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.     

Waves in multilayer ferrite-dielectric transversely magnetized waveguides with an electrically controlled slowing factor

Multilayer wave-guiding structures comprising transversely magnetized ferrites are studied. A numerical theoretical model is constructed with the Galerkin method. An experimental investigation technique is developed. Theoretical and experimental results are found to be in good agreement. Such structures offer a high phase activity and may provide a basis for small-size millimeter-wave phase shifters and a new class of antenna systems, namely, integrated phased arrays.     

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.     

Complexes of Some Pyrido[1,2-a]pyrimidinium Perchlorates with Scandium,Yttrium, and Lanthanum. Crystal and Molecular Structure of 3-Chloro-9-Hydroxy-2,4-Dimethylpyrido[1,2-a]pyrimidinium Perchlorate

Complexes of scandium, yttrium, and lanthanum nitrates with 3-chloro-9-hydroxy-2,4-dimethylpyrido[1,2-a]pyrimidinium perchlorate (HL¹ClO₄) and 9-hydroxy-2,4-dimethylpyrido[1,2-a]pyrimidinium perchlorate (HL²ClO₄) were obtained. Their composition was formulated as Sc(LClO₄)₂(NO₃) and M(LClO₄)₂(NO₃)₂ (L = L¹ or L²; M = Y or La); structures for the complexes obtained were proposed. The crystal and molecular structure of HL¹ClO₄ was determined. Dissociation and complexation of HL¹ClO₄ and HL²ClO₄ in aqueous ethanol were studied using the spectroscopic method. Ligand dissociation and complexation constants were calculated. It was shown that a chlorine-containing organic ligand only slightly changes the composition and stability of the metal complexes.     

The effect of electrical boundary conditions on the characteristics of surface acoustic waves propagating in potassium niobate

The study of the effect of a perfectly conducting plane placed at a certain distance from the surface of a potassium niobate crystal on the characteristics of the generalized Rayleigh and Gulyaev-Bleustein surface waves is continued. In addition, the effect of an infinitely thin conducting layer applied to the surface of the piezoelectric on the characteristics of these waves is analyzed. It is found that a variation in the conductance of this layer can produce a result that completely differs from the result obtained when a perfectly conducting plane is moved toward the surface, although the extreme states of these actions (electrically open and short-circuited surfaces) are identical. A possible physical explanation of this difference is proposed.     

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.     

Comparative analysis of the frequency noise in two distributed circuits of semiconductor self-excited oscillators

Kuibyshev State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 2, pp. 242–245, February, 1989.     

Energy spectrum of <Emphasis Type="Italic">p</Emphasis> electrons in a plane crystal lattice and in a strong magnetic field

Harper equations are derived for a _px, _py electronic system. Analysis is carried out for extreme points of the quasi-continuous spectrum in the cases when the number of magnetic flux quanta through a unit cell is a rational number and calculations are made for square and triangular lattices as well as for a honeycomb lattice with two nonequivalent atoms. The possibility of application of the results for explaining the fractional Hall effect is considered.