Dissipative quantum dynamics of anharmonic oscillators with the multiconfiguration time-dependent Hartree method

We investigate the dissipative dynamics of a Morse oscillator coupled nonlinearly to a heat bath. To this end, we compare several reduced equations of motion with the dynamics of a full-dimensional wave packet with up to 61 spatial degrees of freedom. The discretized bath is converged for the relevant times considered in this paper. The propagations are done with a general purpose implementation of the multiconfiguration time-dependent Hartree method.

[1]  G. S. Agarwal,et al.  Master Equations in Phase-Space Formulation of Quantum Optics , 1969 .

[2]  J. P. Dahl,et al.  The Morse oscillator in position space, momentum space, and phase space , 1988 .

[3]  U. Manthe,et al.  The multi-configurational time-dependent Hartree approach , 1990 .

[4]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[5]  B. West,et al.  Statistical properties of quantum systems: The linear oscillator , 1984 .

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

[7]  R. Kosloff,et al.  DYNAMICS AND RELAXATION IN INTERACTING SYSTEMS : SEMIGROUP METHODS , 1997 .

[8]  P. Saalfrank,et al.  Dissipation in anharmonic molecular systems: beyond the linear coupling limit , 2001 .

[9]  M. Beck,et al.  The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propa , 1999 .

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

[11]  Haobin Wang,et al.  Basis set approach to the quantum dissipative dynamics: Application of the multiconfiguration time-dependent Hartree method to the spin-boson problem , 2000 .

[12]  Hans-Dieter Meyer,et al.  A numerical study on the performance of the multiconfiguration time-dependent Hartree method for density operators , 2000 .

[13]  D. Tannor,et al.  Phase space approach to theories of quantum dissipation , 1997 .

[14]  W. Louisell.  Quantum Statistical Properties of Radiation , 1973 .

[15]  K. Blum.  Density Matrix Theory and Applications , 1981 .

[16]  G. Worth,et al.  Relaxation of a system with a conical intersection coupled to a bath: A benchmark 24-dimensional wave packet study treating the environment explicitly , 1998 .

[17]  Gert-Ludwig Ingold,et al.  Quantum Brownian motion: The functional integral approach , 1988 .

[18]  G. Worth,et al.  Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree method , 2003 .

[19]  R. Friesner,et al.  Solution of the Redfield equation for the dissipative quantum dynamics of multilevel systems , 1994 .

[20]  H. Metiu,et al.  A one‐dimensional model for phonon‐induced desorption , 1983 .

[21]  William H. Miller,et al.  Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density , 2001 .

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

[23]  H. Grabert,et al.  Exact time evolution and master equations for the damped harmonic oscillator , 1996, physics/9610001.