DOI QR코드

DOI QR Code

RESPONSES OF DAMPED HARMONIC OSCILLATORS TO EXCITATIONS OBEYING POISSON DISTRIBUTIONS

  • Lee, Hyoung-In (Research Institute of Mathematics, Seoul National University) ;
  • Mok, Jinsik (Department of Mathematics, Sunmoon University)
  • Received : 2012.08.23
  • Accepted : 2012.11.20
  • Published : 2013.01.30

Abstract

External excitations are employed to investigate properties of optical media, with measurement data often analyzed via linear response theory. In this respect, external forcing is modeled here by well-known Poisson and negative-binomial distributions. Ensuing dynamics is examined with a special attention to the relative decay rates of damped harmonic oscillators to such external forcing, along with its relationship to other physical phenomena.

Keywords

References

  1. A.O. Caldeira, and A. J. Leggett, "Quantum tunneling in a dissipative syste", Ann. Phys. 149 (1983) 374-456 https://doi.org/10.1016/0003-4916(83)90202-6
  2. U. Weiss, Quantum Dissipative Systems, Third Edition, World Scientific, Singapore (2008)
  3. L. Novotny, "Strong coupling, energy splitting, and level crossings: A classical perspective", Am. J. of Physics 78 (2010) 1199 https://doi.org/10.1119/1.3471177
  4. H.-I. Lee, and E.-H. Lee, "Complex relaxation rates of the Drude metals and their effects on the lifetime and symmetry of plasmon resonances", Opt. Ex. 19 (2011) 10410-10422 https://doi.org/10.1364/OE.19.010410
  5. Y.-P. Choi, S.-Y. Ha, S.-B. Yun, "Complete synchronization of Kuramoto oscillators with finite inertia", Physica D 240 (2011) 32-44 https://doi.org/10.1016/j.physd.2010.08.004
  6. N. W. Hone, and M. Senthilvelan, "Note on the Poisson structure of the damped oscillator", J. Math. Phys. 50 (2009) 102902 https://doi.org/10.1063/1.3244216
  7. M. C. Teich, and B. E. A. Saleh, "Observation of sub-Poisson Franck-Hertz light at 253.7 nm", J. Opt. Soc. Am. B 2 (1985) 275-282 https://doi.org/10.1364/JOSAB.2.000275
  8. P. Carruthers, and C. C. Shih, "The phenomenological analysis of hadronic multiplicity distributions", Int. J. of Modern Physics A 2 (1987) 1447-1547 https://doi.org/10.1142/S0217751X87000806
  9. N. Suzuki, M. Biyajima, and G. Wilk, "Stochastic background of negative binomial distribution", Physics Letters B 268 (1991) 447-452 https://doi.org/10.1016/0370-2693(91)91606-V
  10. F. A Popp, J. J. Chang, A. Herzog, Z. Yan, and Y. Yan, "Evidence of non-classical (squeezed) light in biological systems", Physics Letters A 293 (2002) 98-102 https://doi.org/10.1016/S0375-9601(01)00832-5
  11. B. Markussen, Inference for Stochastic Partial Differential Equations and Chaos Decomposition of the Negative Binomial Process, Ph.D. thesis, University of Copenhagen (2002)
  12. Hans-Jrgen Briegel, and Berthold-Georg Englert, "Quantum optical master equations: The use of damping bases", Phys. Rev. A 47 (1993) 3311-3329 https://doi.org/10.1103/PhysRevA.47.3311
  13. T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics", Opt. Ex. 15 (2007) 17172-17205 https://doi.org/10.1364/OE.15.017172
  14. S. van den Bergh, "Magnitudes of Sporadic and Perseid Meteors", Meteoritics 1 (1956) 395-398 https://doi.org/10.1111/j.1945-5100.1956.tb01373.x