Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
A dynamical approach to quantum optimal transport
Dissertation (MSc (Physics))--University of Pretoria, 2021.
Saved in:
| Other Authors: | |
|---|---|
| Format: | Thesis |
| Language: | English |
| Published: |
University of Pretoria
2021
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613695201247232 |
|---|---|
| access_status_str | Open Access |
| author2 | Duvenhage, Rocco |
| author_browse | Duvenhage, Rocco |
| author_facet | Duvenhage, Rocco |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Physics))--University of Pretoria, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/82602 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:40:13.972Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/82602 A dynamical approach to quantum optimal transport Duvenhage, Rocco 14047099@tuks.co.za Mare, Chantel Quantum statistical mechanics UCTD Dissertation (MSc (Physics))--University of Pretoria, 2021. We begin with a brief overview of measure theory and the theory of optimal transport. We then proceed to study a special class of quantum states represented by quantum Markov semi-groups (QMS) on a finite dimensional C*-algebra. We show that these semi-groups are ergodic and have a unique stationary state. We then proceed to define a notion of quantum detailed balance and show that these semi-groups satisfy this detailed balance condition with respect to the unique stationary state. This condition characterises the form of the generator of the QMS. Starting from the form of this generator we proceed to show how one can construct the operators of multiplication, gradient and divergence acting on a direct sum of Hilbert spaces. These notions are then used to obtain a quantum mechanical analog of the continuity equation for probability densities. We define a Riemannian manifold of density matrices and proceed to show that for a given metric, the time evolution of our quantum states can be written as gradient flow for the relative entropy functional. This is a direct quantum analog to the time evolution of probability densities on Rn, which can be written as gradient flow for the Wasserstein metric. Physics MSc (Physics) Unrestricted 2021-11-09T11:30:29Z 2021-11-09T11:30:29Z 2021 2021 Dissertation * A2022 http://hdl.handle.net/2263/82602 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Quantum statistical mechanics UCTD A dynamical approach to quantum optimal transport |
| title | A dynamical approach to quantum optimal transport |
| title_full | A dynamical approach to quantum optimal transport |
| title_fullStr | A dynamical approach to quantum optimal transport |
| title_full_unstemmed | A dynamical approach to quantum optimal transport |
| title_short | A dynamical approach to quantum optimal transport |
| title_sort | dynamical approach to quantum optimal transport |
| topic | Quantum statistical mechanics UCTD |
| url | http://hdl.handle.net/2263/82602 |