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Semiclassical Husimi Function of Simple and Chaotic Systems
Departamento de Física e Matemática, Universidade Federal de S?o Jo?o Del Rei, Ouro Branco, Brazil
- 1 Departamento de Física e Matemática, Universidade Federal de S?o Jo?o Del Rei, Ouro Branco, Brazil
Journal of Modern Physics·Volume 03 (2012)·Pages 694–701·Published 14 August 2012·DOI10.4236/jmp.2012.38094
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Abstract
We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.
KeywordsClassical LimitHusimi FunctionQuantum Chaos
- A. C. Oliveira and M. C. Nemes and K. M. F. Romero, “Quantum Time Scales and the Classical Limit: Analytic Results for Some Simple Systems,” Physical Review E, Vol. 68, No. 3, 2003, Article ID: 036214. doi:10.1103/PhysRevE.68.036214
- A. Einstein, “Zum Quantensatz von Sommerfeld und Epstein on the Quantum Theory of Sommerfeld and Ep- stein,” Deutsche Physikalische Gesellschaft Verhandlungen, Vol. 19, 1917, p. 82.
- M. A. M. de Aguiar, “Einstein and the Quantum Chaos Theory,” Revista de Ensino de Física, Vol. 27, 2005, p. 101.
- M. C. Gutzwiller, “Chaos in Classical and Quantum Me- chanics,” Spring-Verlg, New York, 1990.
- H. J. StockmannHaake, “Quantum Chaos an Introduc- tion,” Cambridge University Press, New York, 1999.
- F. Haake, “Quantum Signatures of Chaos,” Springer- Verlag, Berlin, 2004.
- S. W. McDonald and A. N. Kaufmann, “Spectrum and Eigenfunctions for a Hamiltonian with Stochastic Trajec- tories,” Physical Review Letters, Vol. 42, No. 18, 1979, pp. 1189-1191. doi:10.1103/PhysRevLett.42.1189
- E. B. Bogomolny, “Fine Structure of the Wave Functions of Quantum Systems,” JETP Letters, Vol. 44, No. 9, 1986, pp. 561-565.
- E. B. Bogomolny, “Smoothed Wave Functions of Chaotic Quantum Systems,” Physica D, Vol. 31, No. 2, 1988, pp. 169-189. doi:10.1016/0167-2789(88)90075-9
- E. J. Heller, “Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits,” Physical Review Letters, Vol. 53, No. 16, 1984, pp. 1515- 1518. doi:10.1103/PhysRevLett.53.1515
- E. J. Heller, “Quantum Chaos and Statistical Nuclear Physics,” Springer, Berlin, 1983.
- L. Benet and T. H. Seligman and H. A. Weidenmuller, “Quantum Signatures of Classical Chaos: Sensitivity of Wave Functions to Perturbations,” Physical Review Let- ters, Vol. 71, No. 4, 1993, pp. 529-532. doi:10.1103/PhysRevLett.71.529
- M. Srednicki and F. Stiernelof, “Gaussian Fluctuations in Chaotic Eigenstates,” Journal of Physics A, Vol. 29, No. 18, 1996, p. 5817. doi:10.1088/0305-4470/29/18/013
- L. Benet and F. M. Izrailev and T. H. Seligman and A. Suarez-Moreno, “Semiclassical Properties of Eigenfunc- tions and Occupation Number Distribution for a Model of Two Interacting Particles,” Physics Letters A, Vol. 277, No. 2, 2000, pp. 87-93. doi:10.1016/S0375-9601(00)00692-7