Dissipation in the $1/D$ expansion for planar matrix models

Takanori Anegawa; Norihiro Iizuka; Daniel Kabat

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arXiv · 2409.05981

Dissipation in the $1/D$ expansion for planar matrix models

Takanori Anegawa·Norihiro Iizuka·Daniel Kabat

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Abstract

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.

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Takanori Anegawa, Norihiro Iizuka, Daniel Kabat. 2024-09-09. Dissipation in the $1/D$ expansion for planar matrix models. https://arxiv.org/abs/2409.05981

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