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.     

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.     

On the possibility of a unified approach to investigating the indicatrices of coherent wave scattering by different inhomogeneities of the medium

A general expression describing the coherent scattering indicatrix by arbitrary inhomogeneities of the medium is derived. It is shown that a universal program can be devised for calculation of such indicatrices to avoid difficulties in the analytical and experimental investigations of the media through the wave processes.Institute of Applied Geophysics, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 7, pp. 631–638, July, 1995.     

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     

Differential–algebraic equations in multibody system modeling

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations. This revised version was published online in June 2006 with corrections to the Cover Date.     

α-Trifluoroacetyl-δ-valerolactone: synthesis, acyl-lactone rearrangement and unexpected easy decarboxylation of the rearranged product

Claisen condensation of δ-valerolactone and ethyl trifluoroacetate leads to α-trifluoroacetyl-δ-valerolactone, existing completely in CDCl₃ solution as an enol. Upon treatment of this cyclic 1,3-ketoester with aqueous HCl, an acyl-lactone rearrangement takes place. The structure of the resulting pyran was confirmed by an X-ray analysis. The ability of the rearrangement product to lose its carboxylic group under unexpected mild conditions was used for the synthesis of the corresponding 3-unsubstituted cyclic hemi-ketal.     

Perfectly dissolved boron nitride nanotubes due to polymer wrapping

We report for the first time that boron nitride nanotubes (BNNTs) may be dissolved in organic solvents by wrapping them with a polymer. Transmission electron microscopy and cathodoluminescence studies indicate the strong pi-pi interactions between BNNTs and the polymer. A band gap ranging from 5.2 to 5.5 eV was documented for the BNNTs independent of their geometrical characteristics by using ultraviolet-visible absorption experiments on composite films and thin BNNT films prepared from solutions.