Equilibration of a dissipative quantum oscillator

Annalen der Physik (Leipzig)

Volumn 16, Issue 5-6, 2007, Pages 319-324

  Ambegaokar, Vinay ^a  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

Author keywords

Coupled oscillators; Dissipation; Quantum mechanics

Indexed keywords

CONTINUUM MECHANICS; HARMONIC ANALYSIS;

COUPLED OSCILLATORS; HARMONIC OSCILLATORS; INTERACTING SYSTEMS; QUANTUM OSCILLATORS;

OSCILLATORS (ELECTRONIC);

EID: 34547161999     PISSN: 00033804     EISSN: 15213889     Source Type: Journal    
DOI: 10.1002/andp.200610236     Document Type: Article

References (15)

1. L. P. Kadanoff and G. Baym, Quantum statistical mechanics: Green's function methods in equilibrium and nonequilibrium problems (W. A. Benjamin, New York, 1962).
2. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964)
3. [Sov. Phys.-JETP 20, 1018 (1965)].
4. J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).
5. D. C. Langreth, in: 1975 NATO Advanced Study Institute on Linear and Nonlinear Electron Transport in Solids, edited by J. T. Devreese and V. E. van Doren (Plenum, New York, 1976), p. 3.
6. A. Kamenev, in: Nanophysics: Coherence and Transport, edited by H. Bouchiat et al. (Elsevier, Amsterdam, 2005), p. 177.
7. See, for example, S. Hershfield, Phys. Rev. Lett. 70,2134 (1993);
8. P. W. Brouwer, A. Lamacraft, and K. Flensberg, Phys. Rev. Lett. 94, 136801 (2005).
9. An exception is A. O. Caldeira and A. J. Leggett, Physica 121 A, 587 (1983), where in Eq. (6.35) a result equivalent to a special case - diagonal part of the density matrix; linear dissipation - of the present work is given, but details are omitted on grounds that the "procedure is straightforward but extremely tedious".
10. N.G. van Kampen, J. Stat. Phys. 115, 1057 (2004).
11. For an early use of this strategy, see R.J. Rubin, J. Am. Chem. Soc. 90, 3061 (1968), where many yet earlier references are given.
12. G. W. Ford, J.T. Lewis, and R. F. O'Connell, J. Stat. Phys. 53, 439 (1988).
13. V. Ambegaokar, J. Stat. Phys. 125, 1187 (2006).
14. This is nothing more or less than an example of P. A. M. Dirac's remarkably early observation [Proc. Roy. Soc. A 114, 243 (1927), described in "The Principles of Quantum Mechanics", 3rd ed. (Oxford, 1947), §44, p. 172.] that a continuum of final states is required for a quantum state to decay instead of endlessly oscillating.
15. D. P. Clougherty and W. Kohn, Phys. Rev. B 46, 4921 (1992).