Robert Graham

On the weak-noise limit of Fokker-Planck models

The weak-noise limit of Fokker-Planck models leads to a set of nonlinear Hamiltonian canonical equations. We show that the existence of a nonequilibrium potential in the weak-noise limit requires the existence of whiskered tori in the Hamiltonian system and, therefore, the complete integrability of the latter. A specific model is considered, where the Hamiltonian system in the weak-noise limit is not integrable. Two different perturbative solutions are constructed: the first solution describes analytically the breakdown of the whiskered tori due to the appearance of wild separatrices; the second solution allows the analytic construction of an approximate nonequilibrium potential and an asymptotic expression for the probability density in the steady state.

Noise-induced attractor explosions near tangent bifurcations

Abstract In dynamical systems with periodic attractors which have just emerged from a saddle-node bifurcation the addition of weak noise may induced behaviour. This is accompanied by two remarkable observable effects: noise-induced attractor explosion and noise-induced intermittency. The theory of quasipotentials is used to explain qualitative and universal aspects of these phenomena. The influence of the noise-distribution and its observational implications are discussed.

Supersymmetric general Bianchi type IX cosmology with a cosmological term

Abstract The covariant action of the supersymmetrically extended spatially homogeneous general Bianchi type IX cosmology is given including time reparametrization invariance, inducing the hamiltonian constraint, and the constraints on the supercharges. A supersymmetric cosmological term is also included. A quantization respecting the supersymmetry and the conformal invariance of the superspace of geometrodynamics is given. The problem of the initial condition is naturally solved in this description by demanding that the wave function does not diverge if the anisotropy variables are taken to infinity for fixed scale parameter.

Hydrodynamic excitations of Bose Condensates in anisotropic traps

The collective excitations of Bose condensates in anisotropic axially symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi limit. We identify an additional conserved quantity, besides the axial angular momentum and the total energy, and separate the wave equation in elliptic coordinates. The solution is thereby reduced to the algebraic problem of diagonalizing finite dimensional matrices. The classical quasi-particle dynamics in the local density approximation for energies of the order of the chemical potential is shown to be chaotic.

SUPERSYMMETRIC MINISUPERSPACE WITH NONVANISHING FERMION NUMBER

The Lagrangean of

Hartle-Hawking state in supersymmetric minisuperspace☆

N=1

Shifts and widths of collective excitations in trapped Bose gases determined by the dielectric formalism

supergravity is dimensionally reduced to one (time-like) dimension assuming spatial homogeneity of any Bianchi type within class A of the classification of Ellis and McCallum. The algebra of the supersymmetry generators, the Lorentz generators, the diffeomorphism generators and the Hamiltonian generator is determined and found to close. In contrast to earlier work, infinitely many physical states with non-vanishing even fermion number are found to exist in these models, indicating that minisuperspace models in supergravity may be just as useful as in pure gravity.

Conserving and gapless model of the weakly interacting Bose gas

Abstract The Hartle-Hawking ‘no-boundary’ state is constructed explicitly in the semi-classical limit for the recently developed supersymmetric minisuperspace model with non-vanishing fermion number.

Triad representation of the Chern-Simons state in quantum gravity

We present predictions for temperature-dependent shifts and damping rates. They are obtained by applying the dielectric formalism to set up a self-consistent model of a trapped Bose gas which can be shown to satisfy generalized Ward identities. Within the framework of the model we use lowest-order perturbation theory to determine the first-order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)] are found for the

Exact quantum state for N=1 supergravity

m=2