A. D. Sukhanov, “Schrödinger uncertainty relation for a quantum oscillator in a thermostat”, TMF, 148:2 (2006), 295–308; Theoret. and Math. Phys., 148:2 (2006), 1123

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 148, Number 2, Pages 295–308
DOI: https://doi.org/10.4213/tmf2087 (Mi tmf2087)

This article is cited in 9 scientific papers (total in 9 papers)

Schrödinger uncertainty relation for a quantum oscillator in a thermostat

A. D. Sukhanov

Peoples Friendship University of Russia

Full-text PDF (442 kB) Citations (9)

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DOI: https://doi.org/10.4213/tmf2087

Abstract: 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.

Received: 20.12.2004

English version:
Theoretical and Mathematical Physics, 2006, Volume 148, Issue 2, Pages 1123–1134
DOI: https://doi.org/10.1007/s11232-006-0106-5

Bibliographic databases:

Language: Russian

Citation: A. D. Sukhanov, “Schrödinger uncertainty relation for a quantum oscillator in a thermostat”, TMF, 148:2 (2006), 295–308; Theoret. and Math. Phys., 148:2 (2006), 1123–1134

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https://doi.org/10.4213/tmf2087

https://www.mathnet.ru/eng/tmf/v148/i2/p295

This publication is cited in the following 9 articles:

A.D. Sukhanov, O.N. Golubjeva, V.G. Baryakhtar, “Quantum-Thermal Fluctuations of Effective Macroparameters and Their Correlations”, Ukr. J. Phys., 56:10 (2022), 1120
Rudoy Yu.G. Chekmareva I O., “Geometrical Aspects of the Equilibrium Statistical Thermodynamics”, J. Mech. Contin. Math. Sci., 2019, no. 1, 537–547
Artamonov A.A., Plotnikov E.M., “Thermodynamic and Relativistic Uncertainty Relations”, International Conference on Particle Physics and Astrophysics, Journal of Physics Conference Series, 798, eds. Galper A., Petrukhin A., Taranenko A., Selyuzhenkov I., Skorokhvatov M., Rubin S., Dmitrenko V., Gur, IOP Publishing Ltd, 2017, UNSP 012098
O.N. Golubjeva, S.V. Sidorov, V.G. Bar'yakhtar, “Numerical Simulation of Relaxation of Quantum Thermal Fluctuations”, Ukr. J. Phys., 60:10 (2015), 1062
A. D. Sukhanov, O. N. Golubjeva, “Arbitrary vacuums as a model of stochastic environment: On the problem of incorporating thermodynamics into quantum theory”, Phys. Part. Nuclei Lett., 9:3 (2012), 303
O. N. Golubjeva, A. D. Sukhanov, “Elements of nonequilibrium (ћ, k) dynamics at zero and finite temperatures”, Phys. Part. Nuclei Lett., 8:1 (2011), 1
Sukhanov A.D., Golubjeva O.N., “(A, k)-Dynamics as some generalization of equilibrium quantum statistical mechanics”, Physics of Particles and Nuclei, 41:7 (2010), 1083–1092
A. D. Sukhanov, O. N. Golubeva, “Toward a quantum generalization of equilibrium statistical thermodynamics: $\hbar$ – $k$ Dynamics”, Theoret. and Math. Phys., 160:2 (2009), 1177–1189
A. D. Sukhanov, “A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters”, Theoret. and Math. Phys., 154:1 (2008), 153–164

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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