Transitions in eigenvalue and wavefunction structure in (1+2) -body random matrix ensembles with spin

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 81; no. 3 Pt 2; p. 036212
• Main Authors: Vyas, Manan, Kota, V K B, Chavda, N D
• Format: Journal Article
• Language: English
• Published: United States 01.03.2010
• ISSN: 1550-2376
• DOI: 10.1103/PhysRevE.81.036212

Finite interacting Fermi systems with a mean-field and a chaos generating two-body interaction are modeled by one plus two-body embedded Gaussian orthogonal ensemble of random matrices with spin degree of freedom [called EGOE(1+2)-s]. Numerical calculations are used to demonstrate that, as lambda , the strength of the interaction (measured in the units of the average spacing of the single-particle levels defining the mean-field), increases, generically there is Poisson to GOE transition in level fluctuations, Breit-Wigner to Gaussian transition in strength functions (also called local density of states) and also a duality region where information entropy will be the same in both the mean-field and interaction defined basis. Spin dependence of the transition points lambda_{c} , lambdaF, and lambdad , respectively, is described using the propagator for the spectral variances and the formula for the propagator is derived. We further establish that the duality region corresponds to a region of thermalization. For this purpose we compared the single-particle entropy defined by the occupancies of the single-particle orbitals with thermodynamic entropy and information entropy for various lambda values and they are very close to each other at lambda=lambdad.