Diagonal matrix elements in a scar function basis set

Title Diagonal matrix elements in a scar function basis set
Publication Type Journal Article
Year of Publication 2010
Authors Vergini EG, Sibert, Edwin L. III, Revuelta F, Benito RM, Borondo F
Journal Epl
Volume 89
Date Published Feb
Accession Number ISI:000276100300013
Keywords chaos, homoclinic motion, Periodic-orbits, Physics, Multidisciplinary, quantization, quantum, semiclassical theory, systems
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. Copyright (C) EPLA, 2010
Google Scholar