Wavefunctions, Green's functions and expectation values in terms of spectral determinants

Details Wavefunctions, Green's functions and expectation values in terms of spectral determinants Wavefunctions, Green's functions and expectation values in terms of spectral determinants

2007-06-27

arxiv.org/abs/0706.3899v1

Nonlinearity 20 (2007) 2721

Nonlinear Sciences

Chaotic Dynamics

18 pages, no figures

Scientific paper

10.1088/0951-7715/20/11/013

We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The wavefunctions, Green's functions and expectation values of the unperturbed Hamiltonian are expressed in terms of the spectral determinant of the perturbed Hamiltonian. Semiclassical resummation methods for spectral determinants are applied and yield approximations in terms of a finite number of classical trajectories. The final formulas have a simple form. In contrast to Poincare surface of section methods, the resummation is done in terms of the periods of the trajectories.

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