Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2)_K Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.     

Confinement of atoms with nondegenerate ground states in a three-dimensional dissipative optical superlattice

Based on the developed kinetic theory of rectified radiative forces, we found sufficient conditions for purely optical (nonmagnetic) three-dimensional confinement and cooling of atoms with the J=0 → J=1 quantum transition in a weak field of mutually orthogonal bichromatic standing waves. We show that a deep stable atom localization of atoms in the cells of an effective light superlattice (with a spacing much larger than the light wavelength) can be achieved by controlling the phase shifts (time-difference phase) of the temporal oscillations in orthogonally polarized field components and by specially choosing the field parameters. The proposed scheme of purely optical confinement can be directly used for a large group of atoms like Yb isotopes and alkali-earth elements with even-even nuclei.     

关联函数的长时间渐近行为——波对弛豫过程的影响

本文从非平衡态统计的一般理论出发,系统地讨论了宏观体系中波对弛豫过程的影响,特别是关联函数的非指数型渐近行为。由于表象选择对处理耗散过程的重要性,我们必须从元激发表象出发(而不是自由粒子表象)计算关联函数或输运系数(久保公式)。为此,应用了C代数的基本概念,发展了一套算子展开的方法,用之将流算子在元激发二次量子化表象中一般地表示出来。我们从刘维算子的预解式出发,对元激发间的剩余相互作用作微扰,应用了投影算子方法后,可以比较简单地得到关联函数非指数衰减部分的一般表达式。根据对元激发处理过程的分析,我们将元激 关键词：     

Basin boundaries in asymmetric vibrations of a circular plate

In order to investigate further nonlinear asymmetric vibrations of a clamped circular plate under a harmonic excitation, we reexamine a primary resonance, studied by Yeo and Lee [Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate, Journal of Sound and Vibration 257 (2002) 653-665] in which at most three stable steady-state responses (one standing wave and two traveling waves) are observed to exist. Further examination, however, tells that there exist at most five stable steady-state responses: one standing wave and four traveling waves. Two of the traveling waves lose their stability by Hopf bifurcation and have a sequence of period-doubling bifurcations leading to chaos. When the system has five attractors: three equilibrium solutions (one standing wave and two traveling waves) and two chaotic attractors (two modulated traveling waves), the basin boundaries of the attractors on the principal plane are obtained. Also examined is how basin boundaries of the modulated motions (quasi-periodic and chaotic motions) evolve as a system parameter varies. The basin boundaries of the modulated motions turn out to have the fractal nature.     

A one-channelN/D calculation of the πN partial waves incorporating inelastic unitarity

The present work is a re-analysis of theJ≦3/2πN partial waves in a single channelN/D scheme. The new features are inclusion of (i) inelastic unitarity, and (ii) the forces generated by the exchange of a scalarI=0 meson. The calculation shares the same difficulties with other one-channel treatments in that (a) the D₁₃ resonance is absent, and (b) it is not possible to produce the nucleon as a dynamical bound state and at the same time obtain aP ₁₁ resonance. Apart from theseS ₁₁,P ₁₁ andD ₁₃ waves, one can secure good agreement between theory and experiments in other partial waves.     

Non-trivial saddle points and band structure of bound states of the two-dimensional O(N) vector model

We discuss O(N) invariant scalar field theories in 0 + 1 space-time dimensions (quantum mechanics) and in 1 + 1 space-time dimensions (field theory). Combining ordinary “Large N” saddle point techniques and simple properties of the diagonal resolvent of one-dimensional Schrödinger operators we find non-trivial (non-constant) solutions to the saddle point equations of these models in addition to the saddle point describing the ground state of the theory. In the “Large N” limit these saddle points are exact for the quantum mechanical case, but only approximate in the two-dimensional theory. In the latter case they are the leading contributions to the time evolution kernel at short times, or equivalently, the leading contribution to the high temperature expansion of partition function stemming from space dependent static configurations in case of the Euclidean theory. We interpret these novel saddle points as collective O(N) singlet excitations of the field theory, each embracing a host of finer quantum states arranged in O(N) multiplets, in an analogous manner to the band structure of molecular spectra.     

