Unstable periodic orbits and semiclassical quantisation

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.