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Spin Geometry and Quantum Diffusion

Citation

Gakkhar, Sitanshu (2025) Spin Geometry and Quantum Diffusion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ded0-hn95. https://resolver.caltech.edu/CaltechTHESIS:09162024-065933174

Abstract

This thesis studies diffusion processes on spinor endomorphism algebras. The spinor and connection laplacian generated heat semigroups are shown to quantum dynamical semigroups, and after spectral truncation the existence of Evans-Hudson flows is established. The vacuum state expectation of the process is related to the spectral action principle in noncommutative geometry. Examples where the flow is proven to exist for untruncated laplacians are given. Convergence of finite dimensional approximations, through discretization and truncation, to spectral triples encoding Riemannian geometry and their statespaces as quantum metric spaces is also considered.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:noncommutative geometry, spin geometry, stochastic processes, diffusion, quantum diffusion, noncommutative probability, quantum probability
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Not set
Research Advisor(s):
  • Marcolli, Matilde
Thesis Committee:
  • Makarov, Nikolai G. (chair)
  • Gukov, Sergei
  • Ćaćić, Branimir Josip
  • Marcolli, Matilde
Defense Date:29 August 2024
Funders:
Funding AgencyGrant Number
NSFDMS-2104330
NSFDMS-1707882
FQXiFQXi-RFP-1 804
FQXiFQXi-RFP-CPW-2014
FQXiSVCF 2020-224047
Record Number:CaltechTHESIS:09162024-065933174
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:09162024-065933174
DOI:10.7907/ded0-hn95
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/978-3-031-38271-0_47DOIArticle based on section 5.1, 5.2
ORCID:
AuthorORCID
Gakkhar, Sitanshu0000-0002-2895-9921
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16730
Collection:CaltechTHESIS
Deposited By: Sitanshu Gakkhar
Deposited On:24 Sep 2024 16:24
Last Modified:24 Sep 2024 16:24

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