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Quantum relaxation dynamics using Bohmian trajectories

J. Chem. Phys. 115, 6309 (2001); doi:10.1063/1.1394747

Issue Date: 8 October 2001

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Jeremy B. Maddox and Eric R. Bittner
Department of Chemistry, University of Houston, Houston, Texas 77204
We present a new Bohmian trajectory based treatment of quantum dynamics suitable for dissipative systems. Writing the density matrix in complex-polar form, we derive and define quantum equations of motion for Liouville-space trajectories for a generalized system coupled to a dissipative environment. Our theory includes a vector potential which mixes forward and backwards propagating components and pulls coherence amplitude away from the diagonal region of the density matrix. Quantum effects enter via a double quantum potential, [script Q](x,y), which is a measure of the local curvature of the density amplitude. We discuss how decoherence can be thought of as a balancing between localization brought on by contact with a thermal environment which increases the local curvature of the density matrix and delocalization due to the internal pressure of the quantum force which seeks to minimize the local curvature. The quantum trajectories are then used to propagate an adaptive Lagrangian grid which carries the density matrix, rho(x,y), and the action, A(x,y), thereby providing a complete hydrodynamiclike description of the dynamics. ©2001 American Institute of Physics.
History: Received 19 April 2001; accepted 26 July 2001
Permalink: http://link.aip.org/link/?JCPSA6/115/6309/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ge
    Quantum mechanics, field theories, and special relativity Quantum mechanics Solutions of wave equations: bound states
  • 31.15.-p
    Electronic structure of atoms and molecules: theory Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)
  • YEAR: 2001

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ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (28)
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For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).
  2. L. de Broglie, C. R. Acad. Sci. (Paris) 183, 447 (1926).
  3. E. Madelung, Z. Phys. 40, 322 (1926).
  4. D. Bohm, Phys. Rev. 85, 166 (1952).
  5. D. Bohm, Phys. Rev. 84, 180 (1952).
  6. C. L. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999).
  7. R. E. Wyatt, Chem. Phys. Lett. 313, 189 (1999).
  8. E. R. Bittner, J. Chem. Phys. 112, 9703 (2000).
  9. E. R. Bittner and R. E. Wyatt, J. Chem. Phys. 113, 8888 (2000).
  10. R. E. Wyatt and E. R. Bittner, J. Chem. Phys. 113, 8898 (2000).
  11. J. C. Burant and J. C. Tully, J. Chem. Phys. 112, 6097 (2000).
  12. B. K. Day, A. Askar, and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998).
  13. F. S. Mayor, A. Askar, and H. A. Rabitz, J. Chem. Phys. 111, 2423 (1999).
  14. D. Nerukh and J. H. Frederick, Chem. Phys. Lett. 332, 145 (2000).
  15. E. B. Davies, Quantum Theory of Open Systems (Academic, New York, 1976).
  16. A. O. Caldeira and A. J. Leggett, Physica A 121, 587 (1983).
  17. W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989).
  18. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992).
  19. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 47, 1576 (1993).
  20. E. R. Bittner and P. J. Rossky, J. Chem. Phys. 103, 8130 (1995);
    21. 104, 5942 (1996);
    107, 8611 (1997).
  21. J. P. Paz and W. H. Zurek, Phys. Rev. Lett. 82, 5181 (1999).
  22. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman and Co., New York, 1993).
  23. The +gamma in this equation is countered by a –gamma obtained upon inserting eta-dot and does not lead to g blowing up uniformly in time.
  24. A copy of our code is available from the authors upon request.
  25. E. R. Bittner and J. B. Maddox, Int. J. Quant. Chem. (submitted).
  26. C. Kielpinski, V. Meyer, M. A. Rowe, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Science 291, 1013 (2001).
  27. C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, Science 272, 1131 (1996).
  28. R. E. Wyatt, C. L. Lopreore, and G. Parlant, J. Chem. Phys. 114, 5113 (2001).

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