Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Quantum chaos and random matrix theory for fidelity decay in quantum computations with static imperfections

We determine the universal law for fidelity decay in quantum computations of complex dynamics in presence of internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied to quantum computations in presence of imperfections. The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chaos in the dynamical tent map with up to 18 qubits. The theory developed determines the time scales for reliable quantum computations in absence of the quantum error correction codes. These time scales are related to the Heisenberg time, the Thouless time, and the decay time given by Fermis golden rule which are well-known in the context of mesoscopic systems. The comparison is presented for static imperfection effects and random errors in quantum gates. A new convenient method for the quantum computation of the coarse-grained Wigner function is also proposed.Received: 13 December 2003, Published online: 18 March 2004PACS: 03.67.Lx Quantum computation - 05.45.Pq Numerical simulations of chaotic systems - 05.45.Mt Quantum chaos; semiclassical methods     

Static characteristics of a conduction and radiation dominated electric arc in nitrogen

The time-dependent energy and circuit equations are solved numerically to obtain temperature profiles, current-voltage characteristics and electric field strength vs axis temperature diagrams in the asymptotic region of a wall-stabilized electric arc operated on nitrogen. The numerical calculations demonstrate the splitting of the rising branch of the stationary solutions in the current-voltage characteristic. This phenomenon was earlier found experimentally for air. The computations were made for various channel radii and for various series resistances. We explain the steady-state characteristics and convergence to the single branch of solutions on the basis of the linearized Lyapunov stability theory (LLST). Comparison with available results of other authors shows that the analytical solution based on simple polynomial approximations to thermodynamic and transport functions differs significantly from numerical computations.The author is grateful to Dr. Z. Sedláek and Dr. M. Hrabovský for their stimulating advices, reminders and helpful comments.     

LAMB WAVE MODES IN A TWO-LAYERED SOLID MEDIUM WITH A WEAK INTERFACE

Using the "spring" model for a weak interface between two solids, we derive the charac-teristic equation for the Lamb waves in a two-layered solid composite and make numerical computations for dispersion curves in an aluminum/copper structure with a rigid or slip interface. The influence of the shear stiffness of the interface on the low order Lamb wave modes is considered.     

Nucleon-Deuteron Breakup Scattering in Configuration Space

The configuration-space Faddeev equations for the breakup scattering problem are solved using a new method of partial inversion. Unlike other computations this one keeps the incoming wave in the asymptotic condition. Thus all computations otherwise needed to separate the incident wave are avoided and the number of non-zero components of the inhomogeneous term in the algebraic equations is reduced to one. Speed as well as accuracy improves and we are able to solve the algebraic problem with partial inversion only. Using the standard spline-decomposition for the angle variable and the finite-difference approximation for the hyperradius optimizes considerably the inversion due to the sparse block structure of the matrix. We report on calculations of the inelasticities and phase shifts for nucleon-deuteron scattering for laboratory energies 4.0, 14.1, and 42.0MeV. The results are compared with calculations by other authors.Received November 11, 2001; accepted October 18, 2002 Published online June 27, 2003     

Influence of saturation magnetization inhomogeneities on the third and fourth moments of the FMR line in polycrystalline ferrites

The influence of saturation magnetization inhomogeneities on the third and fourth moments of the FMR line, which describe its asymmetry and pointiness, is considered in this paper. The computations are performed in the weak and strong coupling approximations between the magnetization fluctuations at different points of the specimen. It is shown that the absorption line shape depends substantially on the shape of the specimen and the magnitude of the porosity. The results of computations are compared with experiment in a broad range of variation of the porosity. The influence of the specimen shape on the shape of the FMR curve is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 80–84, May, 1982.     

Quantum Logic as a Basis for Computations

It is shown that computations can be founded on the laws of the genuine(Birkhoff—nvon Neumann) quantum logic treated as a particular version ofukasiewicz infinite-valued logic. A new way of encoding nonexact data whichencodes both the value of a number and its fuzziness is introduced. A simpleexample of a full adder that works in the proposed way is given and it is comparedwith other designs of quantum adders existing in the literature. A controversybetween the meaning of the very term quantum logic as used recently withinthe theory of quantum computations and the traditional meaning of this term isbriefly discussed.     

