Thermodynamics of Squeezed State for Mesoscopic RLC Circuits

We present a density matrix of a mesoscopic RLC circuits to make it possible to analyze the connection between the initial condition and the certain temperature. Our results show that the quantum state evolution will be closely related to the initial condition; the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially. In addition, we also obtain squeezed minimum uncertainty state with satisfying certain condition in mesoscopic RLC circuit.     

Application of inertia-induced excitation theory for nonlinear acoustic modes in colloidal plasma equilibrium flow

Application of inertia-induced acoustic excitation theory offers a new resonant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like colloidal plasma, two well-defined transonic points exist corresponding to the parent ion and the dust grain-associated acoustic modes. As usual, the modified ion acoustic mode (also known as dust ion-acoustic (DIA) wave) dynamics associated with parent ion inertia is excitable for both nanoscale-and micronscale-sized dust grains. It is found that the so-called (ion) acoustic mode (also known as dust-acoustic (DA) wave) associated with nanoscale dust grain inertia is indeed resonantly excitable through the active role of weak but finite parent ion inertia. It is interestingly conjectured that the same excitation physics, as in the case of normal plasma sound mode, operates through the active inertial role of plasma thermal species. Details of the nonlinear acoustic mode analyses of current interest in transonic domains of such impure plasmas in hydrodynamic flow are presented.      

Structural investigation on PEO-based polymer electrolytes dispersed with Al<Subscript>2</Subscript>O<Subscript>3</Subscript> nanoparticles

Thin solid polymer electrolytes based on polyethylene oxide (PEO) and silver triflate (AgCF₃SO₃) dispersed with various concentrations of aluminum oxide (Al₂O₃) nanoparticles have been prepared by solution casting technique. These thin polymer films are found to have thickness of the order of 30 to 100 μm. The X-ray diffraction (XRD) patterns have indicated the amorphous nature of the polymer electrolyte. The differential scanning calorimeter (DSC) traces showed slight change in the glass transition temperature (T _g) whereas the degree of crystallization (X _c) decreases markedly due to the addition of alumina nanoparticles. Fourier transform infrared (FTIR) spectral analysis of all these samples has revealed the presence of absorption bands around 1,000 cm⁻¹; thus indicating the complexation of silver ions with oxygen in PEO. Employing the Wagner’s polarization technique as the standard method, the total ionic transference number for the complexed polymer electrolyte was found to be approximately unity thereby revealing that the significant contribution to electrical conduction was due to ions only. Paper presented at the Third International Conference on Ionic Devices (ICID 2006), Chennai, Tamilnadu, India, December 7–9, 2006     

Measurement Accuracy in Phase-Shifting Point Diffraction Interferometer with Two Optical Fibers

A phase-shifting point diffraction interferometer (PS/PDI) with point sources of two single mode optical fibers has been developed, which will be appropriate for the surface figure measurement of large aperture optics on a sub-nanometer scale. To reduce the measurement error factors, a fiber optic plate (FOP) is used as a projection plane for interference pattern. Errors caused by imperfection of optical alignment, such as position of point sources and tilt of FOP, are minimized by analyzing the measured phase data with an original method. Measurement accuracy in the PS/ PDI is estimated with the interference pattern produced by the two optical fiber sources. If inhomogeneity of the FOP and a systematic error of the PS/PDI are eliminated, the measurement accuracy of the present system is estimated to be less than 4nm P-V and 0.7nm rms, respectively, at a measurement wavelength of 632.8 nm.     

Isotopic Liftings of Clifford Algebras and Applications in Elementary Particle Mass Matrices

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.     

Additional Symmetries and String Equation of the CKP Hierarchy

Based on the Orlov and Shulman’s M operator, the additional symmetries and the string equation of the CKP hierarchy are established, and then the higher order constraints on L ^l are obtained. In addition, the generating function and some properties are also given. In particular, the additional symmetry flows form a new infinite dimensional algebra , which is a subalgebra of W _1+∞.      

Ionic conduction and effect of cation doping in Tl<Subscript>4</Subscript>HgI<Subscript>6</Subscript>

The ionic conduction properties of undoped and doped Tl₄HgI₆ were investigated using electrical conductivity, dielectrics, differential scanning calorimetry, and X-ray diffraction techniques. The heavy Tl⁺-ions diffusion was activated at high temperature, whereas low conductivity at the lower temperature suggested electronic contribution in undoped Tl₄HgI₆. The partial replacement of heavy Tl⁺ ion by suitable cations (Ag⁺ and Cu⁺) enhanced the conductivity by several orders of magnitude, whereas diminution in conductivity results with increasing dopants’ concentration in Tl₄HgI₆. These results can be interpreted in terms of a lattice contraction and vacancy–vacancy interaction (leading to the cluster formation), respectively. The dielectric values of undoped Tl₄HgI₆ system gradually increasing with temperature, followed by a sharp change, were observed around 385 K and can be explained on the basis of increasing number of space charge polarization and ions jump orientation effects. The activation energy of undoped and doped Tl₄HgI₆ systems were calculated, and it was found that ionic conductivity activation energy for 5 mol% of cation dopants is much lower than that of undoped one, and also 10 mol% doped Tl₄HgI₆ systems.     

One-neutron stripping reactions of <Superscript>11</Superscript>Be and <Superscript>19</Superscript>C on light target

We have calculated the one-neutron absorption cross-section and the longitudinal momentum distribution of the core fragment coming out from the breakup of ¹¹Be and ¹⁹C on ⁹Be target at 63 MeV/A and 88 MeV/A beam energies respectively. The reaction mechanism is treated within the framework of the eikonal approximation. The effective range of the nuclear interaction between the core and the valence neutron within the projectile has been determined by comparing the predicted stripping cross-section with the recently measured one. The effective range for ¹⁹C has been found to be smaller than that for ¹¹Be. It qualitatively indicates that ¹⁹C is slightly more halo than ¹¹Be. The smaller width, predicted as well as measured, of the LMD of ¹⁸C than ¹⁰Be also strengthens this fact. The experimental data concerning the LMD of core fragments have been well represented.      

Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

Asymptotic singular behaviour of inhomogeneous cosmologies in Einstein-Maxwell-dilaton-axion theory

We present the study of exact inhomogeneous cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimal interacting electromagnetic, dilaton and axion fields. We focus at Einstein-Rosen solutions of Einstein-Maxwell-dilaton-axion equations. Several cases are analyzed and some of them have asymptotically velocity-term dominated (AVTD) singularities.