Decoding the dynamical information embedded in highly excited vibrational eigenstates: State space and phase space viewpoints

Journal of Physical Chemistry A

Volumn 113, Issue 9, 2009, Pages 1717-1730

  Manikandan, Paranjothy ^a   Semparithi, Aravindan ^a,b   Keshavamurthy, Srihari ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL-QUANTUM CORRESPONDENCES; DELOCALIZED STATE; EIGENSTATES; LIFTING PROCEDURES; LOCAL TIME; LOCALIZED STATE; MULTI-MODE SYSTEMS; NON-LINEAR RESONANCES; NOVEL METHODS; NUMBER OF DEGREES OF FREEDOMS; PARAMETRIC VARIATIONS; PHASE SPACES; QUANTUM EIGENSTATES; QUANTUM NATURES; QUANTUM STATE; STATE SPACES; THREE DEGREES OF FREEDOMS; VIBRATIONAL EIGENSTATES;

DECODING; MECHANICS; RESONANCE;

PHASE SPACE METHODS;

EID: 64149086356     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp807231p     Document Type: Article

References (182)

1. Kellman, M. E. Annu. Rev. Phys. Chem. 1995, 46, 395.
2. Lu, Z.; Kellmam, M. E. Chem. Phys. Lett. 1995, 247, 195.
3. Svitak, J.; Li, Z. M.; Rose, J.; Kellman, M. E. J. Chem. Phys. 1995,102, 4340.
4. Lu, Z.; Kellman, M. E. J. Chem. Phys. 1997, 107, 1.
5. Rose, J. P.; Kellman, M. E. J. Chem. Phys. 1996, 105, 10743.
6. Rose, J. P.; Kellman, M. E. J. Chem. Phys. 1996, 105, 7348.
7. Kellman, M. E.; Rose, J. P.; Tyng, V. Eur. Phys. J. D 2001, 14, 225.
8. Kellman, M. E.; Tyng, V. Acc. Chem. Res. 2007, 40, 243.
9. Ezra, G. S. Adv. Classical Trajectory Methods 1992, 1, 1.
10. Ezra, G. S. Adv. Classical Trajectory Methods 1998, 3, 35.
11. Gomez Llorente, J. M.; Pollak, E. Annu. Rev. Phys. Chem. 1992, 43, 91.
12. Frantos, S. C. Int. Rev. Phys. Chem. 1996, 15, 345.
13. Keshavamurthy, S.; Ezra, G. S. Chem. Phys. Lett. 1996, 259, 81.
14. Keshavamurthy, S.; Ezra, G. S. J. Chem. Phys. 1997, 107, 156.
15. Jacobson, M. P.; Jung, C; Taylor, H. S.; Field, R. W. J. Chem. Phys. 1999, 111, 600.
16. Jung, C; Taylor, H. S.; Jacobson, M. P. J. Phys. Chem. A 2001, 105, 681.
17. Jung, C; Ziemniak, E.; Taylor, H. S. J. Chem. Phys. 2001, 115, 2499.
18. Waalkens, H.; Jung, C; Taylor, H. S. J. Phys. Chem. A 2002, 106, 911.
19. Jung, C.; Taylor, H. S.; Atilgan, E. J. Phys. Chem. A 2002, 106, 3092.
20. Rueda, J.; Jung, C. Mol. Phys. 2006, 104, 1353.
21. Diaz, A.; Jung, C. Mol. Phys. 2008, 106, 787.
22. Jung, C.; Mejia-Monasterio, C.; Taylor, H S J. Chem. Phys. 2004, 120, 4194.
23. Jung, C.; Mejia-Monasterio, C.; Taylor, H. S. Phys. Chem. Chem. Phys. 2004, 6, 3069.
24. Jung, C.; Taylor, H. S.; Sibert, E. L. J. Phys. Chem. A 2006, 110, 5317.
25. Jung, C; Taylor, H. S. J. Phys. Chem. A 2007, 111, 3047.
26. Martens, C. C. J. Stat. Phys. 1992, 68, 207.
27. Wu, G. Z. Chem. Phys. Lett. 1998, 292, 369.
28. Ji, Z. Q.; Wu, G. Z. Chem. Phys. Lett. 2000, 319, 45.
