Volume 89, Number 4, February 2010
|Number of page(s)||6|
|Published online||11 March 2010|
Diagonal matrix elements in a scar function basis set
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: email@example.com
Accepted: 12 February 2010
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.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 03.65.Sq – Semiclassical theories and applications
© EPLA, 2010
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