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Title: Partition of energy for a dissipative quantum oscillator
Authors: Białas, Piotr
Spiechowicz, Jakub
Łuczka, Jerzy
Keywords: quantum oscillator; energy
Issue Date: 2018
Citation: Scientific Reports, Vol. 8, iss. 1 (2018), Art. No. 16080
Abstract: 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 Ek and mean potential energy Ep of the oscillator are expressed as Ek = 〈εk〉 and Ep = 〈εp〉, where 〈εk〉 and 〈εp〉 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 Ek and Ep according to the probability distribution [Formula: see text] and [Formula: see text], 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.
DOI: 10.1038/s41598-018-34385-9
ISSN: 2045-2322
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