A new approach to the diffusive limit of the random schrodinger equation
Abstract/Contents
- Abstract
- In this thesis we introduce a new approach to the diffusive limit of the weakly random Schrodinger equation, first studied by L. Erdos, M. Salmhofer, and H.T. Yau. Our approach is based on a wavepacket decomposition of the evolution operator, which allows us to interpret the Duhamel series as an integral over piecewise linear paths. We relate the geometry of these paths to combinatorial features of a diagrammatic expansion which allows us to express the error terms in the expansion as an integral over paths that are exceptional in some way. These error terms are bounded using geometric arguments. The main term is then shown to have a semigroup property, which allows us to iteratively increase the timescale of validity of an effective diffusion. This is the first derivation of an effective diffusion equation from the random Schrodinger equation that is valid in two and more dimensions.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2023; ©2023 |
| Publication date | 2023; 2023 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Hernandez, Felipe |
|---|---|
| Degree supervisor | Ryzhik, Leonid |
| Thesis advisor | Ryzhik, Leonid |
| Thesis advisor | Chatterjee, Sourav |
| Thesis advisor | Papanicolaou, George |
| Degree committee member | Chatterjee, Sourav |
| Degree committee member | Papanicolaou, George |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Felipe Hernandez. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2023. |
| Location | https://purl.stanford.edu/md719hq5205 |
Access conditions
- Copyright
- © 2023 by Felipe Hernandez
- License
- This work is licensed under a Creative Commons Attribution 3.0 Unported license (CC BY).
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