Reduced Gutzwiller formula with symmetry: case of a finite group

Physics – Mathematical Physics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

20 pages

Scientific paper

10.1063/1.2184890

We consider a classical Hamiltonian $H$ on $\mathbb{R}^{2d}$, invariant by a finite group of symmetry $G$, whose Weyl quantization $\hat{H}$ is a selfadjoint operator on $L^2(\mathbb{R}^d)$. If $\chi$ is an irreducible character of $G$, we investigate the spectrum of its restriction $\hat{H}\_\chi$ to the symmetry subspace $L^2\_\chi(\mathbb{R}^d)$ of $L^2(\mathbb{R}^d)$ coming from the decomposition of Peter-Weyl. We give reduced semi-classical asymptotics of a regularised spectral density describing the spectrum of $\hat{H}\_\chi$ near a non critical energy $E\in\mathbb{R}$. If $\Sigma\_E:=\{H=E \}$ is compact, assuming that periodic orbits are non-degenerate in $\Sigma\_E/G$, we get a reduced Gutzwiller trace formula which makes periodic orbits of the reduced space $\Sigma\_E/G$ appear. The method is based upon the use of coherent states, whose propagation was given in the work of M. Combescure and D. Robert.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Reduced Gutzwiller formula with symmetry: case of a finite group 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 Reduced Gutzwiller formula with symmetry: case of a finite group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reduced Gutzwiller formula with symmetry: case of a finite group will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-624474

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.