Generation of a continuum and stimulated Raman scattering harmonics during scattering of electromagnetic radiation of relativistic intensity

A theory of the propagation instability of plane, monochromatic, circularly polarized electromagnetic waves of relativistic intensity in matter is developed for a spatially three-dimensional geometry including arbitrary polarization of the scattered radiation. Harmonic generation owing to striction and relativistic nonlinearity is examined, as well as scattering owing to electron recoil, the decay instability of the harmonics with formation of scattered electromagnetic waves (Stokes components of the stimulated Raman scattering and plasmons), the interaction of electromagnetic waves in the plasma (antistokes stimulated Raman scattering), and the generation of a radiative continuum. The transition of the three-dimensional theory to a one-dimensional problem in the nonrelativistic limit is discussed. Zh. éksp. Teor. Fiz. 113, 2034–2046 (June 1998)     

Quasi-Particle Theory of Alfven Soliton Interaction in Plasmas

The collision of solitons due to Alfven waves in plasmas is studied in this paper by the aid of quasi-particle theory. The suppression of the interaction of solitons, in presence of the perturbation terms, is acheived by means of this theory. The perturbation terms that are considered in this paper are nonlinear damping, finite conductivity and Landau damping. The numerical simulations support the theory that was developed. PACS Codes: 02.30.Ik, 02.30.Jr, 52.35.Sb.     

Autoignition of ethylene in shock waves

The delay time of ignition of various C₂H₄-O₂-Ar mixtures behind reflected shock waves were measured at temperatures of 1090–1520 K and a pressure of 0.65 ± 0.05 MPa. A kinetic scheme of the ignition of ethylene based on the known rate constants of the key elementary reactions was developed. The scheme satisfactorily describes our own and published data on the ignition of ethylene in shock waves over wide ranges of temperature (1100–2400 K), pressure (0.006–0.64 MPa) and ethylene (0.1–17.4 vol %) and oxygen (0.6–20.7 vol %) concentrations.     

The surface delta interaction in the transuranic nuclei

The Surface Delta Interaction (SDI) is employed to calculate the ernergy of gamma-vibrational and theK=0, 1, 2, and 3 Octupole vibrational band heads in the even-mass Transuranic nuclei. The quasi-particle Random Phase (RPA) and the quasi-particle Tamm Dancov approximations (TDA) are utilized to solve the Hamiltonian. The resulting energies and gamma transitions are compared with the Pairing plus Quadrupole (PQF) or Octupole (POF) force model and the available experimental data. The agreement between theory and experiment is satisfatory. Only theK=0, 1, and 2 Octupole bands are collective. TheK=3 negative parity state is practicaly a pure two quasi-particle state.     

Linear and nonlinear magnetohydrodynamic waves in twisted magnetic flux tubes

Dynamics of axisymmetric Alfvén and slow magnetoacoustic waves in weakly twisted magnetic flux tubes is considered. Linear dispersion relations for the waves are derived and analyzed in the presence of the twisting. The weakly nonlinear dynamics is shown to be governed by the Korteweg-de Vries equation. Nonlinear slow body waves appear as a narrowing of tube in a low β plasma and widening of tube, when β ⪢ 1. Nonlinear Alfvén torsional waves appear as a widening (β > 1) and narrowing (β < 1) of tube, accompanied by the local increase of the tube twisting.     

The decay of 20 min179Re

The decay of 20 min¹⁷⁹Re has been studied by means of Ge(Li) and Si(Li) detectors and a magneticβ-ray spectrometer. From the measured positon endpoint aQ-value of 2690±50 keV has been deduced. The decay scheme given is supported by coincidence relations. Fast beta transitions (logft≈5.1) to levels at 720keV and 1680 keV in¹⁷⁹W can be explained by a three quasi-particle character for these states. Nilsson assignments to these and other levels are discussed.     

The observation of viscous waves in a He I film

The transverse acoustic impedance of a ⁴He film has been measured at 3.11 K and 20.5 MHz and shows the occurence of standing shear waves in the film. This is in good agreement with calculations using transmission line theory and gives a new method of measuring the thickness of liquid films.     