“Naked” Cronin effect in A + A collisions from SPS to RHIC

Baseline computations of the Cronin effect in nuclear collisions at energies spanning the SPS and the RHIC accelerators are performed in the Glauber-Eikonal model, which ascribes the effect to initial-state incoherent multiple parton scatterings. The model accounts very well for the mid-rapidity Cronin effect in hadron-nucleus collisions in the -200 GeV center of mass energy range, and will be extended to nucleus-nucleus collisions. The computations are performed under the assumption that the partons do not interact with the medium produced in the collision. Therefore, medium effects such as energy loss in a quark-gluon plasma may be detected and measured as deviations from the presented baseline computation of the “naked” Cronin effect.Received: 11 February 2005, Published online: 31 May 2005PACS: 12.38.Mh, 24.85. + p, 25.75.-q     

Synthesis of Novel Carbazole Fused Coumarin Derivatives and DFT Approach to Study Their Photophysical Properties

Novel coumarin derivatives have been synthesized by the classical Knoevenagel condensation of 4-hydroxy-9-methyl-9H-carbazole-3-carbaldehyde with active methylene compounds and characterized. Effect of solvent polarity on the photophysical properties, absorption and emission has been studied. The photophysical properties of the synthesized coumarins have been compared with some of the established analogous coumarin derivatives. Investigation of the structural parameters and understanding photophysical properties of the synthesized coumarin derivatives were carried out using Density Functional Theory (DFT) and Time Dependant Density Functional Theory (TDDFT) computations. The experimental values were correlated with the theoretical derived results. The ratio of the excited state and the ground state dipole moments was calculated by using solvatochromic and solvatofluoric data and compared with the values obtained from DFT and TDDFT computations.     

Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature. Received 10 August 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Speed dependent polarization correlations in QED and entanglement

Exact computations of polarizations correlations probabilities are carried out in QED, to the leading order, for initially polarized as well as unpolarized particles. Quite generally they are found to be speed dependent and are in clear violation of Bells inequality of Local Hidden Variables (LHV) theories. This dynamical analysis shows how speed dependent entangled states are generated. These computations, based on QED are expected to lead to new experiments on polarization correlations monitoring speed in the light of Bells theorem. The paper provides a full QED treatment of the dynamics of entanglementReceived: 25 June 2004, Published online: 5 October 2004PACS: 12.20.Ds Specific calculations - 12.20.Fv Experimental tests - 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.)Work supported by a Royal Golden Jubilee Award.     

Two-temperature channel model of a direct current arc

A relatively simple method is proposed for computing the gas and electron temperatures in an arc plasmotron channel within the framework of the self-consistent two-temperature channel model of an arc discharge. This method affords the possibility of obtaining the gas and electron temperature distribution with good enough accuracy for given discharge parameters (current intensity in the discharge, power inserted in the discharge, etc.) as a function of the radial coordinate in both nonequilibrium (T_e T_ai) and quasi-equilibrium (T_e = T_ai within the current conducting channel) cases. The results obtained can be utilized in model computations to estimate the gas and electron temperatures as well, possibly, as in a number of engineering computations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–86, July, 1990.The author is grateful to L. A. Rachevskii for useful discussion of results of the research.     

