Pointwise Control of Eigenfunctions on Quantum Graphs

dc.contributor.author Harrell, Evans M.
dc.contributor.corporatename Georgia Institute of Technology. School of Mathematics en_US
dc.date.accessioned 2017-01-05T21:35:54Z
dc.date.available 2017-01-05T21:35:54Z
dc.date.issued 2016-10-09
dc.description Presented at the QMath13 Conference: Mathematical Results in Quantum Theory, October 8-11, 2016 at the Clough Undergraduate Learning Commons, Georgia Tech. en_US
dc.description Quantum Mechanics on Graphs and Similar Structures - Sunday, October 9th, 2016, Skiles 006 - Chair: Peter Kuchment en_US
dc.description Evans Harrell is with the Georgia Institute of Technology, School of Mathematics. This is joint work with Anna Maltsev of the University of Bristol, CMP, to appear, and work in progress. en_US
dc.description.abstract Pointwise bounds on eigenfunctions are useful for establishing localization of quantum states, and they have implications for the distribution of eigenvalues and for physical properties such as conductivity. In the low-energy regime, localization is associated with exponential decrease through potential barriers. We adapt the Agmon method to control this tunneling effect for quantum graphs with Sobolev and pointwise estimates. It turns out that as a generic matter, the rate of decay is controlled by an Agmon metric related to the classical Liouville- Geen approximation for the line, but more rapid decay is typical, arising from the geometry of the graph. In the high-energy regime one expects states to oscillate but to be dominated by a 'landscape function' in terms of the potential and features of the graph. We discuss the construction of useful landscape functions for quantum graphs. en_US
dc.identifier.uri http://hdl.handle.net/1853/56129
dc.language.iso en_US en_US
dc.publisher Georgia Institute of Technology en_US
dc.relation.ispartofseries QMath13 Conference: Mathematical Results in Quantum Physics
dc.subject Quantum graphs en_US
dc.title Pointwise Control of Eigenfunctions on Quantum Graphs en_US
dc.type Text
dc.type.genre Proceedings
dspace.entity.type Publication
local.contributor.author Harrell, Evans M.
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
local.relation.ispartofseries QMath13 Conference: Mathematical Results in Quantum Physics
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