Semiclassical statistical mechanics ofv-dimensional fluid mixture of hardv-spheres

The problem of calculating the equilibrium properties ofv-dimensional fluid mixture of hardv-spheres is studied. High temperature expansion for the density independent radial distribution function is derived for a hardv-sphere mixture. The ‘excess’ quantum corrections to the second virial coefficient and the excess free energy are also studied. Significant features are the large increase in ‘excess’ quantum correction with increasing dimensionality.     

Examples of gauged Laplacians on noncommutative spaces

We present two (classes of) examples of gauged Laplacian operators. The first one is a model of spin-Hall effect on a noncommutative four-sphere S _ϑ ⁴ with isospin degrees of freedom, coming from a noncommutative instanton, and invariant under the quantum group SO _ϑ (5). The second one, a Hall effect on a quantum 2-dimensional sphere S _q ², describes ‘excitations moving on the quantum sphere’ in the field of a magnetic monopole with symmetry coming from the quantum group SU _q (2). For both models, ample symmetries provide a complete diagonalization.     

Perturbation expansions and series acceleration procedures. Part I. ε-convergence and critical parameters

A simple acceleration of convergence technique known as the ‘ε-convergence algorithm’ (ea) is applied to determine the critical temperatures and exponents. Several illustrations involving well-known series expansions appropriate to two- and three-dimensional Ising models, three-dimensional Heisenberg models, etc., are given. Apart from this, a few recently studied ferrimagnetic systems have also been analysed to emphasise the generality of the approach. Where exact solutions are available, our estimates obtained from this procedure are in excellent agreement. In the case of other models, the critical parameters we have obtained are consistent with other estimates such as those of the Padé approximants and group theoretic methods. The same procedure is applied to the partial virial series for hard spheres and hard discs and it is demonstrated that the divergence of pressure occurs when the close-packing density is reached. The asymptotic form for the virial equation of state is found to beP/ρkT ∼ (1 −ρ/ρ _c ⁻¹ for hard spheres and hard discs. Apart from the estimation of ‘critical parameters’, we have applied theea and the parametrised Euler transformation to sum the partial, truncated virial series for hard spheres and hard discs. The resulting values of pressure so obtained, compare favourably with the molecular dynamics results.     

Glow discharge in low-pressure excilamps

This paper presents a review of the principal publications devoted to the study of the spontaneous radiation sources operating in the uv region and discusses the properties of a low-pressure glow discharge in binary mixtures of inert gases with halides. It has been demonstrated that for variation of the excitation parameters over a wide range more than 10% emission efficiencies are realized for exciplex molecules and thatXeCl ^* andKrCl ^* molecules are formed in the main by the harpoon reaction. The current-voltage characteristics of glow discharges in cylindrical, coaxial, and planar excilamps and the parameters of the radiation ofXeCl ^*,KrCl ^*, andXeF ^* molecules generated on excitation of inert-gas-halide mixtures by normal and high-voltage glow discharges are presented. It is pointed out that low-pressure glow-discharge excilamps enable one to use simple power supplies. Institute of High Current Electronics. Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 50–66, June, 1999.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.     

Isothermal compressibility and sound velocity of binary liquid systems: Application of hard sphere models

Sound velocity and density were measured in six binary liquid mixtures namely,n-heptane+toluene (I);n-heptane+n-hexane (II); toluene+n-hexane (III); cyclohexane+n-heptane (IV); cyclohexane+n-hexane (V), andn-decane+n-hexane (VI) at 298.15 K. The experimental isothermal compressibility has been evaluated from measured values of density and sound velocity. The isothermal compressibility of these mixtures has been calculated theoretically using different models for the hard sphere equation of state and also using Flory’s statistical theory. The computed values of isothermal compressibility were also compared with the experimentally evaluated values. A satisfactory agreement has been observed.     

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration and its associated twistor geometry. Our quantum sphere arises as the unit sphere inside a q-deformed quaternion space . The resulting four-sphere is a quantum analogue of the quaternionic projective space . The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space and use it to study a system of anti-self-duality equations on , for which we find an ‘instanton’ solution coming from the natural projection defining the tautological bundle over .     

High-fidelity copies from a symmetric 1→2 quantum cloning machine

An investigation of an optimal universal unitary Controlled-NOT gate that performs a specific operation on two unknown states of qubits taken from a great circle of the Bloch sphere is presented. The deep analogy between the optimal universal C-NOT gate and the ‘equatorial’ quantum cloning machine (QCM) is shown. In addition, possible applications of the universal C-NOT gate are briefly discussed.     

