TY - JOUR

T1 - Macroscopic limiting dynamics of a class of inhomogeneous mean field quantum systems

AU - Duffield, N. G.

AU - Roos, H.

AU - Werner, R. F.

PY - 1992

Y1 - 1992

N2 - We study a class of Hamiltonian systems with inhomogeneous (i.e. site-dependent) mean field interactions. We define some notions of mean field limit for nets of states converging to a macroscopic limit state. We prove that the existence of such limits is preserved under the time evolution. This leads to a time evolution for the macroscopic limit states, i.e. to a closed set of equations for some macroscopic fields. We establish the basic properties of these equations, and their relation to the equilibrium statistical mechanics of the same systems. We discuss in detail the connection of our work to the problem of local equilibrium states, which motivated it.

AB - We study a class of Hamiltonian systems with inhomogeneous (i.e. site-dependent) mean field interactions. We define some notions of mean field limit for nets of states converging to a macroscopic limit state. We prove that the existence of such limits is preserved under the time evolution. This leads to a time evolution for the macroscopic limit states, i.e. to a closed set of equations for some macroscopic fields. We establish the basic properties of these equations, and their relation to the equilibrium statistical mechanics of the same systems. We discuss in detail the connection of our work to the problem of local equilibrium states, which motivated it.

M3 - Article

VL - 56

SP - 143

EP - 186

JO - Ann. Inst. H. Poincaré Phys. Théor.

JF - Ann. Inst. H. Poincaré Phys. Théor.

IS - 2

ER -