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q-deformations of statistical mechanical systems and motives over finite fields

Marcolli, Matilde and Zhi, Ren (2017) q-deformations of statistical mechanical systems and motives over finite fields. p-Adic Numbers, Ultrametric Analysis and Applications, 9 (3). pp. 204-227. ISSN 2070-0466. http://resolver.caltech.edu/CaltechAUTHORS:20170712-084525536

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Abstract

We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show that the q-deformations obtained in this way can be related to Habiro ring constructions of analytic functions over F_1 and to categorifications of Bost-Connes systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1134/S2070046617030049DOIArticle
https://link.springer.com/article/10.1134%2FS2070046617030049PublisherArticle
https://arxiv.org/abs/1704.06367arXivDiscussion Paper
Additional Information:© 2017 Pleiades Publishing, Ltd. Received: 05 May 2017; First Online: 03 August 2017. The first author was partially supported by NSF grants DMS-1201512, DMS-1707882 and PHY-1205440. The second author was supported by a Summer Undergraduate Research Fellowship at Caltech.
Funders:
Funding AgencyGrant Number
NSFDMS-1201512
NSFDMS-1707882
NSFPHY-1205440
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Subject Keywords:Witt rings, q-analogs, zeta functions, Quantum Statistical Mechanics
Record Number:CaltechAUTHORS:20170712-084525536
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170712-084525536
Official Citation:Marcolli, M. & Ren, Z. P-Adic Num Ultrametr Anal Appl (2017) 9: 204. https://doi.org/10.1134/S2070046617030049
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78989
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jul 2017 17:14
Last Modified:02 Aug 2017 17:20

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