Partition of energy for a dissipative quantum oscillator

We reveal a new face of the old clichéd system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems. Both mean kinetic energy E k and mean potential energy E p of the oscillator are expressed as E...

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Bibliographic Details
Published in:Scientific reports 2018-10, Vol.8 (1), p.16080-12, Article 16080
Main Authors: Bialas, P., Spiechowicz, J., Łuczka, J.
Format: Article
Language:English
Subjects:
639/766/483/640
639/766/530/2804
Humanities and Social Sciences
Kinetic energy
multidisciplinary
Oscillators
Potential energy
Probability distribution
Quantum theory
Science
Science (multidisciplinary)
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Summary:We reveal a new face of the old clichéd system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems. Both mean kinetic energy E k and mean potential energy E p of the oscillator are expressed as E k  = 〈 ε k 〉 and E p  = 〈 ε p 〉, where 〈 ε k 〉 and 〈 ε p 〉 are mean kinetic and potential energies per one degree of freedom of the thermostat which consists of harmonic oscillators too. The symbol 〈...〉 denotes two-fold averaging: (i) over the Gibbs canonical state for the thermostat and (ii) over thermostat oscillators frequencies ω which contribute to E k and E p according to the probability distribution ℙ k ( ω ) and ℙ p ( ω ) , respectively. The role of the system-thermostat coupling strength and the memory time is analysed for the exponentially decaying memory function (Drude dissipation mechanism) and the algebraically decaying damping kernel.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-018-34385-9