9 research outputs found
Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations
The equivalence of multipartite quantum mixed states under local unitary
transformations is studied. A criterion for the equivalence of non-degenerate
mixed multipartite quantum states under local unitary transformations is
presented.Comment: 7 page
Diffusion approximation for equilibrium Kawasaki dynamics in continuum
A Kawasaki dynamics in continuum is a dynamics of an infinite system of
interacting particles in which randomly hop over the space. In
this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs
measure as invariant measure. We study a diffusive limit of such a
dynamics, derived through a scaling of both the jump rate and time. Under weak
assumptions on the potential of pair interaction, , (in particular,
admitting a singularity of at zero), we prove that, on a set of smooth
local functions, the generator of the scaled dynamics converges to the
generator of the gradient stochastic dynamics. If the set on which the
generators converge is a core for the diffusion generator, the latter result
implies the weak convergence of finite-dimensional distributions of the
corresponding equilibrium processes. In particular, if the potential is
from and sufficiently quickly converges to zero
at infinity, we conclude the convergence of the processes from a result in
[Choi {\it et al.}, J. Math. Phys. 39 (1998) 6509--6536]