Title:
Pointwise Control of Eigenfunctions on Quantum Graphs
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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