×

Bound states in curved quantum waveguides. (English) Zbl 0693.46066

Summary: A free quantum particle living on a curved planar strip \(\Omega\) of a fixed width d with Dirichlet boundary conditions is studied. It can serve as a model for electrons in thin films on a cylinder-type substrate, or in a curved quantum wire. Assuming that the boundary of \(\Omega\) is infinitely smooth and its curvature decays fast enough at infinity, it is proved that a bound state with energy below the first transversal mode exists for all sufficiently small d. A lower bound on the critical width is obtained using the Birman-Schwinger technique.

MSC:

46N99 Miscellaneous applications of functional analysis
81R30 Coherent states
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1063/1.1727528 · doi:10.1063/1.1727528
[2] DOI: 10.1016/0003-4916(71)90031-5 · doi:10.1016/0003-4916(71)90031-5
[3] DOI: 10.1007/BF02754884 · doi:10.1007/BF02754884
[4] DOI: 10.1007/BF02906835 · doi:10.1007/BF02906835
[5] DOI: 10.1007/BF02906835 · doi:10.1007/BF02906835
[6] DOI: 10.1007/BF02906835 · doi:10.1007/BF02906835
[7] DOI: 10.1016/0003-4916(77)90351-7 · doi:10.1016/0003-4916(77)90351-7
[8] DOI: 10.1016/0003-4916(77)90351-7 · doi:10.1016/0003-4916(77)90351-7
[9] DOI: 10.1063/1.98066 · doi:10.1063/1.98066
[10] DOI: 10.1109/TMTT.1983.1131585 · doi:10.1109/TMTT.1983.1131585
[11] DOI: 10.1103/PhysRevLett.60.2081 · doi:10.1103/PhysRevLett.60.2081
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.