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

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.81.036212· OSTI ID:21344719

Vyas, Manan ^[1]; Kota, V K. B. ^[1]; Chavda, N D ^[2]

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1. Physical Research Laboratory, Ahmedabad 380 009 (India)
2. Applied Physics Department, Faculty of Technology and Engineering, M.S. University of Baroda, Vadodara 390 001 (India)

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{sub c}, lambda{sub F}, and lambda{sub d}, 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=lambda{sub d}.

• OSTI ID: 21344719
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevE.81.036212; (c) 2010 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BREIT-WIGNER FORMULA
CHAOS THEORY
DEGREES OF FREEDOM
DENSITY
DUALITY
EIGENVALUES
ENTROPY
FLUCTUATIONS
INTERACTIONS
MATRICES
MEAN-FIELD THEORY
PROPAGATOR
RANDOMNESS
SPIN
STRENGTH FUNCTIONS
THERMALIZATION
TWO-BODY PROBLEM
WAVE FUNCTIONS
ANGULAR MOMENTUM
FUNCTIONS
MANY-BODY PROBLEM
MATHEMATICS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
SLOWING-DOWN
THERMODYNAMIC PROPERTIES
VARIATIONS