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- Niall D. Whelan
- 2003

We develop sampling algorithms for multivariate Archimedean copulas. For exchangeable copulas, where there is only one generating function, we first analyse the distribution of the copula itself, deriving a number of integral representations and a generating function representation. One of the integral representations is related, by a form of convolution,… (More)

We study the effect of edge diffraction on the semiclassical analysis of two dimensional quantum systems by deriving a trace formula which incorporates paths hitting any number of vertices embedded in an arbitrary potential. This formula is used to study the cardioid billiard, which has a single vertex. The formula works well for most of the short orbits we… (More)

We study the effect on quantum spectra of the existence of small circular disks in a billiard system. In the limit where the disk radii vanish there is no effect, however this limit is approached very slowly so that even very small radii have comparatively large effects. We include diffractive orbits which scatter off the small disks in the periodic orbit… (More)

- Niall D. Whelan
- 1995

Diffraction, in the context of semiclassical mechanics, describes the manner in which quantum mechanics smooths over discontinuities in the classical mechanics. An important example is a billiard with sharp corners; its semiclassical quantisation requires the inclusion of diffractive periodic orbits in addition to classical periodic orbits. In this paper we… (More)

- Niall D. Whelan
- 1994

We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A generalization of periodic orbit theory allows us to incorporate the second possibility. In both cases we also perform… (More)

- Niall D. Whelan
- 1996

We discuss the symmetry decomposition of the average density of states for the two dimensional potential V = x2y2 and its three dimensional generalisation V = x2y2 + y2z2 + z2x2. In both problems, the energetically accessible phase space is non-compact due to the existence of infinite channels along the axes. It is known that in two dimensions the phase… (More)

- Niall D. Whelan
- Nursing times
- 1995

We consider the extension of the Gutzwiller trace formula to systems of two or more identical particles. We first study the case of two noninteracting particles. Important considerations are the structure of the periodic orbits, which come in families and the symmetry decomposition of the density of states. Interactions cause the periodic orbit families to… (More)

- Niall D. Whelan
- 1996

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori… (More)