Monte Carlo simulations of random non-commutative geometries
Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
IOP Publishing
2016
|
| Online Access: | https://eprints.nottingham.ac.uk/33251/ |
| _version_ | 1848794593362968576 |
|---|---|
| author | Barrett, John W. Glaser, Lisa |
| author_facet | Barrett, John W. Glaser, Lisa |
| author_sort | Barrett, John W. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various qualitatively different types of behaviour of these random Dirac operators are exhibited. Some features are explained in terms of the theory of random matrices but other phenomena remain mysterious. Some of the models with a quartic action of symmetry-breaking type display a phase transition. Close to the phase transition the spectrum of a typical Dirac operator shows manifold-like behaviour for the eigenvalues below a cut-off scale. |
| first_indexed | 2025-11-14T19:18:39Z |
| format | Article |
| id | nottingham-33251 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:18:39Z |
| publishDate | 2016 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-332512020-05-04T17:52:21Z https://eprints.nottingham.ac.uk/33251/ Monte Carlo simulations of random non-commutative geometries Barrett, John W. Glaser, Lisa Random non-commutative geometries are introduced by integrating over the space of Dirac operators that form a spectral triple with a fixed algebra and Hilbert space. The cases with the simplest types of Clifford algebra are investigated using Monte Carlo simulations to compute the integrals. Various qualitatively different types of behaviour of these random Dirac operators are exhibited. Some features are explained in terms of the theory of random matrices but other phenomena remain mysterious. Some of the models with a quartic action of symmetry-breaking type display a phase transition. Close to the phase transition the spectrum of a typical Dirac operator shows manifold-like behaviour for the eigenvalues below a cut-off scale. IOP Publishing 2016-05-11 Article PeerReviewed Barrett, John W. and Glaser, Lisa (2016) Monte Carlo simulations of random non-commutative geometries. Journal of Physics A: Mathematical and Theoretical, 49 (24). ISSN 1751-8113 http://dx.doi.org/10.1088/1751-8113/49/24/245001 doi:10.1088/1751-8113/49/24/245001 doi:10.1088/1751-8113/49/24/245001 |
| spellingShingle | Barrett, John W. Glaser, Lisa Monte Carlo simulations of random non-commutative geometries |
| title | Monte Carlo simulations of random non-commutative geometries |
| title_full | Monte Carlo simulations of random non-commutative geometries |
| title_fullStr | Monte Carlo simulations of random non-commutative geometries |
| title_full_unstemmed | Monte Carlo simulations of random non-commutative geometries |
| title_short | Monte Carlo simulations of random non-commutative geometries |
| title_sort | monte carlo simulations of random non-commutative geometries |
| url | https://eprints.nottingham.ac.uk/33251/ https://eprints.nottingham.ac.uk/33251/ https://eprints.nottingham.ac.uk/33251/ |