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"Diagonal matrix elements in a scar function basis set"
E.G. Vergini, E.L. Sibert III, F. Revuelta, R.M. Benito and F. Borondo
Europhys. Lett. 89(4) (2010) 40013
We provide canonically invariant expressions to evaluate diagonal matrix elements of powers of the Hamiltonian in a scar function basis set. As a function of the energy, each matrix element consists of a smooth contribution associated with the central periodic orbit, plus oscillatory contributions given by a finite set of relevant homoclinic orbits. Each homoclinic contribution depends, in leading order, on four canonical invariants of the corresponding homoclinic orbit; a geometrical interpretation of these not well-known invariants is given. The obtained expressions are verified in a chaotic coupled quartic oscillator.
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