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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.05981 |
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| _version_ | 1866913591821598720 |
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| author | Anegawa, Takanori Iizuka, Norihiro Kabat, Daniel |
| author_facet | Anegawa, Takanori Iizuka, Norihiro Kabat, Daniel |
| contents | We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in $0+1$ dimensions, with $D$ matrices, and use $1/D$ as an expansion parameter. This can be thought of as a non-commutative large-$D$ vector model, with two independent quartic couplings for the two different orderings of the matrices. We compute a thermal two-point correlator to ${\cal O}(1/D)$ and find that the degeneracy present at large $D$ is lifted, with energy levels split by an amount $\sim 1/\sqrt{D}$. This implies a timescale for thermal dissipation $\sim \sqrt{D}$. At high temperatures dissipation is predominantly due to one of the two quartic couplings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05981 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dissipation in the $1/D$ expansion for planar matrix models Anegawa, Takanori Iizuka, Norihiro Kabat, Daniel High Energy Physics - Theory We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in $0+1$ dimensions, with $D$ matrices, and use $1/D$ as an expansion parameter. This can be thought of as a non-commutative large-$D$ vector model, with two independent quartic couplings for the two different orderings of the matrices. We compute a thermal two-point correlator to ${\cal O}(1/D)$ and find that the degeneracy present at large $D$ is lifted, with energy levels split by an amount $\sim 1/\sqrt{D}$. This implies a timescale for thermal dissipation $\sim \sqrt{D}$. At high temperatures dissipation is predominantly due to one of the two quartic couplings. |
| title | Dissipation in the $1/D$ expansion for planar matrix models |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.05981 |