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Abstract: We consider a quantum system weakly coupled to a large heat bath of harmonicoscillators. It is well known that such a boson bath initially at thermalequilibrium thermalises the system. We show that assuming a priori anequilibrium state is not necessary to obtain the thermalisation of the system.We determine the complete Schr\-odinger time evolution of the subsystem ofinterest for an initial pure product state of the composite system consistingof the considered system and the bath. We find that the system relaxes intocanonical equilibrium for almost all initial pure bath states ofmacroscopically well-defined energy. The temperature of the system asymptoticthermal state is determined by the energy of the initial bath state as thecorresponding microcanonical temperature. Moreover, the time evolution of thesystem is identical to the one obtained assuming that the boson bath isinitially at thermal equilibrium with this temperature. A significant part ofour approach is applicable to other baths and we identify the bath featureswhich are requisite for the thermalisation studied.



Author: S. Camalet

Source: https://arxiv.org/







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