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Journal of Chemical Physics / Volume 127 / Issue 7 / ARTICLES / Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

J. Chem. Phys. 127, 074505 (2007); http://dx.doi.org/10.1063/1.2753151 (12 pages)

Continuum limit semiclassical initial value representation for dissipative systems

Eli Pollak

Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel

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(Received 19 April 2007; accepted 6 June 2007; published online 17 August 2007)

In this paper, we consider a dissipative system in which the system is coupled linearly to a harmonic bath. In the continuum limit, the bath is defined via a spectral density and the classical system dynamics is given in terms of a generalized Langevin equation. Using the path integral formulation and factorized initial conditions, it is well known that one can integrate out the harmonic bath, leaving only a path integral over the system degrees of freedom. However, the semiclassical initial value representation treatment of dissipative systems has usually been limited to a discretized treatment of the bath in terms of a finite number of bath oscillators. In this paper, the continuum limit of the semiclassical initial value representation is derived for dissipative systems. As in the path integral, the action is modified with an added nonlocal term, which expresses the influence of the bath on the dynamics. The first order correction term to the semiclassical initial value approximation is also derived in the continuum limit.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. CLASSICAL DISSIPATIVE SYSTEMS
    1. The generalized Langevin equation
    2. Random force statistics
  3. SCIVR FOR DISSIPATIVE SYSTEMS
    1. Preliminaries
    2. SCIVR in the continuum limit
    3. The spin boson problem
  4. SCIVR SERIES EXPANSION IN THE CONTINUUM LIMIT
    1. The formal series representation
    2. The first order correction term
  5. DISCUSSION

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KEYWORDS and PACS

Keywords

quantum theory, Schrodinger equation, harmonic oscillators, differential equations

PACS

  • 03.65.Sq

    Semiclassical theories and applications

  • 03.65.Ge

    Solutions of wave equations: bound states

  • 02.30.Hq

    Ordinary differential equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2753151

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    W. H. Miller, J. Chem. Phys. 53, 3578 (1970)JCPSA6000053000009003578000001.

    E. J. Heller, J. Chem. Phys. 75, 2923 (1981)JCPSA6000075000006002923000001.

    C. Harabati, J. M. Rost, and F. Grossmann, J. Chem. Phys. 120, 26 (2004)JCPSA6000120000001000026000001.

    K. G. Kay, J. Chem. Phys. 100, 4377 (1994)JCPSA6000100000006004377000001;, 100, 4432 (1994)JCPSA6000100000006004432000001;, 101, 2250 (1994)JCPSA6000101000003002250000001.

    G. Campolieti and P. Brumer, Phys. Rev. A 50, 997 (1994).

    K. Thompson and N. Makri, J. Chem. Phys. 110, 1343 (1999)JCPSA6000110000003001343000001.

    K. Thompson and N. Makri, Phys. Rev. E 59, R4729 (1999).

    X. Sun and W. H. Miller, J. Chem. Phys. 110, 6635 (1999)JCPSA6000110000014006635000001.

    M. Thoss, H. Wang, and W. H. Miller, J. Chem. Phys. 114, 9220 (2001)JCPSA6000114000021009220000001.

    S. Zhang and E. Pollak, J. Chem. Phys. 121, 3384 (2004)JCPSA6000121000008003384000001.

    E. Martin-Fierro and E. Pollak, J. Chem. Phys. 125, 164104 (2006)JCPSA6000125000016164104000001.

    E. Pollak and E. Martin-Fierro, J. Chem. Phys. 126, 164107 (2007)JCPSA6000126000016164107000001.

    E. Martin-Fierro and E. Pollak, J. Chem. Phys. 126, 164108 (2007)JCPSA6000126000016164108000001.

    S. Zhang and E. Pollak, Phys. Rev. Lett. 91, 190201 (2003).

    S. Zhang and E. Pollak, J. Chem. Phys. 119, 11058 (2003)JCPSA6000119000021011058000001.

    J. Ankerhold, M. Saltzer, and E. Pollak, J. Chem. Phys. 116, 5925 (2002)JCPSA6000116000014005925000001.

    S. Bonella and D. F. Coker, J. Chem. Phys. 122, 194102 (2005)JCPSA6000122000019194102000001.

    F. Grossmann, J. Chem. Phys. 103, 3696 (1995)JCPSA6000103000009003696000001.

    W. H. Miller, J. Chem. Phys. 95, 9428 (1991)JCPSA6000095000012009428000001.

    M. Thoss, W. H. Miller, and G. Stock, J. Chem. Phys. 112, 10282 (2000)JCPSA6000112000023010282000001.

    J. Shao and N. Makri, J. Chem. Phys. 113, 3681 (2000)JCPSA6000113000009003681000001.

    Y. Elran and P. Brumer, J. Chem. Phys. 121, 2673 (2004)JCPSA6000121000006002673000001.

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).

    G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997).

    M. Thoss and G. Stock, Phys. Rev. A 59, 64 (1999).

    R. Guantes, J. L. Vega, S. Miret-Artes, and E. Pollak, J. Chem. Phys. 120, 10768 (2004)JCPSA6000120000022010768000001 and references therein.

    H. Wang and M. Thoss, J. Chem. Phys. 119, 1289 (2003)JCPSA6000119000003001289000001.

    H. Wang, J. Chem. Phys. 113, 9948 (2000)JCPSA6000113000022009948000001.

    J. T. Stockburger and C. H. Mak, Phys. Rev. Lett. 80, 2657 (1998).

    J. T. Stockburger and C. H. Mak, J. Chem. Phys. 110, 4983 (1999)JCPSA6000110000011004983000001.

    J. T. Stockburger and H. Grabert, Phys. Rev. Lett. 88, 170407 (2002).

    J. Shao, J. Chem. Phys. 120, 5053 (2004)JCPSA6000120000011005053000001.


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