Trapped modes in finite quantum waveguides

Details Trapped modes in finite quantum waveguides Trapped modes in finite quantum waveguides

2011-12-06

arxiv.org/abs/1112.1160v1

Physics

Mathematical Physics

Scientific paper

The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trapped eigenmode of finite L2 norm. We revisit this statement for resonators with long but finite branches that we call "finite waveguides". Although now there is no essential spectrum and all eigenfunctions have finite L2 norm, the trapping can be understood as an exponential decay of the eigenfunction inside the branches. We describe a general variational formalism for detecting trapped modes in such resonators. For finite waveguides with general cylindrical branches, we obtain a sufficient condition which determines the minimal length of branches for getting a trapped eigenmode. Varying the branch lengths may switch certain eigenmodes from non-trapped to trapped states. These concepts are illustrated for several typical waveguides (L-shape, bent strip, crossing of two stripes, etc.). We conclude that the well-established theory of trapping in infinite waveguides may be incomplete and require further development for being applied to microscopic quantum devices.

Affiliated with

Also associated with

No associations

Rating

Trapped modes in finite quantum waveguides 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 Trapped modes in finite quantum waveguides, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trapped modes in finite quantum waveguides will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380290