Abstract
The standard way of describing noise in a quantum system consists in attaching to the system a reservoir or bath, which is assumed to be in thermal equilibrium. Subsequently the combined equation of motion is solved to second order in the interaction and by averaging the result over the bath one gets the density matrix of the system itself. However, the differential equation obtained in this way has a serious flaw, which can be attributed to the inappropriate initial condition. For this reason we here take as starting point the thermal equilibrium of the combined system; the averages and correlation functions of quantities of interest provide us with the required information about the noise. This is explicitly demonstrated on the special model of a harmonic oscillator coupled to a bath of harmonic oscillators at temperature T. The result is compared with the standard calculation and it is shown that the latter is incorrect for time intervals smaller than kT/ħ. As an example the energy fluctuations in equilibrium are computed.
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van Kampen, N.G. A New Approach to Noise in Quantum Mechanics. Journal of Statistical Physics 115, 1057–1072 (2004). https://doi.org/10.1023/B:JOSS.0000022383.06086.6c
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DOI: https://doi.org/10.1023/B:JOSS.0000022383.06086.6c