29. Wang, P. J.; Wu, G. Z. Chem. Phys. Lett. 2003, 371, 238.
30. Wang, H. R.; Wang, P. J.; Wu, G. Z. Chem. Phys. Lett. 2004, 399, 78.
31. Huang, J.; Wu, G. Z. Chem. Phys. Lett. 2007, 439, 231.
32. Keshavamurthy, S. J. Phys. Chem. A 2001, 105, 2668.
33. Semparithi, A.; Charulatha, V.; Keshavamurthy, S. J. Chem. Phys. 2003, 118, 1146.
34. Semparithi, A.; Keshavamurthy, S. Phys. Chem. Chem. Phys. 2003, 5, 5051.
35. Semparithi, A.; Keshavamurthy, S. Chem. Phys. Lett. 2004, 395, 327.
36. Davis, M. J. J. Phys. Chem. 1988, 92, 3124.
37. Davis, M. J. Chem. Phys. Lett. 1992, 192, 479.
38. Davis, M. J. Int. Rev. Phys. Chem. 1995, 14, 15.
39. Davis, M. J. J. Chem. Phys. 1997, 107, 4507.
40. Atkins, K. M.; Logan, D. E. J. Chem. Phys. 1992, 97, 2438.
41. Atkins, K. M.; Logan, D. E. Phys. Lett. A 1992, 162, 255.
42. Zhilinskii, B. Chem Phys. 1989, 137, 1.
43. Sadovskii, D. A.; Zhilinskii, B. Phys. Rev. A 1993, 48, 1035.
44. Zhilinskii, B. Spectrochim. Acta, Part A 1996, 52, 881.
45. Kozin, I. N.; Sadovskii, D.; Zhilinskii, B. I. Spectrochim. Acta, Part A, 2005, 61, 2867.
46. Siebert, E. L., III.; McCoy, A. B. J. Chem. Phys. 1996, 109, 2111.
47. Ishikawa, H.; Field, R. W.; Farantos, S. C; Joyeux, M.; Koput, J.; Beck, C; Schinke, R. Annu. Rev. Phys. Chem. 1999, 50, 443.
48. Weiss, J.; Hauschildt, J.; Grebenshchikov, S. Y.; Duren, R.; Schinke, R.; Koput, J.; Stamatiadis, S.; Farantos, S. C. J. Chem. Phys. 2000, 112, 77.
49. Joyeux, M.; Farantos, S. C; Schinke, R. J. Phys. Chem. A 2002, 106, 5407.
50. Azzam, T.; Schinke, R.; Farantos, S. C; Joyeux, M.; Peterson, K. A. J. Chem. Phys. 2003, 118, 9643.
51. Vanroosmalen, O. S.; Iachello, F.; Levine, R. D.; Dieperink, A. E. L. J. Chem. Phys. 1983, 79, 2515.
52. Iachello, F.; Oss, S. J. Chem. Phys. 1996, 104, 6956.
53. Sako, T.; Yamanouchi, K.; Iachello, F. J. Chem. Phys. 2002, 117, 1641.
54. Iachello, F.; Perez-Bernal, F. Mol. Phys. 2008, 106, 223.
55. Child, M. S. J. Mol. Spectrosc. 2001, 210, 157.
56. Einstein, A. Ver. Dtsch. Phys. Ges. 1917, 19, 82.
57. Brillouin, L. J. Phys. (Paris) 1926, 7, 353. Keller, J. Ann. Phys. 1958, 4, 180.
58. Heller, E. J. Phys. Rev. Lett. 1984, 53, 1515.
59. Shirts, R. B.; Reinhardt, W. P. J. Chem. Phys. 1982, 77, 5204.
60. Wisniacki, D. A.; Vergini, E.; Benito, R. M.; Borondo, F. Phys. Rev. Lett. 2005, 94, 054101.
61. Borondo, F.; Vergini, E.; Wisniacki, D. A.; Zembekov, A. A.; Benito, R. M. J. Chem. Phys. 2005, 122, 111101.
62. Sibert, E. L.; Vergini, E.; Benito, R. M.; Borondo, F. New J. Phys. 2008, 10, 053016.
63. Bacic, Z.; Light, J. C. Annu. Rev. Phys. Chem. 1989, 40, 469.
64. Ribeiro, F.; lung, C; Leforestier, C. J. Theor. Comput. Chem. 2003, 2, 609.
65. Carrington, T. Can. J. Chem. 2004, 82, 900.
66. lung, C; Ribeiro, F.; Sibert, E. L. J. Phys. Chem. A 2006, 110, 5420.
