Space-discretized Verlet-algorithm from a variational principle

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 52, Issue 8-9, 1997, Pages 585-587

  Nadler, Walter ^a   Diebner, Hans H ^a   Rössler, Otto E ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041156959     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.1515/zna-1997-8-906     Document Type: Article

References (18)

1. L. Verlet, Phys. Rev. 159, 98 (1967).
2. D. Levesque and L. Verlet, J. Stat. Phys. 72, 519 (1993).
3. J. M. Haile, Molecular Dynamics Simulations: Elementary Methods, Wiley, New York 1992.
4. J. A. McCammon and S. C. Harvey, Dynamics of Proteins and Nucleic Acids, Cambridge University, Cambridge 1987.
5. H. Goldstein, Classical Mechanics, Addison-Wesley, Reading/Mass. 1950.
6. R. E. Gillilan and K. R. Wilson, J. Chem. Phys. 97, 1757 (1992).
7. R. P. Feynman and A. R. Hibbs, Quantum mechanics and path integrals, McGraw-Hill, New York 1965.
8. H. H. Diebner, Investigations of Exactly Reversible Algorithms for Dynamics Simulations, Diploma Thesis (in German), University of Tübingen 1993; cf. W. Pabst, The Principle of Least Action in Discrete Space-Time, Diploma Thesis (in German), University of Tübingen 1995.
9. H. H. Diebner, Investigations of Exactly Reversible Algorithms for Dynamics Simulations, Diploma Thesis (in German), University of Tübingen 1993; cf. W. Pabst, The Principle of Least Action in Discrete Space-Time, Diploma Thesis (in German), University of Tübingen 1995.
10. H. H. Diebner and O. E. Rössler, Z. Naturforsch. 50a, 1139 (1995).
11. J. L. Lebowitz, Physics Today, September 1993, p.32.
12. J. Orban and A. Bellemans, Phys. Lett. 224, 620 (1967).
13. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. A38, 3688 (1988).
14. D. E. Knuth, The Art of Computer Programming, Vol.II., Addison-Wesley, Reading/Mass, 1981.
15. W. F. Wolff and B. A. Huberman, Z. Phys. B63, 397 (1986).
16. n-1)/2h, as originally suggested by Verlet [1], leads to the same final algorithm (8).
17. Total momentum is no longer conserved in some cases of non-pair potent als (like wall potentials).
18. An algorithm-dependent secular drift in energy should also appear in the time-reversed direction. However, from the time-reversibility property of an algorithm it can be concluded that such a drift must vanish. Apparently, this argument is due to J,-M. Caillol, as cited in [2].