Unstable periodic orbits and semiclassical quantisation

Published under licence by IOP Publishing Ltd
, , Citation A Voros 1988 J. Phys. A: Math. Gen. 21 685 DOI 10.1088/0305-4470/21/3/023

0305-4470/21/3/685

Abstract

The Bohr-Sommerfeld quantisation condition has a meaningful extension to classically chaotic systems whose periodic (unstable) orbits are isolated. It provides a semiclassical Euler factorisation for the functional determinant of the quantal Hamiltonian, in contrast to the Hadamard infinite product over the eigenvalues by which the exact determinant is defined.

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