Classification and stability of simple homoclinic cycles in R^5

The paper presents a complete study of simple homoclinic cycles in R^5. We find all symmetry groups Gamma such that a Gamma-equivariant dynamical system in R^5 can possess a simple homoclinic cycle. We introduce a classification of simple homoclinic cycles in R^n based on the action of the system symmetry group. For systems in R^5, we list all classes of simple homoclinic cycles. For each class, we derive necessary and sufficient conditions for asymptotic stability and fragmentary asymptotic stability in terms of eigenvalues of linearisation near the steady state involved in the cycle. For any action of the groups Gamma which can give rise to a simple homoclinic cycle, we list classes to which the respective homoclinic cycles belong, thus determining conditions for asymptotic stability of these cycles.Comment: 34 pp., 4 tables, 30 references. Submitted to Nonlinearit

Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose-Einstein condensate

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ^87Rb

Observation of Superfluid Flow in a Bose-Einstein Condensed Gas

We have studied the hydrodynamic flow in a Bose-Einstein condensate stirred by a macroscopic object, a blue detuned laser beam, using nondestructive {\em in situ} phase contrast imaging. A critical velocity for the onset of a pressure gradient has been observed, and shown to be density dependent. The technique has been compared to a calorimetric method used previously to measure the heating induced by the motion of the laser beam.Comment: 4 pages, 5 figure

Analysis of the shearing instability in nonlinear convection and magnetoconvection

Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced

Evaporative Cooling of a Two-Component Degenerate Fermi Gas

We derive a quantum theory of evaporative cooling for a degenerate Fermi gas with two constituents and show that the optimum cooling trajectory is influenced significantly by the quantum statistics of the particles. The cooling efficiency is reduced at low temperatures due to Pauli blocking of available final states in each binary collision event. We compare the theoretical optimum trajectory with experimental data on cooling a quantum degenerate cloud of potassium-40, and show that temperatures as low as 0.3 times the Fermi temperature can now be achieved.Comment: 6 pages, 4 figure

Dynamical response of a Bose-Einstein condensate to a discontinuous change in internal state

A two-photon transition is used to convert an arbitrary fraction of the 87Rb atoms in a |F=1,m_f=-1> condensate to the |F=2,m_f=1> state. Transferring the entire population imposes a discontinuous change on the condensate's mean-field repulsion, which leaves a residual ringing in the condensate width. A calculation based on Gross-Pitaevskii theory agrees well with the observed behavior, and from the comparison we obtain the ratio of the intraspecies scattering lengths for the two states, a_|1,-1> / a_|2,1> = 1.062(12).Comment: 4 pages, 3 figure

A method for collective excitation of Bose-Einstein condensate

It is shown that by an appropriate modification of the trapping potential one may create collective excitation in cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally --- it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.Comment: 4 pages, 4 figures; major revision, several references added, interacting particles case adde

Temperature Dependence of Damping and Frequency Shifts of the Scissors Mode of a trapped Bose-Einstein Condensate

We have studied the properties of the scissors mode of a trapped Bose-Einstein condensate of $^{87}$Rb atoms at finite temperature. We measured a significant shift in the frequency of the mode below the hydrodynamic limit and a strong dependence of the damping rate as the temperature increased. We compared our damping rate results to recent theoretical calculations for other observed collective modes finding a fair agreement. From the frequency measurements we deduce the moment of inertia of the gas and show that it is quenched below the transition point, because of the superfluid nature of the condensed gas.Comment: 5 pages, 4 figure