Eigenfunction statistics of Wishart Brownian ensembles. (4th October 2017)

• Record Type: Journal Article
• Authors: Shukla, Pragya
• Is Part Of: Journal of physics. Volume 50:Number 43(2017)
• Publication Date: 2017-10-04
• Subjects: random matrix -- Wishart ensembles -- eigenfunctions -- fluctuations; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa8bd7
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear.