Integrating the quantum Hamilton–Jacobi equations by wavefront expansion and phase space analysis
In this paper we report upon our computational methodology for numerically integrating the quantum Hamilton–Jacobi equations using hydrodynamic trajectories. Our method builds upon the moving lea...
In this paper we report upon our computational methodology for numerically integrating the quantum Hamilton–Jacobi equations using hydrodynamic trajectories. Our method builds upon the moving lea...
Hartree–Fock and Kohn–Sham atomic-orbital based time-dependent response theory
A reformulation of general time-dependent Hartree–Fock and Kohn–Sham response theories that refers strictly to the atomic-orbital basis is presented. It is based on a recently proposed expon...
A reformulation of general time-dependent Hartree–Fock and Kohn–Sham response theories that refers strictly to the atomic-orbital basis is presented. It is based on a recently proposed expon...
Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids
J. Chem. Phys. 113, 8898 (2000); doi:10.1063/1.1319988
Issue Date: 22 November 2000
You are not logged in to this journal. Log in
The quantum trajectory method was recently developed to solve the hydrodynamic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for fluid elements ("particles") moving under the influence of the combined force from the potential surface and the quantum potential. To accurately compute the quantum potential and the quantum force, it is necessary to obtain the derivatives of a function given only the values on the unstructured mesh defined by the particle locations. However, in some regions of space–time, the particle mesh shows compression and inflation associated with regions of large and small density, respectively. Inflation is especially severe near nodes in the wave function. In order to circumvent problems associated with highly nonuniform grids defined by the particle locations, adaptation of moving grids is introduced in this study. By changing the representation of the wave function in these local regions (which can be identified by diagnostic tools), propagation is possible to much longer times. These grid adaptation techniques are applied to the reflected portion of a wave packet scattering from an Eckart potential. ©2000 American Institute of Physics.
| History: | Received 14 July 2000; accepted 1 September 2000 |
| Permalink: |
http://link.aip.org/link/?JCPSA6/113/8898/1 |
| BUY THIS ARTICLE | (US$24) |
|
|
|
|
Connotea
CiteULike
del.icio.us
BibSonomy
EDITORIALLY RELATED
- Integrating the quantum Hamilton–Jacobi equations by wavefront expansion and phase space analysis
Eric R. Bittner et al.
J. Chem. Phys. 113, 8888 (2000)
KEYWORDS and PACS
RELATED DATABASES
PUBLICATION DATA
0021-9606 (print)
1089-7690 (online)
AIP
REFERENCES (32)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- E. Madelung,
Z. Phys. 40, 322 (1926) . - L. de Broglie, C. R. Séances Acad. Sci. 183, 447 (1926);
- 184, 273 (1927).
- D. Bohm,
Phys. Rev. 85, 166 (1952) ; - 85, 180 (1952).
- D. Bohm, B. J. Hiley, and P. N. Kaloyerou,
Phys. Rep. 144, 321 (1987) . - D. Bohm and B. J. Hiley, The Undivided Universe (Routeledge, London, 1993).
- D. Bohm, B. J. Hiley, and P. N. Kaloyerou,
Phys. Rep. 144, 321 (1987) . - P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, New York, 1993).
- H. E. Wilhelm, Phys. Rev. D 1, 2278 (1970).
- C. Philippidis, C. Dewdney, and B. J. Hiley,
Nuovo Cimento Soc. Ital. Fis., B 52B, 15 (1979) . - J. H. Weiner and Y. Partom, Phys. Rev. 187, 1134 (1969).
- J. H. Weiner and A. Askar, J. Chem. Phys. 54, 1108 (1971);
- C. Lopreore and R. E. Wyatt, Phys. Rev. Lett. 82, 5190 (1999).
- F. Sales Mayor, A. Askar, and H. A. Rabitz, J. Chem. Phys. 111, 2423 (1999).
- C. Lopreore and R. E. Wyatt,
Chem Phys. Lett. 325, 73 (2000) . - R. E. Wyatt, J. Chem. Phys. 111, 4406 (1999).
- R. E. Wyatt,
Chem. Phys. Lett. 313, 189 (1999) . - D. K. Hoffman and D. J. Kouri, in Proceedings of the 3rd International Conference on Mathematical and Numerical Aspects of Wave Propagation (SIAM, Philadalphia, 1995).
- D. K. Hoffman, T. L. Marchioro II, M. Arnold, Y. Huang, W. Zhu, and D. J. Kouri,
J. Math. Chem. 20, 117 (1996) . - R. E. Wyatt, D. Kouri, and D. Hoffman, J. Chem. Phys. 112, 10730 (2000).
- E. R. Bittner, J. Chem. Phys. 112, 9703 (2000).
- E. R. Bittner and R. E. Wyatt, J. Chem. Phys. 113, 8888 (2000), previous paper.
- M. J. Fritts, W. P. Crowley, and H. Trease, The Free-Lagrange Method (Springer-Verlag, New York, 1985).
- H. Trease, M. J. Fritts, and W. P. Crowley, Advances in the Free-Lagrange Method (Springer-Verlag, New York, 1990).
- P. A. Zegeling, in Handbook of Grid Generation, edited by J. F. Thompson, B. K. Soni, and N. P. Weatherill (CRC, New York, 1999).
- G. F. Carey, Computational Grids (Taylor and Francis, Washington, D.C., 1997).
- Y. Kallinderis, Grid Adaptation by Redistribution and Local Embedding, Lecture notes for the 27th Computational Fluid Dynamics Lecture Series (Von Karmen Institute, Brussles, 1996).
- X. Gallez, P. Halin, G. Lielens, R. Keunings, and V. Legat,
Comput. Methods Appl. Mech. Eng. 180, 345 (1999) . - P. MacNeice, K. M. Olson, C. Mobarry, R. de Fainchtein, and C. Packer,
Comput. Phys. Commun. 126, 330 (2000) . - N. Pinto-Neto and E. Santini, Phys. Rev. D 59, 123517 (1999).
- C. A. J. Fletcher, Computational Techniques for Fluid Dynamics (Springer-Verlag, New York, 1991).
- B. Fornberg, A Practical Guide to Pseudospectral Methods (Cambridge University Press, New York, 1996).
- The corrected subroutine may be obtained by contacting the authors of this study.
