Diabatic and Adiabatic Collective Motion in a Model Pairing System

Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field theory or a direct parametrisation of the time-dependent Schr\"odinger equation. A modified local harmonic equation is formulated to take account of the Nambu-Goldstone mode. It turns out that in some cases the system selects a diabatic path. Requantizing the collective Hamiltonian, a reasonable agreement with an exact calculation for the low-lying levels are obtained for both weak and strong pairing force. This improves on results of the conventional Born-Oppenheimer approximation.Comment: 23 pages, 7 ps figures. Latex, uses revtex and graphic

Collective coordinates, shape transitions and shape coexistence: a microscopic approach

We investigate a description of shape-mixing and shape-transitions using collective coordinates. To that end we apply a theory of adiabatic large-amplitude motion to a simplified nuclear shell-model, where the approximate results can be contrasted with exact diagonalisations. We find excellent agreement for different regimes, and contrast the results with those from a more standard calculation using a quadrupole constraint. We show that the method employed in this work selects diabatic (crossing) potential energy curves where these are appropriate, and discuss the implications for a microscopic study of shape coexistence.Comment: 20 pages, including 6 ps file

On the nature of the phase transitions in two-dimensional type II superconductors

We have simulated the thermodynamics of vortices in a thin film of a type-II superconductor. We make the lowest Landau level approximation, and use quasi-periodic boundary conditions. Our work is consistent with the results of previous simulations where evidence was found for an apparent first order transition between the vortex liquid state and the vortex crystal state. We show, however, that these results are just an artifact of studying systems which are too small. There are substantial difficulties in simulating larger systems using traditional approaches. By means of the optimal energy diffusion algorithm we have been able to study systems containing up to about one thousand vortices, and for these larger systems the evidence for a first order transition disappears. By studying both crystalline and hexatic order, we show that the KTHNY scenario seems to apply, where melting from the crystal is first to the hexatic liquid state and next to the normal vortex liquid, in both cases via a continuous transition.Comment: 26 pages, 26 composite figures. Pre-proof versio

Quantising the B=2 and B=3 Skyrmion systems

We examine the quantisation of a collective Hamiltonian for the two-baryon system derived by us in a previous paper. We show that by increasing the sophistication of the approximations we can obtain a bound state - or a resonance - not too far removed from the threshold with the quantum numbers of the deuteron. The energy of this state is shown to depend very sensitively on the parameters of the model. Subsequently we construct part of a collective Hamiltonian for the three baryon system. Large-amplitude quantum fluctuations play an important r\^ole in the intrinsic wave function of the ground-state, changing its symmetry from octahedral to cubic. Apart from the tetrahedron describing the minimum of the potential, we identify a ``doughnut'' and a ``pretzel'' as the most important saddle points in the potential energy surface. We show that it is likely that inclusion of fluctuations through these saddle points lead to an energy close to the triton's value.Comment: 32 pages, 19 Postscript figures, uses epsfig.sty and elsart.st