Quantum-elastic bump on a surface
Quantum Physics
2016-11-23 v3 Mathematical Physics
math.MP
Biological Physics
Abstract
We use an exact solution of the elastic membrane shape equation, representing the curvature, which will serve as a quantum potential in the quantum mechanical two dimensional Schrodinger equation for a (quasi-) particle on the surface of the membrane. Surface curvature in the quasi one-dimensional case is related to an unexpected static formation: on one hand the elastic energy has a maximum where surface curvature has a maximum and on the other hand the concentration of the expectation value to find the (quasi-) particle is again where the elastic energy is concentrated, namely where surface curvature has a maximum. This represents a particular form of a conformon.
Cite
@article{arxiv.1402.2078,
title = {Quantum-elastic bump on a surface},
author = {Victor Atanasov and Rossen Dandoloff},
journal= {arXiv preprint arXiv:1402.2078},
year = {2016}
}