The Library
Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimensions d <=3
Tools
Fröhlich, Jürg, Knowles, Antti, Schlein, Benjamin and Sohinger, Vedran (2017) Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimensions d <=3. Communications in Mathematical Physics, 356 (3). pp. 883-980. doi:10.1007/s00220-017-2994-7 ISSN 0010-3616.
|
PDF
WRAP-Gibbs-measures-nonlinear-Schrödinger-equations-Sohinger-2017.pdf - Accepted Version - Requires a PDF viewer. Download (1633Kb) | Preview |
Official URL: https://doi.org/10.1007/s00220-017-2994-7
Abstract
We prove that Gibbs measures of nonlinear Schr¨odinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions
in dimensions d = 1, 2, 3. The many-body quantum thermal states that we consider are the grand canonical ensemble for d = 1 and an appropriate modification of the grand canonical ensemble for d = 2, 3. In dimensions d = 2, 3, the Gibbs measures are supported on singular distributions, and a renormalization of the chemical potential is necessary. On the many-body quantum side, the need for renormalization is manifested by a rapid growth of the number of particles. We relate the original many-body quantum problem to a renormalized version obtained by solving a counterterm problem. Our proof is based on ideas from field theory, using a perturbative expansion in the interaction, organized by using a diagrammatic representation, and on Borel resummation of the resulting series.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Schrödinger equation, Quantum theory | ||||||||
Journal or Publication Title: | Communications in Mathematical Physics | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0010-3616 | ||||||||
Official Date: | December 2017 | ||||||||
Dates: |
|
||||||||
Volume: | 356 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 883-980 | ||||||||
DOI: | 10.1007/s00220-017-2994-7 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 3 October 2017 | ||||||||
Date of first compliant Open Access: | 6 October 2018 |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year