2 research outputs found
Fidelity and level correlations in the transition from regularity to chaos
Mean fidelity amplitude and parametric energy--energy correlations are
calculated exactly for a regular system, which is subject to a chaotic random
perturbation. It turns out that in this particular case under the average both
quantities are identical. The result is compared with the susceptibility of
chaotic systems against random perturbations. Regular systems are more
susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur
A note on biorthogonal ensembles
We consider ensembles of random matrices, known as biorthogonal ensembles,
whose eigenvalue probability density function can be written as a product of
two determinants. These systems are closely related to multiple orthogonal
functions. It is known that the eigenvalue correlation functions of such
ensembles can be written as a determinant of a kernel function. We show that
the kernel is itself an average of a single ratio of characteristic
polynomials. In the same vein, we prove that the type I multiple polynomials
can be expressed as an average of the inverse of a characteristic polynomial.
We finally introduce a new biorthogonal matrix ensemble, namely the chiral
unitary perturbed by a source term.Comment: 20 page