Singularities in the spectra of random matrices

PAUL N. WALKE DEPARTMENT OF PHYSPAUL WALKER, MARÍA JOSÉ SÁNCHEZ AND MICHAEL WILKINSON

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: American Institute of Physics; Año: 1996 vol. 37 p. 5019 - 5032

0022-2488

We consider singularities of the set of energy levels E n (X) of a quantum Hamiltonian, obtained by varying a set of d parameters Xϭ(X 1 ,..,X d ). Singularities suchas minima, degeneracies, branch points, and avoided crossings can play an impor-tant role in physical applications. We discuss a general method for counting thesesingularities, and apply it to a random matrix model for the parameter dependenceof energy levels. We also show how the density of avoided crossing singularities isrelated to a non-analyticity of a correlation function describing the energy levels