A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators

Details A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators

2002-04-09

arxiv.org/abs/math-ph/0204018v1

Commun. Math. Phys. 247 (2004) 391-419

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-004-1064-0

We study the semiclassical time evolution of observables given by matrix valued pseudodifferential operators and construct a decomposition of the Hilbert space $L^2(\rz^d)\otimes\kz^n$ into a finite number of almost invariant subspaces. For a certain class of observables, that is preserved by the time evolution, we prove an Egorov theorem. We then associate with each almost invariant subspace of $L^2(\rz^d)\otimes\kz^n$ a classical system on a product phase space $\TRd\times\cO$, where $\cO$ is a compact symplectic manifold on which the classical counterpart of the matrix degrees of freedom is represented. For the projections of eigenvectors of the quantum Hamiltonian to the almost invariant subspaces we finally prove quantum ergodicity to hold, if the associated classical systems are ergodic.

Affiliated with

Also associated with

No associations

Rating

A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A semiclassical Egorov theorem and quantum ergodicity for matrix valued operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-387469