## Local dynamics of mean-field Quantum Systems (1991)

Citations: | 6 - 1 self |

### BibTeX

@MISC{Duffield91localdynamics,

author = {N.G. Duffield and R.F. Werner},

title = {Local dynamics of mean-field Quantum Systems},

year = {1991}

}

### OpenURL

### Abstract

. In this paper we extend the theory of mean-field-dynamical semigroups given in [DW1,Du1] to treat the irreversible mean-field dynamics of quasi-local mean-field observables. These are observables which are site averaged except within a region of tagged sites. In the thermodynamic limit the tagged sites absorb the whole lattice, but also become negligible in proportion to the bulk. We develop the theory in detail for a class of interactions which contains the mean-field versions of quantum lattice interactions with infinite range. For this class we obtain an explicit form of the dynamics in the thermodynamic limit. We show that the evolution of the bulk is governed by a flow on the one-particle state space, whereas the evolution of local perturbations in the tagged region factorizes over sites, and is governed by a cocycle of completely positive maps. We obtain an H-theorem which suggests that local disturbances typically become completely delocalized for large times, and we show this...