Schr\"odinger uncertainty relation for a~quantum oscillator in a~thermostat
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 295-308
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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.
@article{TMF_2006_148_2_a9,
author = {A. D. Sukhanov},
title = {Schr\"odinger uncertainty relation for a~quantum oscillator in a~thermostat},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {295--308},
publisher = {mathdoc},
volume = {148},
number = {2},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a9/}
}
TY - JOUR AU - A. D. Sukhanov TI - Schr\"odinger uncertainty relation for a~quantum oscillator in a~thermostat JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2006 SP - 295 EP - 308 VL - 148 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a9/ LA - ru ID - TMF_2006_148_2_a9 ER -
A. D. Sukhanov. Schr\"odinger 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/