Geodesic
Schrödinger uncertainty relation for a quantum oscillator in a thermostat
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 295-308 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce the Schrödinger correlator as the holistic characteristic of two types of fluctuation correlations in quantum dynamics and in statistical thermodynamics. We are the first to derive it using methods of thermofield dynamics for the coordinate–momentum variables of a quantum oscillator in a thermostat. We show that the obtained value ensures that the Schrödinger uncertainty relation becomes an equality at all temperatures. We find that the thermal equilibrium for the quantum oscillator has the sense of the thermal correlated coherent state and can be adequately described by a wave function with temperature-dependent amplitude and phase.
Keywords: Schrödinger correlator, saturated Schrödinger uncertainty relation, nonadditivity of quantum and thermal fluctuations, thermal correlated coherent state, thermal noise in pure state. 
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A. D. Sukhanov. Schrödinger uncertainty relation for a quantum oscillator in a thermostat. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 295-308. http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a9/

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