67. Christiansen, O. Phys. Chem. Chem. Phys. 2007, 9, 2942.
68. Pasin, G.; lung, C; Gatti, F.; Meyer, H. D. J. Chem. Phys. 2007, 126, 024302.
69. Yagi, K.; Hirata, S.; Hirao, K. Phys. Chem. Chem. Phys. 2008, 10, 1781.
70. For reviews spanning nearly three decades see. Smalley, R. E. Annu. Rev. Phys. Chem. 1983, 34, 129.
71. Hamilton, C. E.; Kinsey, J. L.; Field, R. W. Annu. Rev. Phys. Chem. 1986, 37, 493.
72. Quack, M. Annu. Rev. Phys. Chem. 1990, 41, 839.
73. Uzer, T. Phys. Rep. 1991, 199, 73.
74. Lehmann, K. K.; Scoles, G.; Pate, B. H. Annu. Rev. Phys. Chem. 1994, 45, 241.
75. Nesbitt, D. J.; Field, R. W. J. Phys. Chem. 1996, 100, 12735.
76. Crim, F. F. J. Phys. Chem. 1996, 100, 12725.
77. Leitner, D. M.; Wolynes, P. G. ACH-Models Chem. 1997, 134, 663.
78. Gruebele, M.; Bigwood, R. Int. Rev. Phys. Chem. 1998, 17, 91.
79. Leitner, D. M. Int. J. Quantum Chem. 1999, 75, 523.
80. Keske, J. C; Pate, B. H. Annu. Rev. Phys. Chem. 2000, 51, 323.
81. Nordholm, S.; Back, A. Phys. Chem. Chem. Phys. 2001, 3, 2289.
82. Callegari, A.; Rizzo, T. R. Chem. Soc. Rev. 2001, 30, 214.
83. Bar, I.; Rosenwaks, S. Int. Rev. Phys. Chem. 2001, 20, 711.
84. Grebenshchikov, S. Yu.; Schinke, R.; Hase, W. L. In Comprehensive Chemical Kinetics, Part I; Green, N. J. B., Ed.; Elsevier: Amsterdam, 2003; Vol. 39,Chapter 3. Assman, J.; Kling, B.; Abel, B. Angew. Chem., Int. Ed. 2003, 42, 2226.
85. Gruebele, M.; Wolynes, P. G. Acc. Chem. Res. 2004, 37, 261.
86. Carpenter, B. K. Annu. Rev. Phys. Chem. 2005, 56, 57.
87. Elles, C. G.; Crim, F. F. Annu. Rev. Phys. Chem. 2006, 57, 273.
88. Leitner, D. M. Annu. Rev. Phys. Chem. 2008, 59, 233.
89. Jacobson, M. P.; Field, R. W. J. Phys. Chem. A 2000, 104, 3073.
90. Field, R. W.; O'Brien, J. P.; Jacobson, M. P.; Solina, S. A. B.; Polik, W. F.; Ishikawa, H. Adv. Chem. Phys. 1997, 101, 463.
91. Quack, M. J. Mol. Struct. 1995, 347, 245.
92. Marquardt, R.; Quack, M. Encyclopedia of Chemical Physics and Physical Chemistry I; Moore, J. H., Spencer, N. D., Eds.; IOP: Bristol, 2001; p 897.
93. Quack, M.; Stohner, J.; Willeke, M. Annu. Rev. Phys. Chem. 2008, 59, 741.
94. Beil, A.; Hollenstein, H.; Monti, O. L. A.; Quack, M.; Stohner, J. J. Chem. Phys. 2000, 113, 2701.
95. Pochert, J.; Quack, M.; Stohner, J.; Willeke, M. J. Chem. Phys. 2000, 113, 2719.
96. Cushman, R. H.; Duistermaat, J. J. Bull. Am. Math. Soc. 1988, 19, 475. Joyeux, J.; Sadovskii, D. A.; Tennyson, J. Chem. Phys. Lett. 2003, 382, 439.
97. Cooper, C. D.; Child, M. S. Phys. Chem. Chem. Phys. 2005, 7, 2731.
98. Davis, M. J.; Heller, E. J. J. Chem. Phys. 1981, 75, 246.
99. Heller, E. J. J. Phys. Chem. 1995, 99, 2625. Heller, E. J. J. Phys. Chem. A 1999, 103, 10433.
100. Keshavamurthy, S. J. Chem. Phys. 2003, 119, 161.
101. Keshavamurthy, S. J. Chem. Phys. 2005, 122, 114109.
102. Keshavamurthy, S. Phys. Rev. E 2005, 72, 045203(R).
103. Keshavamurthy, S. Int. Rev. Phys. Chem. 2007, 26, 521.
104. Sundberg, R. L.; Abramson, E.; Kinsey, J. L.; Field, R. W. J. Chem. Phys. 1985, 83, 466.
105. Sitja, G.; Pique, J. P. Phys. Rev. Lett. 1994, 73, 232.
106. Keske, J.; McWhorter, D. A.; Pate, B. H. Int. Rev. Phys. Chem. 2000, 19, 363.
107. Leitner, D. M.; Gruebele, M. Mol. Phys. 2008, 106, 433.
108. Annesley, C. J.; Berke, A. E.; Crim, F. F. J. Phys. Chem. A 2008, 112, 9448.
109. Dunham, J. L. Phys. Rev. 1932, 41, 721.
110. Joyeux, M.; Sugny, D. Can. J. Phys. 2002, 80, 1459.
111. McCoy, A. B.; Sibert, E. L. In Computational Molecular Spectroscopy; Jensen, P., Bunker, P. R., Eds.; Wiley: Chichester, U.K., 2000.
