K. Imre, E. Özizmir, M. Rosenbaum, and P. F. Zwiefel, J. Math. Phys. 0022-2488 5, 1097 (1967); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
28. E. P. Wigner, Phys. Rev. 0031-899X 10.1103/PhysRev.40.749 40, 749 (1932); K. Imre, E. Özizmir, M. Rosenbaum, and P. F. Zwiefel, J. Math. Phys. 0022-2488 5, 1097 (1967); M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
29. One may show that the evolution equation involving the differential operator i LW (X) is equivalent to the integro-differential equation derived by S. Filinov, Y. V. Medvedev, and V. L. Kamskyi, Mol. Phys. 0026-8976 85, 711 (1995); V. S. Filinov, Mol. Phys. 0026-8976 10.1080/00268979650025605 88, 1517 (1996); V. S. Filinov, Mol. Phys. 88, 1529 (1996).
30. One may show that the evolution equation involving the differential operator i LW (X) is equivalent to the integro-differential equation derived by S. Filinov, Y. V. Medvedev, and V. L. Kamskyi, Mol. Phys. 0026-8976 85, 711 (1995); V. S. Filinov, Mol. Phys. 0026-8976 10.1080/00268979650025605 88, 1517 (1996); V. S. Filinov, Mol. Phys. 88, 1529 (1996).
31. One may show that the evolution equation involving the differential operator i LW (X) is equivalent to the integro-differential equation derived by S. Filinov, Y. V. Medvedev, and V. L. Kamskyi, Mol. Phys. 0026-8976 85, 711 (1995); V. S. Filinov, Mol. Phys. 0026-8976 10.1080/00268979650025605 88, 1517 (1996); V. S. Filinov, Mol. Phys. 88, 1529 (1996).
32. R. P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972).
33. D. Mac Kernan, G. Ciccotti, and R. Kapral, J. Phys.: Condens. Matter 14, 9069 (2002).
34. A. Sergi and R. Kapral, J. Chem. Phys. 118, 8566 (2003).
35. H. Kim and R. Kapral (unpublished).
36. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
37. I. Burghardt and G. Parlant, J. Chem. Phys. 120, 3055 (2004).