Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

An Algebraic Version of Haag’s Theorem

Under natural conditions (such as split property and geometric modular action of wedge algebras) it is shown that the unitary equivalence class of the net of local (von Neumann) algebras in the vacuum sector associated to double cones with bases on a fixed space-like hyperplane completely determines an algebraic QFT model. More precisely, if for two models there is a unitary connecting all of these algebras, then — without assuming that this unitary also connects their respective vacuum states or spacetime symmetry representations — it follows that the two models are equivalent. This result might be viewed as an algebraic version of the celebrated theorem of Rudolf Haag about problems regarding the so-called “interaction-picture” in QFT. Original motivation of the author for finding such an algebraic version came from conformal chiral QFT. Both the chiral case as well as a related conjecture about standard half-sided modular inclusions will be also discussed.     

An arena for model building in the Cohen—Glashow very special relativity

The Cohen—Glashow Very Special Relativity (VSR) algebra is defined as the part of the Lorentz algebra which upon addition of CP or T invariance enhances to the full Lorentz group, plus the space—time translations. We show that noncommutative space—time, in particular noncommutative Moyal plane, with light- like noncommutativity provides a robust mathematical setting for quantum field theories which are VSR invariant and hence set the stage for building VSR invariant particle physics models. In our setting the VSR invariant theories are specified with a single deformation parameter, the noncommutativity scale ╕_NC. Preliminary analysis with the available data leads to ╕_NC ≳ 1–10 TeV.     

Correlation Inequalities for Interacting Particle Systems with Duality

We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other—a process which we call here the symmetric inclusion process (SIP)—or repel each other—a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction,—the so-called Brownian momentum process, and the Brownian energy process. These inequalities are counterparts of the inequalities (in the opposite direction) for the symmetric exclusion process, showing that the SIP is a natural bosonic analogue of the symmetric exclusion process, which is fermionic. Finally, we consider a boundary driven version of the SIP for which we prove duality and then obtain correlation inequalities.     

Antipolarization effect in quantum wells in a strong external alternating field

It is shown that when a strong ac electric field acts on an electron in a double quantum well, the dipole moment is an almost periodic function of the dc voltage applied to the structure. An antipolarization effect — the structure is polarized in a direction opposite to the external field — appears during one half of the period. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 386–391 (25 September 1999)     

An alternative definition of the electron propagator in the superoperator form and its relation to linear response theory in a coupled-cluster framework

In this paper it is shown that (i) there exists an alternative definition of the superoperator resolvent for calculation of difference energy satisfying linked cluster theorem for a coupled-cluster choice of the ground-state function which may even be approximate; (ii) the pole-structure of this propagator-like function in superoperator form is shown to contain information similar to that contained in the conventional propagator. (iii) It is demonstrated that suitable “Killer conditions” and completeness of the “operator manifold”—essential for understanding the pole-structure of the propagator—can be established both for an exact and an approximate ground state function in a coupled-cluster form. (iv) It is also demonstrated that difference energies calculated with these propagator-like functions are identical to those obtained from a linear response theory in a coupled-cluster form put forward recently by Mukherjeeet al and Monkhorst.     

On the possibility of investigating the dispersion of the energy bands of a crystal using resonant x-ray emission spectra

It is shown that, when the dispersion of the energy bands of crystals is investigated by resonant x-ray emission (RXE), an ambiguity can arise in the determination of k _tr — the transition point in k space — as a result of the characteristic features of the band structure and the value of the matrix elements. It is proposed that calculations of the distribution of partial contributions to interband optical transitions in the Brillouin zone (BZ) be used as a means of obtaining a simplified estimate of k _tr. The basic properties of this distribution are examined for lithium hydride, which is a convenient model object having a simple band structure and interband transitions which have been studied in detail. It is shown that the k points of the general position, which form a complex figure in the BZ, make the main contribution to the interband transitions. The contribution of high-symmetry points is much smaller mainly because of their small representativeness. This make it easier to understand the reason for the possible nonmonotonic variation of k _tr in RXE measurements of the dispersion of the energy bands of crystals or the sharp changes in the resonance-fluorescence intensity. Fiz. Tverd. Tela (St. Petersburg) 41, 1597–1601 (September 1999)     

Collective states of odd nuclei in a model with quadrupole-octupole degrees of freedom

We apply the collective axial quadrupole—octupole Hamiltonian to describe the rotation—vibration motion of odd nuclei with Coriolis coupling between the even-even core and the unpaired nucleon.We consider that the core oscillates coherently with respect to the quadrupole and octupole axialdeformation variables. The coupling between the core and the unpaired nucleon provides a split paritydoublet structure of the spectrum. The formalism successfully reproduces the parity-doublet splitting in a wide range of odd-A nuclei. It provides model estimations for the third angular-momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure. The text was submitted by the authors in English.     

