Dynamical and quenched random matrices and homolumo gap

Author:

Andrić Ivan1,Jonke Larisa1,Jurman Danijel1,Nielsen Holger Bech2

Affiliation:

1. Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička 54, 10000 Zagreb, Croatia

2. The Niels Bohr Institute, Copenhagen DK 2100, Denmark

Abstract

We consider a rather general type of matrix model, where the matrix M represents a Hamiltonian of the interaction of a bosonic system with a single fermion. The fluctuations of the matrix are partly given by some fundamental randomness and partly dynamically, even quantum mechanically. We then study the homolumo-gap effect, which means that we study how the level density for the single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In the case of the quenched randomness (the fundamental one) dominating the quantum mechanical one we show that in the first approximation the homolumo gap is characterized by the absence of single-fermion levels between two steep gap boundaries. The filled and empty level densities are in this first approximation just pushed, each to its side. In the next approximation these steep drops in the spectral density are smeared out to have an error-function shape. The studied model could be considered as a first step toward the more general case of considering a whole field of matrices — defined say on some phase space — rather than a single matrix.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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