Local dynamics of mean-field quantum systems

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OriginalspracheEnglisch
Seiten (von - bis)1016-1054
Seitenumfang39
FachzeitschriftHelv. Phys. Acta
Jahrgang65
Ausgabenummer8
PublikationsstatusVeröffentlicht - 1992

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 to be true for a dense set of interactions. We characterize all limiting evolutions for certain subclasses of interactions, and also exhibit some possibilities beyond the class we study in detail: for example, the limiting evolution of the bulk may exist, while the local cocycle does not. In another case the bulk evolution is given by a diffusion rather than a flow, and the local evolution no longer factorizes over sites.

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Local dynamics of mean-field quantum systems. / Duffield, N. G.; Werner, R. F.
in: Helv. Phys. Acta, Jahrgang 65, Nr. 8, 1992, S. 1016-1054.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Duffield, NG & Werner, RF 1992, 'Local dynamics of mean-field quantum systems', Helv. Phys. Acta, Jg. 65, Nr. 8, S. 1016-1054.
Duffield, N. G., & Werner, R. F. (1992). Local dynamics of mean-field quantum systems. Helv. Phys. Acta, 65(8), 1016-1054.
Duffield NG, Werner RF. Local dynamics of mean-field quantum systems. Helv. Phys. Acta. 1992;65(8):1016-1054.
Duffield, N. G. ; Werner, R. F. / Local dynamics of mean-field quantum systems. in: Helv. Phys. Acta. 1992 ; Jahrgang 65, Nr. 8. S. 1016-1054.
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TY - JOUR

T1 - Local dynamics of mean-field quantum systems

AU - Duffield, N. G.

AU - Werner, R. F.

PY - 1992

Y1 - 1992

N2 - 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 to be true for a dense set of interactions. We characterize all limiting evolutions for certain subclasses of interactions, and also exhibit some possibilities beyond the class we study in detail: for example, the limiting evolution of the bulk may exist, while the local cocycle does not. In another case the bulk evolution is given by a diffusion rather than a flow, and the local evolution no longer factorizes over sites.

AB - 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 to be true for a dense set of interactions. We characterize all limiting evolutions for certain subclasses of interactions, and also exhibit some possibilities beyond the class we study in detail: for example, the limiting evolution of the bulk may exist, while the local cocycle does not. In another case the bulk evolution is given by a diffusion rather than a flow, and the local evolution no longer factorizes over sites.

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VL - 65

SP - 1016

EP - 1054

JO - Helv. Phys. Acta

JF - Helv. Phys. Acta

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ER -

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