Diagonal matrix elements in a scar function basis set

¹  Departamento de Física, Comisión Nacional de Energía Atómica - Av. del Libertador 8250, 1429 Buenos Aires, Argentina
²  Departamento de Física, E.T.S.I. Agrónomos, Universidad Politécnica de Madrid - 28040 Madrid, Spain, EU
³  Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison Madison, WI-53706, USA
⁴  Departamento de Química C–IX, Universidad Autónoma de Madrid - Cantoblanco, 28049 Madrid, Spain, EU

Corresponding author: vergini@tandar.cnea.gov.ar

Received: 12 October 2009
Accepted: 12 February 2010

Abstract

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.