Higher algebraic structures and quantization

We derive (quasi-)quantum groups in 2+1 dimensional topological field theory directly from the classical action and the path integral. Detailed computations are carried out for the Chern-Simons theory with finite gauge group. The principles behind our computations are presumably more general. We extend the classical action in ad+1 dimensional topological theory to manifolds of dimension less thand+1. We then construct a generalized path integral which ind+1 dimensions reduces to the standard one and ind dimensions reproduces the quantum Hilbert space. In a 2+1 dimensional topological theory the path integral over the circle is the category of representations of a quasi-quantum group. In this paper we only consider finite theories, in which the generalized path integral reduces to a finite sum. New ideas are needed to extend beyond the finite theories treated here.The author is supported by NSF grant DMS-8805684, a Presidential Young Investigators award DMS-9057144, and by the O'Donnell Foundation. He warmly thanks the Geometry Center at the University of Minnesota for their hospitality while this work was undertaken     

Numerical simulation of the flow with a pseudo-shock in an axisymmetric expanding duct with a frontal inlet

The results of the numerical modeling of a flow with a pseudo-shock in an axisymmetric duct are presented. The duct included a frontal inlet with the initial funnel-shaped compression part and the cylindrical throat part as well as the subsequent expanding diffuser. To create a flow with a pseudo-shock, the duct was throttled with the use of the outlet converging insert. Numerical computations of the axisymmetric flow have been conducted on the basis of the solution of the Reynolds-averaged Navier?Stokes equations and with the use of the k-ω SST turbulence model. As a result of computations, such parameters of the flow were determined as the location of the beginning of the pseudo-shock, the length of its supersonic part, the velocity profiles in different cross sections of the pseudo-shock, the pressure distribution on the duct wall, the total pressure recovery factor, and others. The behavior of these parameters at the freestream Mach number М = 6 was analyzed versus the diffuser opening angle and different degree of the inlet duct throttling.     

The density of superconductivity in domains with corners

We compute the \(L^2\)-norm of any minimizer of the Ginzburg–Landau functional in a planar domain with a finite number of corners. Our computations are valid for a uniform applied magnetic field, large Ginzburg–Landau parameter and in the regime where superconductivity is confined near the corners of the domain.     

Quantum computing with an always-on Heisenberg interaction

Many promising schemes for quantum computing (QC) involve switching "on" and "off" a physical coupling between qubits. This may prove extremely difficult to achieve experimentally. Here we show that systems with a constant Heisenberg coupling can be employed for QC if we actively "tune" the transition energies of individual qubits. Moreover, we can collectively tune the qubits to obtain an exceptionally simple scheme: computations are controlled via a single "switch" of only six settings. Our schemes are applicable to a wide range of physical implementations, from excitons and spins in quantum dots through to bulk magnets.     

EFFECT OF INTERFACE LAYER ON LAMB WAVE PROPAGATION IN SOLID ADHESIVE JOINTS: A PERTURBATION MODEL

This paper presents a perturbation model for calculating the approximate Lamb wave velocities in solid adhesive joints. The numerical computations show that the approximate values of the Lamb wave velocities are very close to the exact ones if the thickness of the interface layer is small. A comparison of the perturbation analysis with the approximate "spring" model is given. The significance of the perturbation model is discussed for the inverse deduction of the mechanical properties of the interface layer from Lamb wave measurements.     

Uncovering the detailed structure of the algebra formed by the invariant charges of closed bosonic strings moving in 1+2-dimensional Minkowski space

For the Nambu-Goto theory of closed, bosonic strings moving in three space-time dimensions, generating relations of degree 6 for the Poisson algebra of the infinitesimal generators of observable symmetry transformations have been computed. These computations result in a deeper insight into the structure of the symmetry algebra. In addition, a parametrization of the quantum corrections for the generating relations of degree 3 is given.This work was supported by Volkswagenstiftung     

Breakdown of a topological phase: quantum phase transition in a loop gas model with tension

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model--the toric code--which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of "magnetic" vortices, leading to confinement of the elementary "charge" excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and relate our results to error rates for topological quantum computations.     

Graphene edge from armchair to zigzag: the origins of nanotube chirality?

The energy of an arbitrary graphene edge, from armchair (A) to zigzag (Z) orientation, is derived in analytical form. It contains a "chemical phase shift" determined by the chemical conditions at the edge. Direct atomistic computations support the universal nature of the relationship, definitive for graphene formation, and shapes of the voids or ribbons. It has further profound implications for nanotube chirality selection and possibly control by chemical means, at the nucleation stage.