Axiomatic construction of quantum Langevin equations. (arXiv:1809.08975v2 [cond-mat.stat-mech] UPDATED)

A phenomenological construction of quantum Langevin equations, based on the
physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo
formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation
theorem is presented. The case of a single harmonic oscillator coupled to a
large external bath is analysed in detail. This allows to distinguish a
markovian semi-classical approach, due to Bedeaux and Mazur, from a
non-markovian full quantum approach, due to to Ford, Kac and Mazur. The
quantum-fluctuation-dissipation theorem is seen to be incompatible with a
markovian dynamics. Possible applications to the quantum spherical model are
discussed.

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