Hyperangular momenta and energy partitions in multidimensional many-particle classical mechanics: The invariance approach to cluster dynamics

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 72, Issue 3, 2005, Pages

  Sevryuk, Mikhail B ^a   Lombardi, Andrea ^b   Aquilanti, Vincenzo ^b  

^a SEMENOV INSTITUTE OF CHEMICAL PHYSICS   (Russian Federation)

^b UNIVERSITY OF PERUGIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER DYNAMICS; NANOAGGREGATES; SINGULAR VALUE DECOMPOSITION (SVD);

COMPUTER PROGRAMMING; DECOMPOSITION; DYNAMICS; KINEMATICS; KINETIC ENERGY;

CONTINUUM MECHANICS;

EID: 28844499841     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.72.033201     Document Type: Article

References (57)

1. V. Aquilanti, A. Lombardi, and E. Yurtsever, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 10.1039/b206197j 4, 5040 (2002).
2. V. Aquilanti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 113402 93, 113402 (2004).
3. V. Aquilanti, A. Lombardi, and M. B. Sevryuk, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1785785 121, 5579 (2004).
4. V. Aquilanti, Comput. Mater. Sci. CMMSEM 0927-0256 (to be published);
5. see also http://bong.chm.unipg.it/CVs/aquila.html/Partitions/examples
6. V. Aquilanti (unpublished).
7. F. T. Smith, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1730598 31, 1352 (1959).
8. F. T. Smith, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.120.1058 120, 1058 (1960).
9. V. Aquilanti and S. Cavalli, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.451223 85, 1355 (1986).
10. V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.451224 85, 1362 (1986).
11. R. G. Littlejohn and M. Reinsch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.2035 52, 2035 (1995).
12. R. G. Littlejohn and M. Reinsch, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.69.213 69, 213 (1997).
13. R. G. Littlejohn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.3718 58, 3718 (1998).
14. A. Kuppermann, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp9708207 101, 6368 (1997).
15. D. Wang and A. Kuppermann, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1412603 115, 9184 (2001).
16. A. Kuppermann, J. Phys. Chem. A JPCAFH 1089-5639 108, 8894 (2004).
17. V. Aquilanti, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.10278 89, 277 (2002).
18. V. Aquilanti, A. Lombardi, and R. G. Littlejohn, Theor. Chem. Acc. TCACFW 1432-881X 10.1007/s00214-003-0526-3 111, 400 (2004).
19. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic, Orlando, FL, 1985).
20. R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed. (Cambridge University Press, Cambridge, U.K., 1990).
21. G. W. Stewart and J.-G. Sun, Matrix Perturbation Theory (Academic, Boston, 1990).
22. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, 2nd ed. (Cambridge University Press, Cambridge, U.K., 1994).
23. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, 1996).
24. L. Dieci and T. Eirola, SIAM J. Matrix Anal. Appl. SJMAEL 0895-4798 10.1137/S0895479897330182 20, 800 (1999).
25. A. V. Filinov, M. Bonitz, and Yu. E. Lozovik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3851 86, 3851 (2001).
26. V. Aquilanti, S. Cavalli, and C. Coletti, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(96)00310-2 214, 1 (1997).
27. V. Aquilanti, Int. Rev. Phys. Chem. IRPCDL 0144-235X 10.1080/ 01442350110075926 20, 673 (2001).
28. Dimensional Scaling in Chemical Physics, edited by, D. R. Herschbach, J. Avery, and, O. Goscinski, (Kluwer Academic, Dordrecht, 1993).
29. R. Radau, Ann. Sci. Ec. Normale Super. 0012-9593 5, 311 (1868).
30. R. Radau, J. Math. Pures Appl. JMPAAM 0021-7824 14, 167 (1869).
31. F. T. Smith, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.45. 1157 45, 1157 (1980).
32. V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer, New York, 1989).
33. I. M. James, The Topology of Stiefel Manifolds (Cambridge University Press, Cambridge, U.K., 1976).
34. D. B. Fuks and V. A. Rokhlin, Beginner's Course in Topology: Geometric Chapters (Springer, Berlin, 1984).
35. A. Edelman, T. A. Arias, and S. T. Smith, SIAM J. Matrix Anal. Appl. SJMAEL 0895-4798 10.1137/S0895479895290954 20, 303 (1998).
36. V. I. Arnold, Funct. Anal. Appl. FAAPBZ 0016-2663 6, 94 (1972).
37. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (Pergamon Press, Oxford, 1977).
38. V. I. Arnold, S. M. Gusein-Zade, and A. N. Varchenko, Singularities of Differentiable Maps. Vol. I. The Classification of Critical Points, Caustics and Wave Fronts (Birkhäuser, Boston, 1985).
39. M. W. Hirsch, Differential Topology, 2nd ed. (Springer, New York, 1994).
40. P. G. Mezey, Shape in Chemistry: An Introduction to Molecular Shape and Topology (VCH, New York, 1993).
41. F. T. Smith, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1724275 3, 735 (1962).
42. A. Bunse-Gerstner, Numer. Math. NUMMA7 0029-599X 10.1007/BF01385712 60, 1 (1991).
43. F. Rellich, Math. Ann. MAANA3 0025-5831 113, 600 (1936).
44. F. Rellich, Perturbation Theory of Eigenvalue Problems, 2nd ed. (Gordon and Breach, New York, 1969).
45. T. Kato, Perturbation Theory for Linear Operators, 2nd ed. (Springer, Berlin, 1976).
46. H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators (Akademie-Verlag, Berlin, 1984).
47. W. Wasow, Result. Math. 1422-6383 2, 206 (1979).
48. W. Govaerts and B. Werner, Numer. Math. NUMMA7 0029-599X 10.1007/s002110050121 70, 303 (1995).
49. J.-L. Chern and L. Dieci, SIAM J. Matrix Anal. Appl. SJMAEL 0895-4798 10.1137/S0895479899353622 22, 772 (2000).
50. M. Baumann and U. Helmke, FGCS, Future Gener. Comput. Syst. 0167-739X 10.1016/S0167-739X(02)00162-0 19, 353 (2003).
51. J.-G. Sun, J. Comput. Math. 0254-9409 6, 258 (1988).
52. J.-G. Sun, J. Comput. Math. 0254-9409 10.1017/S1355838200992161 6, 325 (1988).
53. K. Wright, Numer. Math. NUMMA7 0029-599X 10.1007/BF01385862 63, 283 (1992).
54. M. A. Wicks and R. A. DeCarlo, SIAM J. Matrix Anal. Appl. SJMAEL 0895-4798 10.1137/S089547989222758X 16, 123 (1995).
55. L. Qiu, Automatica ATCAA9 0005-1098 10.1016/0005-1098(95)00024-Q 31, 879 (1995).
56. G. W. Stewart, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/0024- 3795(84)90128-9 56, 231 (1984).
57. V. Aquilanti, S. Cavalli, and M. B. Sevryuk, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.530652 35, 536 (1994).