PT-symmetric models in curved manifolds

Details PT-symmetric models in curved manifolds PT-symmetric models in curved manifolds

2010-01-18

arxiv.org/abs/1001.2988v1

J. Phys. A: Math. Theor. 43 (2010) 485204

Physics

Mathematical Physics

37 pages, PDFLaTeX with 11 figures

Scientific paper

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.

Affiliated with

Also associated with

No associations

Rating

PT-symmetric models in curved manifolds 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 PT-symmetric models in curved manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and PT-symmetric models in curved manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-660926