Details
| Original language | Undefined/Unknown |
|---|---|
| Pages (from-to) | 383-424 |
| Number of pages | 42 |
| Journal | Rev. Math. Phys. |
| Volume | 4 |
| Issue number | 3 |
| Publication status | Published - 1992 |
Abstract
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In: Rev. Math. Phys., Vol. 4, No. 3, 1992, p. 383-424.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mean-field dynamical semigroups on C*-algebras
AU - Duffield, N. G.
AU - Werner, R. F.
PY - 1992
Y1 - 1992
N2 - We study a notion of the mean-field limit of a sequence of dynamical semigroups on the n-fold tensor products of a C*-algebra A with itself. In analogy with the theory of semigroups on Banach spaces we give abstract conditions for the existence of these limits. These conditions are verified in the case of semigroups whose generators are determined by the successive resymmetrizations of a fixed operator, as well as generators which can be approximated by generators of this type. This includes the time evolutions of the mean-field versions of quantum lattice systems. In these cases the limiting dynamical semigroup is given by a continuous flow on the state space of A. For a class of such flows we show stability by constructing a Liapunov function. We also give examples where the limiting evolution is given by a diffusion, rather than a flow on the state space of A.
AB - We study a notion of the mean-field limit of a sequence of dynamical semigroups on the n-fold tensor products of a C*-algebra A with itself. In analogy with the theory of semigroups on Banach spaces we give abstract conditions for the existence of these limits. These conditions are verified in the case of semigroups whose generators are determined by the successive resymmetrizations of a fixed operator, as well as generators which can be approximated by generators of this type. This includes the time evolutions of the mean-field versions of quantum lattice systems. In these cases the limiting dynamical semigroup is given by a continuous flow on the state space of A. For a class of such flows we show stability by constructing a Liapunov function. We also give examples where the limiting evolution is given by a diffusion, rather than a flow on the state space of A.
U2 - 10.1142/S0129055X92000108
DO - 10.1142/S0129055X92000108
M3 - Article
VL - 4
SP - 383
EP - 424
JO - Rev. Math. Phys.
JF - Rev. Math. Phys.
SN - 1793-6659
IS - 3
ER -