Accelerating Universe with a Special Form of Decelerating Parameter

In this article, we try to investigate the quintessence model with a minimally coupled scalar field by taking a special form of decelerating parameter q in such a way that which provides an early deceleration and late time acceleration for barotropic fluid and Chaplygin gas dominated models. We have shown that the potential function V(φ) is always decreases with the scalar field φ for barotropic and Chaplygin both models. The {r,s} diagram shows the behaviour of the universe in different stages during the evolution.     

Structural transformations of the cumulene form of amorphous carbyne at high pressure

Structural transformations of the cumulene form of amorphous carbyne which are induced by heating at high pressure (7.7 GPa) are investigated. These can be described by the sequence amorphous phase — crystal — amorphous phase — disordered graphite. Raman scattering shows that predominately the chain structure of carbyne remains at the first three stages. It was found that the intermediate crystalline phase is an unknown modification of carbon whose structure is identified as cubic (a=3.145 Å). A mechanism of structural transformations in carbyne that involves the formation of new covalent bonds between chains is discussed. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 237–242 (25 August 1997)     

Switching effects in composite films based on the conjugated polymer polyfluorene and ZnO nanoparticles

The S- and N-shaped current—voltage characteristics have been studied for composite films of the conjugated polymer polyfluorene and ZnO nanoparticles deposited onto Al and In₂O₃/SnO₂ electrodes with and without an intermediate sublayer of the conducting polymer PEDT/PSS. The differences in the current— voltage characteristics of the systems (the N- and S-types, respectively) are interpreted using the electro-thermal switching model, which takes into account the structural and electric properties of PEDT/PSS. The switching provides both alignment of polymer molecules and tunneling of charge carriers, which leads to an increase in conductivity. The current flow in this structure causes an increase in temperature of conducting channels; when the temperature reaches certain levels, the conductivity of the channels decreases because the alignment of polymer molecules is upset, which creates an N-shaped form of the current—voltage characteristics.     

A Rayleigh-type wave at the plane interface of two homogeneous fluid half-spaces

It is shown that at the plane interface of two homogeneous fluid semi-infinite media, of which one is an ordinary fluid and the other a double negative—i.e., a fluid with negative density and negative compressibility—there can exist a Rayleigh-type wave propagating without attenuation, whose amplitude exponentially decreases with distance on both sides of the interface. In the parameter space of the media, the range of its existence is determined and the main properties are studied. A unique feature of this wave is the arbitrarily small propagation velocity, which does not depend on frequency, and the energy concentration in an arbitrarily thin layer close to the interface.     

Static and switching characteristics of field-controlled integrated thyristor

The static parameters of and switching transients in an advanced high-voltage high-speed switching device—a MOSFET-controlled integrated thyristor—and their dependences on the geometry and electrophysical properties of base layers in the n ⁺ pnn’p ⁺ device structure are studied experimentally. It is shown that the residual resistance of the high-voltage (∼2.5 kV) microthyristor chip in the on-state is much smaller than that of the high-voltage IGBT with the speed of the former kept at a sufficiently high level. The new device is multifunctional and can operate under different operating conditions. Specifically, it can be turned off by shunting the n ⁺ p emitter by an add-on MOSFET, by applying a gate current pulse, and in the cascode turn-off regime. In these regimes, the ultimate value of the turn-off current noticeably grows.     

Models for the 3D singular isotropic oscillator quadratic algebra

We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential—differential or differential—difference and difference—difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.     

Multiple bands: A key to high-temperature superconductivity in iron arsenides?