112. Van Vleck, J. H. Rev. Mod. Phys. 1951, 23, 213.
113. Birkhoff, G. D. Dynamical Systems, Colloq. Pub. No. 9, revised edition; American Mathematical Society: Providence, RI, 1979.
114. Gustavson, F. G. Astron. J. 1966, 71, 670.
115. Kellman, M. E. J. Chem. Phys. 1990, 93, 6630.
116. Fried, L. E.; Ezra, G.S.J. Chem. Phys. 1987, 86, 6270.
117. Lefebvre-Brion, H.; Field, R. W. The Spectra and Dynamics of Diatomic Molecules; Elsevier: Amsterdam, 2004.
118. Kuzmin, M. V.; Nemov, I. V.; Stuchebrukhov, A. A.; Bagratashvili, V. N.; Letokhov, V. S. Chem. Phys. Lett. 1986, 124, 522.
119. Kuzmin, M. V.; Stuchebrukhov, A. In Laser Spectroscopy of Highly Vibrationally Excited Molecules; Letokhov, V. S., Ed.; Adam Hilger: Bristol, 1989.
120. Heisenberg, W. Z. Phys. 1925, 33, 879. Translated in Sources of Quantum Mechanics; Van der Waerden, B. L., Ed.; Dover: Mineola, NY, 1967.
