Dynamical and quenched random matrices and homolumo gap

International Conference and Exhibition on Mesoscopic & Condensed Matter Physics

June 22-24, 2015 Boston, USA

H B Nielsen2, I Andric1, L Jonke1 and D Jurman1

1Rudjer Bo�?�?skovi�?´c Institute, Croatia 2The Niels Bohr Institute, Denmark

Posters-Accepted Abstracts: J Material Sci Eng

Abstract :

We consider a rather general type of matrix model, which is partly given by some â�?�?fundamental randomnessâ�? and partly dynamical even quantum mechanically. We then study the homolumo-gap effect, which means that we study how the level density gets attenuated near the Fermi surface, while considering the matrix as the Hamiltonian matrix for a type of fermion interacting with this matrix. In the case of the quenched randomness (the â�?�?fundamentalâ�? one) dominating the quantum mechanical one and the coupling to the fermions is not too small we calculate a homolumo gap that in first approximation consists of there being essentially no levels for the a single fermion between two steep limits (box-shape). The filled and empty state densities are in this first approximation just pushed each to its side. In next approximation these steep falls in the spectral density are smeared out to have an error function shape. The studied model could be considered as a first step towards the more general case of considering a whole field of matrices - defined say on some phase space - rather than a single matrix.

Biography :

H B Nielsen is a Danish theoretical physicist, Professor emeritus at the Niels Bohr Institute, at the University of Copenhagen, where he started studying physics in 1961. He has made original contributions to theoretical particle physics specifically in the field of string theory. He was the first to propose that the Veneziano model was actually a theory of strings and is considered among the fathers of string theory. He was awarded the highly esteemed Humboldt Prize in 2001 for his scientific research. Several physics concepts are named after him, e.g. Nielsen-Olesen Vortex and the Nielsen-Ninomiya no-go theorem for representing chiral fermions on the lattice. He is known in Denmark for his enthusiastic public lectures on physics and string theory, and he is often interviewed in daily news, especially on matters regarding particle physics.

Email: hbech@nbi.dk