Izvestiya of Saratov University.


ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Lazerson A. G., Boykov A. A. Dynamical Chaos In Quantum Systems. Izvestiya of Sarat. Univ. Physics. , 2010, vol. 10, iss. 1, pp. 58-64. DOI: 10.18500/1817-3020-2010-10-1-58-64

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 81)
530.145.61: 530.182

Dynamical Chaos In Quantum Systems

Lazerson Alexandr Grigor'evich, Saratov State University
Boykov Alexey Alekseevich, Saratov State University

Complex dynamics of a quantum periodically driven square well is considered. It is shown that analysis of its ensemble average energy time series provides an identification of its dynamics to be either regular or chaotic. It has been found that enhancement of the driving force causes the energy spectrum to look like a spectrum of some random process, which may be identified as the signature of chaos in a quantum system. 

  1. Reichl L.E. The transition to chaos in conservative classical systems: quantum manifestations. N.Y.: Springer-Verlag, 1992. 
  2. Reichl LE., Lin W.A. Exact quantum model of field-induced resonance overlap // Phys. Rev. A. 1986. Vol.33. P.3598. 
  3. Lin W.A., Reichl L.E. Transition of spectral statistics due to overlap of quantum resonance zones // Phys. Rev. A. 1987. Vol.36. P.5099.
  4. Lin W.A.. Reichl L.E. Spectral analysis of quantum resonance zones, quantum Kolmogorov-Arnold-Moser theorem and quantum resonance overlap // Phys. Rev. A. 1988. Vol.37. P.3972. 
  5. Reichl L.E., Li Haoming. Self-similarity in quantum dynamics // Phys. Rev. A. 1990. Vol.42. P.4543. 
  6. Ju-Yong Sh., Hai-Woong L. Floquet analysis of quantum resonance in a driven nonlinear system // Phys. Rev. E. 1994. Vol.50. P.902. 
  7. Hollhaus M. On the classical-quantum correspondence for periodically time dependent systems // Chaos. Solitons & Fractals. 1995. Vol.5. P.1143. 
  8. Cocke S., Reichl L.E. Static-field effects on the nonlinear quantum resonances and the ionization spectrum of a simple bound particle//Phys. Rev. A. 1995. Vol.52. P.4515. 
  9. Farini A., BoccaleUi S., Arecchi F.T. Quantum-classical comparison in chaotic systems // Phys. Rev. E. 1996. Vol.53. P.4447. 
  10. Morrow G.O.. Reichl L.E. Planck's-constant dependence of the scaling of localization length in quantum dynamics // Phys. Rev. E. 1998. Vol.57. P.5266.
  11. Demikhovskii V.Y.. Kamenev D.L, Luna-Acosta G.A. Quantum weak chaos in a degenerate system // Phys. Rev. E. 1999. Vol.59. P.294.
  12. Mirbach В., Casali G. Transition from quantum ergodicity to adiabaticity: dynamical localization in an amplitude modulated pendulum // Phys. Rev. Lett. 1999. Vol.83. P. 1327.
  13. Loinaz W., Newman T.J. Quantum revivals and caфets in some exactly solvable systems // J. Phys. A: Math. Gen. 1999. Vol.32. P.8
  14. Timberlake Т., Reichl I..E. Phase-space picture of resonance creation and avoided crossings // Phys. Rev. A. 2001. Vol.64. P.033404. 
  15. Sankaranarayanan R., Lakshminarayan A., Sheorey V.B. Quantum chaos of a particle in a square well: Competing length scales and dynamical localization // Phys. Rev. E. 2001. Vol.64. P.0462I0.
  16. Emmanouilidou A.. Reichl L.E. Floquet scattering and classical-quantum correspondence in strong time-periodic fields // Phys. Rev. A. 2002. Vol.65. P.033405.
  17. Korsch H. J., Leyes W. Quantum and classical phase space evolution: a local measure of derealization // New J. Phys. 2002. Vol.4. P.62.
  18. Lin fV.A., Reichl L.E. External field induced chaos in an infinite square well potential // Physica D. 1986. Vol.19. P.145.
  19. Fuka M.Z., MclverJ.K., Becker W., Orszag M, Ramirez R. Driven particle in an infinite square well: Representation and breakdown of the invariant tori in a multiple-resonance case // Phys. Rev. E. 1995. Vol.51. P.1935. 
  20. Заславский Г.М. Стохастичность динамических систем. М.: Наука, 1984.
  21. Дженкинс Г., Ватте Д. Спектральный анализ и его приложения. М.: Мир, 1971. 22. Лихтенберг А., Либерман М. Регулярная и стохастическая динамика. М.: Мир, 1984.
  22. Ландау Л.Д., .Нифшиц Е.М. Квантовая .механика. М.: Наука. 1989.
  23. Марпл-мл. С.Л. Цифровой спектральный анализ и его приложения. М.: Мир, 1990.
  24. Ландау Л.Д., Лифшиц Е.М. Механика. М.: Наука, 1988.
  25. Рабинович М.И., Трубецков Д. И. Введение в теорию колебаний и волн. М.: Наука, 1992.