Related papers: Soft quantum waveguides in three dimensions

Soft quantum waveguides in three dimensions

URL: http://arxiv.org/abs/2108.13142v2
Date: Fri, 8 Apr 2022 07:54:38 GMT
Title: Soft quantum waveguides in three dimensions
Authors: Pavel Exner
Abstract summary: We discuss a three-dimensional soft quantum waveguide with an attractive potential supported by an infinite tube and keeping its transverse profile fixed. We show that if the tube is straight, the distance between its ends is unbounded, and its twist satisfies the so-called Tang condition. We derive a sufficient condition, expressed in terms of the tube geometry, for the discrete spectrum of such an operator to be nonempty.
Score: 0.0
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: We discuss a three-dimensional soft quantum waveguide, in other words, Schr\"odinger operator in $\R^3$ with an attractive potential supported by an infinite tube and keeping its transverse profile fixed. We show that if the tube is asymptotically straight, the distance between its ends is unbounded, and its twist satisfies the so-called Tang condition, the esential spectrum is not affected by smooth bends. Furthermore, we derive a sufficient condition, expressed in terms of the tube geometry, for the discrete spectrum of such an operator to be nonempty.

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