Exact diagonalization of two quantum models for the damped harmonic oscillator

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作者
Rosenau, Da Costa, M.
Caldeira, A.O.
Dutra, S.M.
Westfahl, Jr., H.
机构
[1] Inst. de Fis. Gleb Wataghin, Universidade Estadual de Campinas, Unicamp, Caixa Postal 6165, 13083-970 Campinas, São Paulo, Brazil
[2] Huygens Laboratory, University of Leiden, P. O. Box 9504, 2300 RA Leiden, Netherlands
[3] Dept. Phys. Illinois Urbana-C., 1110 West Green Street, Urbana, IL 61801-3080, United States
来源
Physical Review A - Atomic, Molecular, and Optical Physics | 2000年 / 61卷 / 02期
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摘要
The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions deserve a thorough investigation. In this work, we apply a method that allows us to diagonalize exactly the dissipative Hamiltonians that are frequently adopted in the literature. Using this method, we derive the conditions of validity of the rotating-wave approximation (RWA) and show how this approximate description relates to more general ones. We also show that the existence of dissipative coherent states is intimately related to the RWA. Finally, through the evaluation of the dynamics of the damped oscillator, we notice an important property of the dissipative model that has not been properly accounted for in previous works, namely the necessity of new constraints to the application of the factorizable initial conditions.
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页码:221071 / 221071
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