Collective Tunnelling of Strongly Interacting Cold Atoms in a Double-Well Potential

It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually.     

Long Abelian ideals

We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra.     

Characteristics of high-power radiating imploding discharge with cold start

A qualitative model of the dynamics of a multiterawatt radiating Z-pinch with cold start and high rate of current rise is proposed. The model is used to analyze discharges with currents I ～ 2–5 MA (with dI/dt > 10¹³ A/s) through uniform or structured plasma-producing loads, including wire arrays. The most important consequence of cold start is that spatially nonuniform plasma production is prolonged to almost the entire current rise time. Under these conditions, the Ampére force begins to play a dominant role in the plasma dynamics before the plasma-producing load is completely transformed into an accelerated plasma. The results of computations of wire-array vaporization are presented. A formula is proposed for estimating the highest attainable velocity of plasma flow into a heterogeneous liner driven by the Ampére force. It is shown that local imbalance between radial motion of the produced plasma and supply of the plasma-producing substance to be ionized leads to axially nonuniform breakthrough of magnetic flux into the liner, which precedes plasma collapse. The magnetic-flux breakthrough gives rise to a chaotic azimuthal-axial plasma structure consisting of radial plasma jets of relatively small diameter, which is called a radial plasma rainstorm. The breaking-through azimuthal magnetic flux obstructs further current flow in the breakthrough region. Analyses of Z-pinch implosion based on the theory of Rayleigh-Taylor instability or the snowplow model are incorrect under the plasma-rainstorm conditions. The processes taking place in a stagnant Z-pinch include conversion of the energy carried by the current-generated magnetic field into turbulent MHD flow of the ion component of the plasma, its convective mixing with magnetic field, heating, energy transfer from ions to electrons, and emission from the plasma. Under typical experimental conditions, emission plays a key role in the energy balance in an imploding pinch. Z-pinch is modeled by an electric-circuit component that has a time-dependent nonlinear impedance and consumes the magnetic energy supplied by a generator through a magnetically insulated transmission line (MITL). The peak power reached in the circuit is comparable to the peak soft X-ray power output emitted by the pinch in terms of magnitude and timing. Optimum matching conditions are formulated for the generator-MITL-pinch circuit.     

Regioselective 1,4-trifluoromethylation of α,β-enones using ‘protect-in-situ’ methodology

In a convenient and efficient procedure, the nucleophilic 1,4-trifluoromethylation of several α,β-enones using (trifluoromethyl)trimethylsilane was achieved. The high regioselectivity of the reaction has been reached by blocking the carbonyl moiety of the electrophile with a bulky aluminum-centered Lewis acid.     

New Plasmon Waveguides Composed of Twin Metal Wedges with a Nano Gap

We have numerically shown the existence of coupled wedge plasmons (CWPs) which propagates along a nano gap of a twin metal wedge. The CWPs are formed by wedge plasmons which can interact with each other. The dispersion relations of the wavenumber, propagation distance, and beam area of CWPs, are described and show that the characteristics of CWPs are similar to those of wedge plasmons and of gap plasmons. We also propose a new plasmon waveguide composed of twin metal wedges with a nano gap.     

A mathematical model of the response of the semicircular canal and otolith to vestibular system rotation under gravity

A mathematical model of the system composed of two sensors, the semicircular canal and the sacculus, is suggested. The model is described by three lines of blocks, each line of which has the following structure: a biomechanical block, a mechanoelectrical transduction mechanism, and a block describing the hair cell ionic currents and membrane potential dynamics. The response of this system to various stimuli (head rotation under gravity and falling) is investigated. Identification of the model parameters was done with the experimental data obtained for the axolotl (Ambystoma tigrinum) at the Institute of Physiology, Autonomous University of Puebla, Mexico. Comparative analysis of the semicircular canal and sacculus membrane potentials is presented. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 207–220, 2005.     

Fractional Hamiltonian Monodromy

We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems. Communicated by Eduard Zehnder Submitted: February 25, 2005; Accepted: November 17, 2005     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.