Of heat capacity at homologous temperatures for metals showing h.c.p. ⇄ b.c.c. transformation

Some interesting aspects of the temperature dependence of the Planck’s functionφ and heat capacities of metals exhibiting the h.c.p. ⇄ b.c.c. transformation have been brought to light by the use of reduced temperature (T*) and Planck’s function (-φ T*). It has been shown that tangents drawn to the -φ T* vsT* plots of these metals at any chosen value ofT* intersect at a point whose coordinates are defined by the slope and intercept ofφ vs entropy plots at any homologous temperature and the selectedT* value. A generalized expression obtained for the temperature dependence ofφ has been used to demonstrate that the heat capacity of these metals may be visualized to have structural and material components.     

Continuity of a Quantum Stochastic Process

We investigate a quantum counterpart of the classical notion of a stochastic process continuous with probability one, and prove that the L ²-limit of quantum martingales ‘continuous with probability one’ is a quantum martingale ‘continuous with probability one’. Applications of this result to a number of concrete situations is presented.     

Local Index Formula on the Equatorial Podleś Sphere

We discuss spectral properties of the equatorial Podleś sphere S _q ². As a preparation we also study the ‘degenerate’ (i.e. q=0) case (related to the quantum disk). Over S _q ² we consider two different spectral triples:one related to the Fock representation of the Toeplitz algebra and the isopectral one given in [7]. After the identification of the smooth pre-C ^*-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the C ^*-algebra (the nontrivial generator of the K ₀-group) as well as the pairing with the q-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.     

Solvatochromic Effect on the Photophysical Properties of Two Coumarins

The absorption and emission spectra of two coumarins namely 7, 8 benzo-4-azidomethyl coumarin (C₁) and 6-methoxy-4-azidomethyl coumarin (C₂) have been recorded at room temperature in solvents of different polarities. The ground state dipole moments (μ _g ) of two coumarins were determined experimentally by Guggenheim method. The exited state (μ _e ) dipole moments were estimated from Lippert’s, Bakhshievs and Chamma-Viallet’s equations by using the variation of Stoke’s shift with the solvent dielectric constant and refractive index. The ground and excited state dipole moments were calculated by means of solvatochromic shift method and also the excited state dipole moments are determined in combination with ground state dipole moments. It was observed that dipole moments of excited state were higher than those of the ground state, indicating a substantial redistribution of the π-electron densities in a more polar excited state for two coumarins.     

Dielectric relaxation of binary polar liquid mixture measured in benzene at 10 GHz frequency

The dielectric relaxation times τ _jk ’s and dipole moments μ _jk ’s of the binary (jk) polar liquid mixture of N,N-dimethyl acetamide (DMA) and acetone (Ac) dissolved in benzene (i) are estimated from the measured real σ′ _ijk and imaginary σ″ _ijk parts of complex high frequency conductivity σ* _ijk of the solution for different weight fractions w _jk ’s of 0.0, 0.3, 0.5, 0.7 and 1.0 mole fractions x _j of Ac and temperatures (25, 30, 35 and 40°C) respectively under 9.88 GHz electric field. τ _jk ’s are obtained from the ratio of slopes of σ″ _ijk -w _jk and σ′ _ijk -w _jk curves at w _jk → 0 as well as linear slope of σ″ _ijk -σ′ _ijk curves of the existing method (Murthy et al, 1989) in order to eliminate polarpolar interaction in the latter case. The calculated τ’s are in excellent agreement with the reported τ’s due to Gopalakrishna’s method. μ _jk ’s are also estimated from slopes β’s of total conductivity σ _ijk -w _jk curves at w _jk → 0 and the values agree well with the reported μ’s from G.K. method. The variation of τ _jk ’s and μ _jk ’s with x _j of Ac reveals that solute-solute molecular association occurs within 0.0–0.3x _j of Ac beyond which solute-solvent molecular association is predicted. The theoretical dipole moments μ _theo’s are calculated from bond angles and bond moments to have exact μ’s only to show the presence of inductive, mesomeric and electromeric effects in the substituent polar groups. The thermodynamic energy parameters are estimated from ln(τ _jk T) against 1/T linear curve from Eyring’s rate theory to know the molecular dynamics of the system and to establish the fact that the mixture obeys the Debye-Smyth relaxation mechanism.      

Dielectric behaviour of ketone-amine binary mixtures at microwave frequencies

Values of dielectric constant (ε′) and loss factor (ε″) have been experimentally determined for binary liquid mixtures of ethyl methyl ketone+ethylenediamine and methyl isobutyl ketone+ethylenediamine at 9.44 GHz microwave frequencies at 30°C. The values ofε′ andε″ have been used to evaluate the molar polarization, apparent polarization and the excess permittivities. Excess refractive index, viscosity and activation energy of viscous flow have also been estimated. These parameters have been used to explain the formation of 1:1 complexes for both the systems.     

