Path integrals for dissipative systems by tensor multiplication. Condensed phase quantum dynamics for arbitrarily long time

Abstract Feynman's influence functional that arises from many-particle environments is nonlocal in time but the nonlocality has finite range, even at very low temperature. Use of our numerically constructed quasi-adiabatic propagators permits large time steps in the path integral, such that the nonlocality of the influence functional spans only a few time steps. We exploit these observations to propose an iterative scheme for the evaluation of path integrals by stepwise multiplication of a propagator tensor, thereby making exact quantum dynamics calculations in condensed phase systems feasible for arbitrarily long times.

[1]  A. Leggett,et al.  Quantum tunnelling in a dissipative system , 1983 .

[2]  G. W. Ford,et al.  Statistical Mechanics of Assemblies of Coupled Oscillators , 1965 .

[3]  J. Doll,et al.  Equilibrium and dynamical Fourier path integral methods , 2007 .

[4]  R. Feynman,et al.  Space-Time Approach to Non-Relativistic Quantum Mechanics , 1948 .

[5]  Nancy Makri,et al.  System-specific discrete variable representations for path integral calculations with quasi-adiabatic propagators , 1993 .

[6]  N. Makri.  Improved Feynman propagators on a grid and non-adiabatic corrections within the path integral framework , 1992 .

[7]  R. Feynman,et al.  The Theory of a general quantum system interacting with a linear dissipative system , 1963 .

[8]  W. Miller.  REACTION PATH DYNAMICS FOR POLYATOMIC SYSTEMS , 1983 .

[9]  Local Approximation of Potential‐Energy Surfaces by Surfaces Permitting Separation of Variables , 1964 .

[10]  Rudolph A. Marcus,et al.  Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates , 1968 .

[11]  Makarov,et al.  Tunneling dynamics in dissipative curve-crossing problems. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[12]  Peter Talkner,et al.  The failure of the quantum regression hypothesis , 1986 .

[13]  Nancy Makri,et al.  Multidimensional path integral calculations with quasiadiabatic propagators : quantum dynamics of vibrational relaxation in linear hydrocarbon chains , 1992 .

[14]  N. Makri,et al.  Quasi-adiabatic propagator path integral methods. Exact quantum rate constants for condensed phase reactions , 1993 .

[15]  G. L. Hofacker,et al.  Model Approach to Nonadiabatic Reaction Processes , 1969 .

[16]  Rudolph A. Marcus,et al.  On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions , 1966 .

[17]  N. Makri.  Feynman path integration in quantum dynamics , 1991 .

[18]  John E. Adams,et al.  Reaction path Hamiltonian for polyatomic molecules , 1980 .