In the framework of four-band model of superconductivity in iron arsenides proposed by Barzykin and Gor’kov we analyze the gap ratios on hole—like and electron—like Fermi—surface cylinders. It is shown that experimentally observed (ARPES) gap ratios can be obtained only within rather strict limits on the values of pairing coupling constants. The difference of T _c values in 1111 and 122 systems is reasonably explained by the relative values of partial densities of states. The multiple bands electronic structure of these systems leads to a significant enhancement of effective pairing coupling constant determining T _c , so that high enough T _c values can be achieved even for the case of rather small intraband and interband pairing interactions. The article is published in the original.     

Predictability of ion transport properties from the structure of solid electrolytes

The concept of bond valence (BV) is widely used in crystal chemical considerations, e.g. to assess equilibrium positions of atoms in crystal structures from an empirical relationship between bond lengthR _M−X and bond valenceS _A−X =exp [(R ₀ −R _M−X ) /b] as sites where the BV sumV(A)=∑ s _M−X equals the formal valenceV _id of the cationM ⁺ . Our modified BV approach that systematically accounts for the softness of the bond may then be effectively used to study the interplay between structure and properties of solid electrolytes. This is exemplified for correlations to experimental data from IR, NMR, and impedance spectroscopy. Combining the bond valence approach with reverse Monte Carlo (RMC) modeling or molecular dynamics (MD) simulations provides a deeper understanding of ion transport mechanisms, especially in highly disordered or amorphous solids. Local structure models for crystalline electrolytes are derived by combining crystallographic structure information with simulations. A method for the prediction of the activation energy of the ionic conductivity from the bond valence analysis of the crystal structure is proposed. Taking into account the mass dependence of the conversion factor from bond valence mismatch into an activation energy scale, we could establish a correlation that holds for different types of mobile ions. The strong coupling of the H⁺ transfer to the anion motion in proton conductors requires a special treatment. For glassy solid electrolytes RMC structure models are BV-analyzed to assess the total number of equilibrium sites and to identify transport pathways for the mobile ions. Recently, we have reported a correlation between the pathway volume fraction and the transport properties that permits to predict both absolute value and activation energy of the dc ionic conductivities of disordered solids (including mixed alkali glasses) directly from their structural models. Here we discuss a corresponding BV analysis of molecular dynamics simulation trajectories that allows quantifying the evolution of pathways in time and the influence of temperature on the transport pathways. Paper presented at the Patras Conference on Solid State Ionics — Transport Properties, Patras, Greece, Sept. 14 — 18, 2004.     

Critical Points Inside the Gaps of Ground State Laminations for Some Models in Statistical Mechanics

We consider models of interacting particles situated in the points of a discrete set Λ. The state of each particle is determined by a real variable. The particles are interacting with each other and we are interested in ground states and other critical points of the energy (metastable states). Under the assumption that the set Λ and the interaction are symmetric under the action of a group G—which satisfies some mild assumptions—, that the interaction is ferromagnetic, as well as periodic under addition of integers, and that it decays with the distance fast enough, it was shown in a previous paper that there are many ground states that satisfy an order property called self-conforming or Birkhoff. Under some slightly stronger assumptions all ground states satisfy this order property. Under the assumption that the interaction decays fast enough with the distance, we show that either the ground states form a one dimensional family or that there are other Birkhoff critical points which are not ground states, but lying inside the gaps left by ground states. This alternative happens if and only if a Peierls–Nabarro barrier vanishes. The main tool we use is a renormalized energy. In the particular case that the set Λ is a one dimensional lattice and that the interaction is just nearest neighbor, our result establishes Mather’s criterion for the existence of invariant circles in twist mappings in terms of the vanishing of the Peierls–Nabarro barrier. The work of RdlL was supported by NSF grants. The work of EV was supported by GNAMPA and MIUR Variational Methods and Nonlinear Differential Equations.     

N = 4 mechanics,WDVV equations and polytopes

N = 4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten—Dijkgraaf—Verlinde—Verlinde (WDVV) equation for F. The solutions are encoded by the finite Coxeter systems and certain deformations thereof, which can be encoded by particular polytopes. We provide A _n and B ₃ examples in some detail. Turning on the prepotential U in a given F background is very constrained for more than three particles and nonzero central charge. The standard ansatz for U is shown to fail for all finite Coxeter systems. Three-particle models are more flexible and based on the dihedral root systems.     

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.