Semiclassical Theory for Parametric Correlation of Energy Levels

Details Semiclassical Theory for Parametric Correlation of Energy Levels Semiclassical Theory for Parametric Correlation of Energy Levels

2006-07-30

arxiv.org/abs/nlin/0607070v1

J. Phys. A: Math. Theor. 40 (2007) 47

Nonlinear Sciences

Chaotic Dynamics

25 pages, no figure

Scientific paper

10.1088/1751-8113/40/1/003

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 $K(\tau)$ is shown to be in agreement with the prediction of parameter dependent random-matrix theory to all orders in $\tau$.

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