Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times

Details Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times

2004-02-03

arxiv.org/abs/math/0402038v1

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-005-1319-4

We study the behaviour of time evolved quantum mechanical expectation values in Lagrangian states in the limit $\hbar\to 0$ and $t\to\infty$. We show that it depends strongly on the dynamical properties of the corresponding classical system. If the classical system is strongly chaotic, i.e. Anosov, then the expectation values tend to a universal limit. This can be viewed as an analogue of mixing in the classical system. If the classical system is integrable, then the expectation values need not converge, and if they converge their limit depends on the initial state. An additional difference occurs in the timescales for which we can prove this behaviour, in the chaotic case we get up to Ehrenfest time, $t\sim \ln(1/\hbar)$, whereas for integrable system we have a much larger time range.

Affiliated with

Also associated with

No associations

Rating

Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times 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 Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Semiclassical behaviour of expectation values in time evolved Lagrangian states for large times will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-546738