Some exact correlations in the Dyson Brownian motion model for transitions to the CUE

Abstract

The Dyson Brownian motion model for transistions to the CUE is considered. For initial eigenvalue probability density functions corresponding to the COE and CSE, the density-density correlation function between an eigenvalue at position lambda' initially (tau = 0) and an eigenvalue at position lambda for general tau, is calculated. Theoretical predictions for the asymptotic behaviour are verified, and the distribution for the initial rate of change of the eigenvalues is calculated. Also, for initial conditions corresponding to equi-spaced eigenvalues, the n-point equal parameter distribution is computed. The extension of the calculation of these quantities to a multiparameter version of the theory is given.

19 pages, latex, no figures

References in corpus (2)

• Random-Matrix Theory of Parametric Correlations in the Spectra of Disordered Metals and Chaotic Billiards
• Crossover Driven by Time-reversal Symmetry Breaking in Quantum Chaos

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• Dip-ramp-plateau for Dyson Brownian motion from the identity on $U(N)$
• Exact and asymtotic formulas for overdamped Brownian dynamics
• Efficient circular Dyson Brownian motion algorithm
• Spectral Correlations in the Crossover Transition from a Superposition of Harmonic Oscillators to the Gaussian Unitary Ensemble