Abstract
Non-adiabatic dynamics in mixed quantum-classical systems is investigated. The mixed quantum-classical system comprises a quantum system coupled to a classical environment. The starting point for the analysis is an evolution equation for the density matrix expressed in a basis of adiabatic quantum states that describes the full quantum dynamics of the subsystem and its coupling to the bath. Since the quantum dynamics influences the evolution of the “classical” degrees of freedom, a description in terms of single Newtonian trajectories is not possible. Through explicit calculations of a two-level quantum system coupled to a low dimensional bath we examine the details of mixed quantum-classical dynamics and its representation in terms of an ensemble of surface-hopping classical trajectory segments.
Similar content being viewed by others
REFERENCES
P. Pechukas, Phys. Rev. 181:166, 174 (1969).
E. Wigner, Phys. Rev. 40:749 (1932); K. Imre, E. Özizmir, M. Rosenbaum, and P. F. Zwiefel, J. Math. Phys. 5:1097 (1967).
R. Kapral and G. Ciccotti, J. Chem. Phys. 110:8919 (1999).
W. Y. Zhang and R. Balescu, J. Plasma Phys. 40:199 (1988); R. Balescu and W. Y. Zhang, J. Plasma Phys. 40:215 (1988).
Two-level mixed quantum-classical systems have been considered in C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106:4918 (1996); A. Donoso and C. C. Martens, J. Phys. Chem. 102:4291 (1998).
See, for example, A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59:1 (1987).
S. Nielsen, R. Kapral, and G. Ciccotti, J. Chem. Phys. 112, April 15 (2000).
J. C. Tully, in Modern Methods for Multidimensional Dynamics Computations in Chemistry, D. L. Thompson, ed. (World Scientific, New York, 1998), p. 34; M. F. Herman, Annu. Rev. Phys. Chem. 45:83 (1994).
H. J. Berendsen and J. Mavri, J. Phys. Chem. 97:13464 (1993); P. Bala, B. Lesyng, and J. A. McCammon, Chem. Phys. Lett. 219:259 (1994); F. A. Bornemann, P. Nettesheim, and C. Schütte, J. Chem. Phys. 105:1074 (1996).
Y. Tanimura and S. Mukamel, J. Chem. Phys. 101:3094 (1994).
J. C. Tully, J. Chem. Phys. 93:1061 (1990); J. C. Tully, Int. J. Quantum Chem. 25:299 (1991); D. S. Sholl and J. C. Tully, J. Chem. Phys. 109:7702 (1998); S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101:4657 (1994); Kohen, F. Stillinger, and J. C. Tully, J. Chem. Phys. 109:4713 (1998).
L. Xiao and D. F. Coker, J. Chem. Phys. 100:8646 (1994); D. F. Coker and L. Xiao, J. Chem. Phys. 102:496 (1995); H. S. Mei and D.F. Coker, J. Chem. Phys. 104:4755 (1996).
F. Webster, P. J. Rossky, and P. A. Friesner, Comp. Phys. Comm. 63:494 (1991); F. Webster, E. T. Wang, P. J. Rossky, and P. A. Friesner, J. Chem. Phys. 100:483 (1994).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nielsen, S., Kapral, R. & Ciccotti, G. Non-Adiabatic Dynamics in Mixed Quantum-Classical Systems. Journal of Statistical Physics 101, 225–242 (2000). https://doi.org/10.1023/A:1026458004345
Issue Date:
DOI: https://doi.org/10.1023/A:1026458004345