Semiclassical theory for parametric correlation of energy levels

Abstract

Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric energy-level correlation depending on the magnetic field difference. The small-time expansion of the spectral form factor K(τ) is shown to be in agreement with the prediction of parameter dependent random matrix theory to all orders in τ.