The localization of local and gap modes by the sign count method

In the theory of local states it is usual to bring the linear problem ¦glI _N ?D¦=0 into a non-linear one ¦R(λ)¦=0, where the ordern of the condensed stiffness matrixR(λ) is much smaller than the orderN of the matrixD. Powerful methods exist for determining the number of the eigenvalues ofD in some interval without solving the equation ¦glI _N ?D¦=0 explicitly. It is shown, that analogous methods can be applied to the condensed matrix R(λ), when computing the eigen-valuesλ outside the frequency spectrum of the ideal lattice.     

A new compact difference scheme for second derivative in non-uniform grid expressed in self-adjoint form

A single-parameter family of self-adjoint compact difference (SACD) schemes is developed for discretizing the Laplacian operator in self-adjoint form. Developed implicit scheme is formally second-order accurate (with respect to truncation error) with a free parameter, α which helps control the numerical properties in the spectral plane. The SACD scheme is analyzed in the spectral plane for its resolution properties for both periodic and non-periodic problems using the matrix spectral analysis [T.K. Sengupta, G. Ganeriwal, S. De, Analysis of central and upwind schemes, J. Comput. Phys. 192 (2) (2003) 677–694]. The major objective here is to identify the advantages of the new scheme over the traditional explicit second order CD2 scheme, in discretizing the Laplacian operator in self-adjoint form. This appears in Navier–Stokes equation and in other transport equations and boundary value problems (bvp) expressed in orthogonal co-ordinate systems, either in physical or in transformed plane. We also compare the developed method with the higher order compact schemes for non-uniform grids. To demonstrate the accuracy of SACD scheme we have tested it for: (i) bi-directional wave propagation problem, given by the second order wave equation and (ii) an elliptic bvp, as in the Stommel ocean model for the stream function. These examples help infer the properties of SACD scheme when solving different types of partial differential equations. Most importantly the effects of grid-stretching and choice of value of the free parameter (α) are investigated here. We also compare the present implicit compact method with explicit compact method known as the higher order compact (HOC) method.Also, the practical applications of the SACD scheme are explored by solving the Navier–Stokes equation for the cases of: (a) a flow inside a lid-driven cavity and (b) the receptivity and instability of an external adverse pressure gradient flow over a flat plate. In the former, unsteadiness of the flow is captured and in the latter, the receptivity of the flow is studied in causing flow instability by triggering Tollmien–Schlichting waves. The new scheme shows a marked improvement over the explicit scheme for low Reynolds number steady flow in lid driven cavity. Whereas for the flow in the same geometry at higher Reynolds numbers, efficacy of the scheme is established by showing the formation of a triangular vortex and secondary vortical structures. Presented scheme is perfectly capable of expressing the diffusion operator accurately as shown via the capturing of instability waves inside the shear layer.     

Nonlinear interaction of magnetoacoustic waves in yttrium orthoferrite

The phenomenon of energy transfer, both monotonic and oscillating, between the fundamental and higher harmonics of standing acoustic waves is observed during the laser generation of sound in YFeO₃ crystals. An analogous phenomenon for traveling light waves is well known in nonlinear optics. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 12, 789–792 (25 December 1999)     

Transverse instability threshold in counterpropagating light beams for a nonlinear medium with local photorefractive response

We derive the threshold conditions for the instability of counterpropagating waves in a nonlinear medium with local photorefractive response against the excitation of transverse small-angle structures. These conditions allow for all the important types of diffraction from refractive-index reflection gratings and are not limited to the case of strict frequency degeneracy of the waves. We study the dependence of the crystal-thickness threshold and the secondary wave emission angle on the crystal parameters and the pump conditions. We show that when the pump wave intensities differ considerably, excitation of standing light structures is replaced by excitation of traveling structures. Finally, we discuss the applications of the theory to experiments with the photorefractive crystals LiNbO₃ and LiTaO₃. Zh. éksp. Teor. Fiz. 111, 1611–1623 (May 1977)     

Interplay of valence-shell clusters and the vibrational field in58Ni

The level scheme and electromagnetic properties of⁵⁸Ni are described in the two-particle cluster core coupling model without parameter fitting. The present results are compared to previous shell-model and quasi-particle calculations. To explain the enhancedE2 transitions a neutron effective charge ofe is needed, while the bare value for the vibrator charge has been used.