Dip-ramp-plateau for Dyson Brownian motion
from the identity on U(N)

Forrester, Peter J.; Kieburg, Mario; Li, Shi-Hao; Zhang, Jiyuan

doi:10.2140/pmp.2024.5.321

Prob. Math. Phys.

2024

DOI: 10.2140/pmp.2024.5.321

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Dip-ramp-plateau for Dyson Brownian motion from the identity on U(N)

Peter J. Forrester,

Mario Kieburg,

Shi-Hao Li

et al.

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2024

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Efficient circular Dyson Brownian motion algorithm

Buijsman

2024

Phys. Rev. Research

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Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it describes the level dynamics of unitary (“circular”) matrices. A common scenario is that one wants to know about an initial configuration evolved over a certain interval of time, without being interested in the intermediate dynamics. Numerical evaluation of this is computationally expensive as the time-evolution algorithm is accurate only on short time intervals because of an underlying perturbative approximation. This work proposes an efficient and easy-to-implement improved circular Dyson Brownian motion algorithm for the unitary class (Dyson index β=2, physically corresponding to broken time-reversal symmetry). The algorithm allows one to study time evolution over arbitrarily large intervals of time at a fixed computational cost, with no approximations being involved. Published by the American Physical Society 2024

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Efficient circular Dyson Brownian motion algorithm

Buijsman

2024

Phys. Rev. Research

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Dip-ramp-plateau for Dyson Brownian motion from the identity on U(N)

Cited by 1 publication

References 84 publications

Efficient circular Dyson Brownian motion algorithm

Efficient circular Dyson Brownian motion algorithm

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