Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice

We experimentally investigate diffraction of a Rb-87 Bose-Einstein condensate from a 1D optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to quantum mechanical and classical simulations, with quantitative and qualitative agreement, respectively. The classical simulation predicts that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.Comment: 7 pages, 6 figure

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio

Generation of scalar-tensor gravity effects in equilibrium state boson stars

Boson stars in zero-, one-, and two-node equilibrium states are modeled numerically within the framework of Scalar-Tensor Gravity. The complex scalar field is taken to be both massive and self-interacting. Configurations are formed in the case of a linear gravitational scalar coupling (the Brans-Dicke case) and a quadratic coupling which has been used previously in a cosmological context. The coupling parameters and asymptotic value for the gravitational scalar field are chosen so that the known observational constraints on Scalar-Tensor Gravity are satisfied. It is found that the constraints are so restrictive that the field equations of General Relativity and Scalar-Tensor gravity yield virtually identical solutions. We then use catastrophe theory to determine the dynamically stable configurations. It is found that the maximum mass allowed for a stable state in Scalar-Tensor gravity in the present cosmological era is essentially unchanged from that of General Relativity. We also construct boson star configurations appropriate to earlier cosmological eras and find that the maximum mass for stable states is smaller than that predicted by General Relativity, and the more so for earlier eras. However, our results also show that if the cosmological era is early enough then only states with positive binding energy can be constructed.Comment: 20 pages, RevTeX, 11 figures, to appear in Class. Quantum Grav., comments added, refs update

Topological classification of black Hole: Generic Maxwell set and crease set of horizon

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

Cosmological zoo -- accelerating models with dark energy

ecent observations of type Ia supernovae indicate that the Universe is in an accelerating phase of expansion. The fundamental quest in theoretical cosmology is to identify the origin of this phenomenon. In principle there are two possibilities: 1) the presence of matter which violates the strong energy condition (a substantial form of dark energy), 2) modified Friedmann equations (Cardassian models -- a non-substantial form of dark matter). We classify all these models in terms of 2-dimensional dynamical systems of the Newtonian type. We search for generic properties of the models. It is achieved with the help of Peixoto's theorem for dynamical system on the Poincar{\'e} sphere. We find that the notion of structural stability can be useful to distinguish the generic cases of evolutional paths with acceleration. We find that, while the $\Lambda$CDM models and phantom models are typical accelerating models, the cosmological models with bouncing phase are non-generic in the space of all planar dynamical systems. We derive the universal shape of potential function which gives rise to presently accelerating models. Our results show explicitly the advantages of using a potential function (instead of the equation of state) to probe the origin of the present acceleration. We argue that simplicity and genericity are the best guide in understanding our Universe and its acceleration.Comment: RevTeX4, 23 pages, 10 figure

Canonical Melnikov theory for diffeomorphisms

We study perturbations of diffeomorphisms that have a saddle connection between a pair of normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for invariant manifolds and show that a generalized Melnikov function or Melnikov displacement can be written in a canonical way. This function is defined to be a section of the normal bundle of the saddle connection. We show how our definition reproduces the classical methods of Poincar\'{e} and Melnikov and specializes to methods previously used for exact symplectic and volume-preserving maps. We use the method to detect the transverse intersection of stable and unstable manifolds and relate this intersection to the set of zeros of the Melnikov displacement.Comment: laTeX, 31 pages, 3 figure

Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Macroscopic resonant tunneling between the two lowest lying states of a bistable RF-SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian shaped profile that is not peaked at the resonance point, but is shifted to a bias at which the initial well is higher than the target well. The r.m.s. amplitude of the noise, which is proportional to the decoherence rate 1/T_2^*, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low frequency (1/f) flux noise in this device is a quantum mechanical environment in thermal equilibrium.Comment: 4 pages 4 figure

Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

Anatomy and origin of authochthonous late Pleistocene forced regression deposits, east Coromandel inner shelf, New Zealand: implications for the development and definition of the regressive systems tract

High-resolution seismic reflection data from the east Coromandel coast, New Zealand, provide details of the sequence stratigraphy beneath an autochthonous, wave dominated inner shelf margin during the late Quaternary (0-140 ka). Since c. 1 Ma, the shelf has experienced limited subsidence and fluvial sediment input, producing a depositional regime characterised by extensive reworking of coastal and shelf sediments during glacio-eustatic sea-level fluctuations. It appears that only one complete fifth-order (c. 100 000 yr) depositional sequence is preserved beneath the inner shelf, the late Pleistocene Waihi Sequence, suggesting any earlier Quaternary sequences were mainly cannibalised into successively younger sequences. The predominantly Holocene-age Whangamata Sequence is also evident in seismic data and modern coastal deposits, and represents an incomplete depositional sequence in its early stages of formation. A prominent aspect of the sequence stratigraphy off parts of the east Coromandel coast is the presence of forced regressive deposits (FRDs) within the regressive systems tract (RST) of the late Pleistocene Waihi Sequence. The FRDs are interpreted to represent regressive barrier-shoreface sands that were sourced from erosion and onshore reworking of underlying Pleistocene sediments during the period of slow falling sea level from isotope stages 5 to 2 (c. 112-18 ka). The RST is volumetrically the most significant depositional component of the Waihi Sequence; the regressive deposits form a 15-20 m thick, sharp-based, tabular seismic unit that downsteps and progrades continuously across the inner shelf. The sequence boundary for the Waihi Sequence is placed at the most prominent, regionally correlative, and chronostratigraphically significant surface, namely an erosional unconformity characterised in many areas by large incised valleys that was generated above the RST. This unconformity is interpreted as a surface of maximum subaerial erosion generated during the last glacial lowstand (c. 18 ka). Although the base of the RST is associated with a prominent regressive surface of erosion, this is not used as the sequence boundary as it is highly diachronous and difficult to identify and correlate where FRDs are not developed. The previous highstand deposits are limited to subaerial barrier deposits preserved behind several modern Holocene barriers along the coast, while the transgressive systems tract is preserved locally as incised-valley fill deposits beneath the regressive surface of erosion at the base of the RST. Many documented late Pleistocene RSTs have been actively sourced from fluvial systems feeding the shelf and building basinward-thickening, often stacked wedges of FRDs, for which the name allochthonous FRDs is suggested. The Waihi Sequence RST is unusual in that it appears to have been sourced predominantly from reworking of underlying shelf sediments, and thus represents an autochthonous FRD. Autochthonous FRDs are also present on the Forster-Tuncurry shelf in southeast Australia, and may be a common feature in other shelf settings with low subsidence and low sediment supply rates, provided shelf gradients are not too steep, and an underlying source of unconsolidated shelf sediments is available to source FRDs. The preservation potential of such autochthonous FRDs in ancient deposits is probably low given that they are likely to be cannibalised during subsequent sea-level falls