Polymer mixtures in confined geometries: Model systems to explore phase transitions

While binary (A,B) symmetric polymer mixtures ind = 3 dimensions have an unmixing critical point that belongs to the 3d Ising universality class and crosses over to mean field behavior for very long chains, the critical behavior of mixtures confined into thin film geometry falls in the 2d Ising class irrespective of chain length. The critical temperature always scales linearly with chain length, except for strictly two-dimensional chains confined to a plane, for whichT _c ∝N ^5/8 (this unusual exponent describes the fractal contact line between segregated chains in dense melts in two spatial dimensions,d = 2). When the walls of the thin film are not neutral, but preferentially attract one species, complex phase diagrams occur due to the interplay between capillary condensation and wetting phenomena. For ‘competing walls’ (one wall prefers A, the other prefers B) particularly interesting interface localization-delocalization transitions occur, while analogous phenomena in wedges are related to the ‘filling transition’.     

Infrared intensity analysis of some MXY2 type molecules

Infrared intensity analysis of MXY₂ type molecules has been attempted. The dipole momentμ of C=O is obtained to be different for different moleculesviz. for CH₂O, 1.9052; for COCl₂, 1.1517; for COF₂, 0.6340; and for COBr₂, 0.7687. Similarly in the case of CSF₂ and CSCl₂ μ _C=S it was found to be 0.2473 and 0.2983 respectively. This shows that the effect of the electro-negative halogen atoms is very important. Presented at the ‘National Symposium on Molecular Spectroscopy’, Annamalai University, Annamalainagar on 28 February 1976.     

Quantum Spheres and Projective Spaces as Graph Algebras

 The C ^* -algebras of continuous functions on quantum spheres, quantum real projective spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras corresponding to suitable directed graphs. Structural results about these quantum spaces, especially about their ideals and K-theory, are then derived from the general theory of graph algebras. It is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively. Received: 31 January 2001 / Accepted: 29 July 2002 Published online: 7 November 2002 RID="*" ID="*" Supported by grant No. R04–2001–000–00117–0 from the Korea Science & Engineering Foundation. RID="**" ID="**" Partially supported by the Research Management Committee of the University of Newcastle.     

Diffusing wave spectroscopy of dense colloids: Liquid,crystal and glassy states

Using intensity autocorrelation of multiply scattered light, we show that the increase in interparticle interaction in dense, binary colloidal fluid mixtures of particle diameters 0.115μm and 0.089μm results in freezing into a crystalline phase at volume fractionφ of 0.1 and into a glassy state atφ=0.2. The functional form of the field autocorrelation functiong ⁽¹⁾(t) for the binary fluid phase is fitted to exp[−γ(6k ₀ ² D _eff t)^1/2] wherek ₀ is the magnitude of the incident light wavevector andγ is a parameter inversely proportional to the photon transport mean free pathl*. TheD _eff is thel* weighted average of the individual diffusion coefficients of the pure species. Thel* used in calculatingD _eff was computed using the Mie theory. In the solid (crystal or glass) phase, theg ⁽¹⁾(t) is fitted (only with a moderate success) to exp[−γ(6k ₀ ² W(t))^1/2] where the mean-squared displacementW(t) is evaluated for a harmonically bound overdamped Brownian oscillator. It is found that the fitted parameterγ for both the binary and monodisperse suspensions decreases significantly with the increase of interparticle interactions. This has been justified by showing that the calculated values ofl* in a monodisperse suspension using Mie theory increase very significantly with the interactions incorporated inl* via the static structure factor.     

Topos theory and consistent histories: The internal logic of the set of all consistent sets

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some way. However, in this paper the alternative approach is considered in which all consistent sets are kept, leading to a type of ‘many-world-views’ picture of the quantum theory. It is shown that a natural way of handling this situation is to employ the theory of varying sets (presheafs) on the spaceB of all nontrivial Boolean subalgebras of the orthoalgebraUP of history propositions. This approach automatically includes the feature whereby probabilistic predictions are meaningful only in the context of a consistent set of history propositions. More strikingly, it leads to a picture in which the ‘truth values’ or ‘semantic values’ of such contextual predictions are not just two-valued (i.e., true and false) but instead lie in a larger logical algebra—a Heyting algebra—whose structure is determined by the spaceB of Boolean subalgebras ofUP. This topos-theoretic structure thereby gives a coherent mathematical framework in which to understand the internal logic of the many-world-views picture that arises naturally in the approach to quantum theory based on the ideas of consistent histories.