Sequential short-time propagation of quantum-classical dynamics

An algorithm for the simulation of quantum–classical dynamics is presented. Quantum–classical evolution is effected by a propagator exp (i t) involving the quantum classical Liouville operator that describes the evolution of a quantum subsystem coupled to a classical bath. Such a mixed description provides a means to study the dynamics of complex many-body systems where certain degrees of freedom are treated quantum mechanically. The algorithm is constructed by decomposing the time interval t into small segments of length Δt and successively applying the propagator in the short time segments to obtain the evolution for long times. The algorithm is shown to be a discretization of the iterated Dyson form of the propagator whose direct solution is vexatious. The sequential short-time propagation algorithm is applied to the spin-boson model for a range of values of the Kondo parameter and shown to be effective.

[1]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

[2]  Giovanni Ciccotti,et al.  ARTICLES Surface-hopping dynamics of a spin-boson system , 2002 .

[3]  Giovanni Ciccotti,et al.  A Statistical Mechanical Theory of Quantum Dynamics in Classical Environments , 2002 .

[4]  G. Ciccotti,et al.  Mixed quantum-classical dynamics , 1999 .

[5]  Nancy Makri,et al.  Influence functionals with semiclassical propagators in combined forward-backward time , 1999 .

[6]  Nancy Makri,et al.  The Linear Response Approximation and Its Lowest Order Corrections: An Influence Functional Approach , 1999 .

[7]  D. Coker,et al.  Methods for molecular dynamics with nonadiabatic transitions , 1994, chem-ph/9408002.

[8]  D. Sholl,et al.  A generalized surface hopping method , 1998 .

[9]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[10]  Giovanni Ciccotti,et al.  Statistical mechanics of quantum-classical systems , 2001 .

[11]  Giovanni Ciccotti,et al.  Mixed quantum-classical surface hopping dynamics , 2000 .

[12]  R. Levine,et al.  Molecular Collision Dynamics on Several Electronic States , 1997 .

[13]  D. Coker,et al.  The influence of nonadiabatic rotational transitions on the line shapes of the rotational Raman spectrum of H2 in liquid argon , 1994 .

[14]  S. Hammes-Schiffer,et al.  Proton transfer in solution: Molecular dynamics with quantum transitions , 1994 .

[15]  David F. Coker,et al.  QUANTUM MOLECULAR DYNAMICS STUDIES OF H2 TRANSPORT IN WATER , 1996 .

[16]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

[17]  G. Ciccotti,et al.  Non-Adiabatic Dynamics in Mixed Quantum-Classical Systems , 2000 .

[18]  Craig C. Martens,et al.  Semiclassical-limit molecular dynamics on multiple electronic surfaces , 1997 .

[19]  J. Tully.  Nonadiabatic molecular dynamics , 1991 .

[20]  Richard A. Friesner,et al.  Nonadiabatic processes in condensed matter: semi-classical theory and implementation , 1991 .

[21]  Jeremy Schofield,et al.  Mixed quantum-classical molecular dynamics: Aspects of the multithreads algorithm , 2000 .

[22]  Craig C. Martens,et al.  Simulation of Coherent Nonadiabatic Dynamics Using Classical Trajectories , 1998 .

[23]  Richard A. Friesner,et al.  Stationary phase surface hopping for nonadiabatic dynamics: Two-state systems , 1994 .

[24]  Donald L Thompson,et al.  Modern Methods for Multidimensional Dynamics Computations in Chemistry , 1998 .

[25]  Gerhard Stock,et al.  Quantum-classical Liouville description of multidimensional nonadiabatic molecular dynamics , 2001 .

[26]  J. Tully.  Molecular dynamics with electronic transitions , 1990 .