Abstract
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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