Random phase approximation theory of higher surface plasma modes

Using the random phase approximation and analytical calculation we show that a higher surface plasma mode can exist near a plane metal-vacuum interface provided the oscillation is sufficiently localized. This conclusion is confirmed for the infinite potential barrier model of the surface where a mode with long-wavelength frequency _p in sodium is predicted.     

Kinematics of deformable media

We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations. The analytical solutions allow us to study the dependence of the kinematical quantities on initial conditions. In particular, we are able to identify regions of the space of initial conditions that lead to a singularity in finite time. Some generic features of the deformations are also discussed in detail. We conclude by indicating the feasibility and utility of a similar exercise for fluid and geodesic flows in a flat and curved spacetimes.     

Synthesis of LaB6 micro/nano structures using picosecond (Nd:YAG) laser and its field emission investigations

Micro/nano structures have been obtained by laser surface treatment on sintered LaB₆ pellets employing a picosecond pulsed Nd:YAG laser at a pressure of ∼1×10⁻³ mbar. The X-ray diffraction pattern of the laser treated pellet shows a set of well defined diffraction peaks, indexed to the cubic phase of LaB₆ only. The scanning electron microscope studies reveal formation of micro and nano structures upon laser treatment and the resultant surface morphology is found to be strongly influenced by the laser fluence. Field electron emission studies made on the LaB₆ pellet, treated with optimized laser fluence, have been performed in a planar diode configuration under ultra high vacuum conditions. The threshold field required to draw an emission current density of ∼10 μA/cm² has been found to be ∼2.3 V/μm and a current density of ∼530 μA/cm² has been drawn at an applied field of 5.2 V/μm. The Fowler-Nordheim plot is found to be linear in accordance with the quantum mechanical tunneling phenomenon, confirming the metallic nature of the emitter. The emission current at the pre-set value ∼10 μA shows very good stability over a period of more than 3 hours. The present results emphasize the effectiveness of a picosecond laser treatment towards fabrication of a nano metric LaB₆ emitter for high current density applications.     

Dynamics in quantum Ising chain driven by inhomogeneous transverse magnetization

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states having product structure in fermionic momentum-space and satisfying certain criteria, produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field Γ. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. At each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically with an exponent which is invariant for all such special initial states. The frequency of this oscillation varies differently with external field in ordered and disordered phases. The local magnetization after infinite time also characterizes the quantum phase transition.     

The unprecedented reaction of dimethylsulfonium methylide with Michael acceptors: synthesis of 1-substituted vinyl silanes and styrenes

Rather than the usual cyclopropanation, conditions for an unprecedented elimination reaction from the adduct of dimethylsulfonium methylide and various Michael acceptors have been established leading to functionalized 1-substituted alkenes. In silyl substituted substrates (2a and 2h), where a facile Peterson-type olefination is possible from the adduct; elimination took place instead to give functionalized 1-substituted vinyl silanes. Aryl substituted Michael acceptors (2b-e, 2g and 2i-k) also underwent a similar kind of olefination to give 1-substituted styrene derivatives with moderate yields along with a side product, which arose by nucleophilic demethylation from the adduct of dimethylsulfonium methylide and arylidene malonates. Hammett studies revealed that selectivity for olefination vs. demethylation increases as the aryl substituent becomes more electron deficient. Alkylidene malonates (2f and 2l) with a beta-alkyl substituent did not favour the olefination process. Sequential addition of Michael acceptors and alkyl halides to a mixture of dimethylsulfonium methylide and sodium dimsylate provided olefination followed by alkylation on the active methine group. A mechanistic pathway has been formulated from the studies of a few sulfonium methylides.     

First measurement of the transverse spin asymmetries of the deuteron in semi-inclusive deep inelastic scattering

First measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarized 6LiD target are presented. The data were taken in 2002 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. The Collins asymmetry turns out to be compatible with zero, as does the measured Sivers asymmetry within the present statistical errors.     

Design of dispersion-compensating Bragg fiber with an ultrahigh figure of merit

We report a novel idea for achieving highly efficient dispersion-compensating Bragg fiber by exploiting a modified quarter-wave stack condition. Our Bragg fiber yielded an average dispersion of approximately -1800 ps/(nm km) across the C band for the fundamental TE mode and an ultrahigh figure of merit of approximately 180,000 ps/(nm dB), which is at least 2 orders of magnitude higher than that of conventional dispersion-compensating fibers. The proposed methodology could be adopted for the design of a dispersion compensator across any desired wavelength range.     

A novel reaction of dimethylsulfonium methylide with Michael acceptors: application to the synthesis of difficultly accessible vinyl silanes and styrenes

Rather than the usual cyclopropanation and Peterson-type olefination, conditions for a novel elimination reaction from the adduct of dimethylsulfonium methylide and 2-silylalkylidene/arylidene malonate/cyanoacetate/phosphonoacetate leading to geminally substituted vinyl silanes or styrenes, respectively, have been established.