Quantum Oscillator in a Blackbody Radiation Field

Ford, G. W.; Lewis, J. T.; O’Connell, R. F.

doi:10.1103/physrevlett.55.2273

Cited by 230 publications

(259 citation statements)

References 6 publications

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“…The quantum Langevin equation can be considered as the basis of the macroscopic description of a quantum particle coupled to an environment or a heat bath [8], [9].…”

Section: Quantum Dynamicsmentioning

confidence: 99%

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Electromagnetic field quantization in a linear polarizable and magnetizable medium

Kheirandish

Amooshahi

2006

Phys. Rev. A

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By modeling a linear polarizable and magnetizable medium (magnetodielectric) with two quantum fields, namely E and M, electromagnetic field is quantized in such a medium consistently and systematically. A Hamiltonian is proposed from which, using the Heisenberg equations, Maxwell and constitutive equations of the medium are obtained. For a homogeneous medium, the equation of motion of the quantum vector potential, A, is derived and solved analytically. Two coupling functions which describe the electromagnetic properties of the medium are introduced. Four examples are considered showing the features and the applicability of the model to both absorptive and nonabsorptive magneto-dielectrics.

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“…The quantum Langevin equation can be considered as the basis of the macroscopic description of a quantum particle coupled to an environment or a heat bath [8], [9].…”

Section: Quantum Dynamicsmentioning

confidence: 99%

“…The macroscopic description of a quantum damped harmonic oscillator with frequency ω 0 is represented in terms of the Langevin equation [8,9,10]:…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic field quantization in a linear polarizable and magnetizable medium

Kheirandish

Amooshahi

2006

Phys. Rev. A

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“…As expected, the frequency shifts are different from the usual RWA results but the question still remains as to whether or not they are correct. This question can be answered by virtue of the fact that we have previously calculated the exact energy shift for the problem [3] and it is our purpose here to compare the various results. …”

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confidence: 99%

“…In particular, for our system there should be a contribution to the entropy arising from the population distribution over the continuum of energy levels. The overall result [3] is that temperature-dependent shifts in both energy and free energy occur, which arise from off-resonant contributions, which are especially important for super-Ohmic reservoirs (Re +~(|)t| a , where a>0), such as the radiation reservoir (Re +~(|)t| 2 ). Such off-resonant contributions do not appear in weak coupling calculations.…”

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confidence: 99%

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Frequency Shifts and Master Equations for a Quantum Oscillator Coupled to a Reservoir

Ford

O’Connell

1998

Annals of Physics

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For a quantum oscillator coupled to a reservoir, master equations obtained under the assumptions of weak coupling and use of a rotating-wave Hamiltonian (RWA) are known to give incorrect frequency shifts. Here, we show that a calculation which does not invoke the RWA gives results for the frequency shifts, which agree with exact results for Lamb-type (temperature T=0) shifts. However, for non-zero T, we point out that, in general, corresponding energy and free energy shifts for the system require exact treatments since off-resonant contributions (which are automatically excluded in weak coupling calculations) are important in the case of super-Ohmic reservoirs. Academic PressMaster equations are pervasive in many areas of physics, particularly quantum optics. They give information, primarily, on the time dependence of the reduced density matrix but they also give information on energy shifts (i.e., Lamb-type shifts). Most derivations in the literature assume (a) weak coupling and (b) the rotating-wave approximation (RWA) but it is well-known that the energy shifts resulting from these calculations are not correct. In particular, Ackerhalt et al.[1], among others, have correctly pointed out that counter-rotating terms (which are dropped in the RWA) make a major contribution to the Lamb shift.Recently, we have derived a master equation for an oscillator coupled to a very general dissipative environment (in particular, the electromagnetic field) without using the RWA [2]. As expected, the frequency shifts are different from the usual RWA results but the question still remains as to whether or not they are correct. This question can be answered by virtue of the fact that we have previously calculated the exact energy shift for the problem [3] and it is our purpose here to compare the various results.

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Dissipative and fluctuation phenomena in quantum mechanics with applications

O’Connell

1996

Int. J. Quantum Chem.

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mClassical dissipative and fluctuation phenomena have a long history beginning with the experimental work on Brownian motion in 1827 and its theoretical explanation by Einstein in 1905, followed by Langevin's elegant explanation in 1908 when he introduced the idea of a stochastic differential equation. While we briefly review this history, our emphasis is on stochastic phenomena requiring quantum mechanics. We discuss many problems in a variety of areas and point out the merits of a quantum generalized Langevin equation in providing a universal framework for the solution of such problems.As an example, we analyze in detail the problem of radiation reaction in quantum electrodynamics. 0 1996 John Wiley & Sons, Inc.

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Quantum Oscillator in a Blackbody Radiation Field

Cited by 230 publications

References 6 publications

Electromagnetic field quantization in a linear polarizable and magnetizable medium

Electromagnetic field quantization in a linear polarizable and magnetizable medium

Frequency Shifts and Master Equations for a Quantum Oscillator Coupled to a Reservoir

Dissipative and fluctuation phenomena in quantum mechanics with applications

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