121. Lichtenberg, A. J.; Lieberman, M. A. Regular and Chaotic Dynamics, 2nd ed.; Springer: Berlin, 1992.
122. Feynman, R. P. Phys. Rev. 1939, 56, 340.
123. Noid, D. W.; Koszykowski, M. L.; Tabor, M.; Marcus, R. A. J. Chem. Phys. 1980, 72, 6169.
124. Ramachandran, B.; Kay, K. G. J. Chem. Phys. 1993, 99, 3659.
125. Pechukas, P. Phys. Rev. Lett. 1983, 51, 943.
126. Yukawa, T. Phys. Rev. Lett. 1985, 54, 1883.
127. Nakamura, K.; Lakshmanan, M. Phys. Rev. Lett. 1986, 57, 1661.
128. Wilkinson, M. J. Phys. A: Math. Gen. 1987, 20, 2415.
129. Takami, T.; Hasegawa, H. Phys. Rev. Lett. 1992, 68, 419.
130. Simons, B. D.; Altshuler, B. L. Phys. Rev. Lett. 1993, 70, 4063.
131. Fyodorov, Y. V. Phys. Rev. Lett. 1994, 73, 2688.
132. Zakrzewski, J.; Delande, D. Phys. Rev. E 1993, 47, 1650.
133. Guarneri, I.; Zyckowski, K.; Zakrzewski, J.; Molinari, L.; Casati, G. Phys. Rev. E 1995, 52, 2220.
134. Sano, M. Phys. Rev. E 1996, 54, 3591. Kuntsman, P.; Zyckowski, K.; Zakrzewski, J. Phys. Rev. E 1997, 55, 2446.
135. Lakshminarayan, A.; Cerruti, N. R.; Tomsovic, S. Phys. Rev. E 1999, 60, 3992.
136. Cerruti, N. R.; Keshavamurthy, S.; Tomsovic, S. Phys. Rev. E 2003, 68, 056205.
137. Schnirelman, A. I. Usp. Mat. Nauk 1974, 29, 181.
138. Colin de Verdiere, Y. Commun. Math. Phys. 1985, 102, 497.
139. Zelditch, S. Duke Math. J. 1987, 55, 919.
140. Kaplan, L.; Heller, E. J. Physica D 1998, 121, 1.
141. Bäck, A.; Nordholm, S.; Nyman, G. J. Phys. Chem. A 2004, 108, 8782.
142. Bäcker, A.; Schubert, R.; Stifter, P. Phys. Rev. E 1998, 57, 5425.
143. Peres, A. Phys. Rev. A 1984, 30, 504.
144. Feingold, M.; Moiseyev, N.; Peres, A. Phys. Rev. A 1984, 30, 509.
145. Feingold, M.; Moiseyev, N.; Peres, A. Chem. Phys. Lett. 1985, 117, 344.
146. Feingold, M.; Peres, A. Phys. Rev. A 1986, 34, 591.
147. Eckhardt, B.; Fishman, S.; Keating, J.; Agam, O.; Main, J.; Müller, K. Phys. Rev. E 1995, 52, 5893.
148. Mehlig, B.; Müller, K.; Eckhardt, B. Phys. Rev. E 1999, 59, 5272.
149. Boose, D.; Main, J. Phys. Rev. E 1999, 60, 2831.
150. 63 Jacobson, M. P.; Silbey, R. J.; Field, R. W. J. Chem. Phys. 1999, 110, 845.
151. Roberts, F. L.; Jaffé, C. J. Chem. Phys. 1993, 99, 2495.
152. Husimi, K. Proc. Math. Soc. Jpn. 1940, 22, 264.
153. Wigner, E. P. Phys. Rev. 1932, 40, 749.
154. Martens, C. C; Davis, M. J.; Ezra, G. S. Chem. Phys. Lett. 1987, 142, 519.
155. Tang, H.; Jang, S. M.; Zhao, M. S.; Rice, S. A. Chem. Phys. Lett. 1998, 285, 143.
156. Semparithi, A.; Keshavamurthy, S. J. Chem. Phys. 2006, 125, 141101.
157. Shojiguchi, A.; Li, C.-B.; Komatsuzaki, T.; Toda, M. Laser Phys. 2006, 17, 1097.
158. Shojiguchi, A.; Li, C.-B.; Komatsuzaki, T.; Toda, M. Phys. Rev. E 2007, 75, 035204(R).
159. Shojiguchi, A.; Li, C.-B.; Komatsuzaki, T.; Toda, M. Phys. Rev. E 2007, 76, 056205.
160. Bach, A.; Hostettler, J. M.; Chen, P. J. Chem. Phys. 2005, 123, 021101.
161. Bach, A.; Hostettler, J. M.; Chen, P. J. Chem. Phys. 2006, 125, 024304.
162. Paskauskas, R.; Chandre, C; Uzer, T. Phys. Rev. Lett. 2008, 100, 083001.
163. Shchekinova, E.; Chandre, C; Lan, Y.; Uzer, T. J. Chem. Phys. 2004, 121, 3471.
164. Teramoto, H.; Komatsuzaki, T. Phys. Rev. E 2008, 78, 017202.
165. Vela-Arevalo, L. V.; Wiggins, S. Int. J. Bifurcation Chaos Appl. Sci. Eng. 2001, 11, 1359.
166. Chandre, C; Wiggins, S.; Uzer, T. Physica D 2003, 181, 171.
167. Laskar, J. Physica D 1993, 67, 257.
168. Honjo, S.; Kaneko, K. Adv. Chem. Phys. 2005, 130, 437.
169. Ding, M. Z.; Bountis, T.; Ott, E. Phys. Lett. A 1990, 151, 395.
170. Perry, A. D.; Wiggins, S. Physica D 1994, 71, 102. Tsiganis, K.; Anastasiadis, A.; Varvoglis, H. Chaos, Solitons Fractals 2000, 11, 2281.
171. Zaslavsky, G. M. Physica D 2002, 168, 292. Sun, Y. S.; Zhou, L. Y.; Zhou, J. L. Celest. Mech. Dyn. Astron. 2005, 92, 257.
172. Bunimovich, L. A. Nonlinearity 2008, 21, T13.
173. Schofield, S.; Wolynes, P. G. J. Chem. Phys. 1993, 98, 1123.
174. Schofield, S.; Wolynes, P. G. J. Phys. Chem. 1995, 99, 2753.
175. Wong, V.; Gruebele, M. J. Phys. Chem. A 1999, 103, 10083.
176. Keshavamurthy, S.; Cerruti, N. R.; Tomsovic, S. J. Chem. Phys. 2002, 117, 4168.
177. Jacobson, M. P.; Field, R. W. Chem. Phys. Lett. 2000, 320, 553.
178. Pearman, R.; Gruebele, M. J. Chem. Phys. 1998, 108, 6561.
179. Leitner, D. M.; Wolynes, P. G. J. Chem. Phys. 1996, 105, 11226.
180. Wiggins, S. Normally Hyperbolic Invariant Manifolds in Dynamical Systems; Springer: Berlin, 1994.
181. Gillilan, R. E.; Ezra, G. S. J. Chem. Phys. 1991, 94, 2648.
182. Begie, D. Chaos, Solitons Fractals 1995, 5, 111.