Non-spherical contributions to the vacancy formation energy

A linear response formalism is presented which allows the calculation of the non-spherically symmetric (angular momentum index, l ≠ 0) response to a random external charge perturbation when the spherically symmetric response is available. This procedure is applied to the problem of the energy of vacancy formation so that the electron charge depletion in the vicinity of vacancy is taken into account. The non-spherical contribution to the energy formation for the alkali metals is estimated and found to be non-negligible.     

Single particles in a reflection-asymmetric potential

Single particles moving in a reflection-asymmetric potential are investigated by solving the Schr ¨odinger equation of the reflectionasymmetric Nilsson Hamiltonian with the imaginary time method in 3 D lattice space and the harmonic oscillator basis expansion method. In the 3 D lattice calculation, the l2 divergence problem is avoided by introducing a damping function, and the(l~2) Nterm in the non-spherical case is calculated by introducing an equivalent N-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3 D lattice space. The evolution of the single-particle levels in a reflection-asymmetric potential is obtained and discussed by the above two numerical methods, and their consistency is shown in the obtained single-particle energies with the differences smaller than 10~(-4)[hω_0].     

Noises- and delay-enhanced stability in a bistable dynamical system describing chemical reaction

The energy spectrum of a graphene sheet subject to a single barrier potential having a time periodic oscillating height and subject to a magnetic field is analyzed. The corresponding transmission is studied as function of the incident energy and potential parameters. Quantum interference within the oscillating barrier has an important effect on quasiparticles tunneling. In particular the time-periodic electrostatic potential generates additional sidebands at energies ? + l?ω (l = 0, ±1,...) in the transmission probability originating from the photon absorption or emission within the oscillating barrier. Due to numerical difficulties in truncating the resulting coupled channel equations we limited ourselves to low quantum channels, i.e. l = 0, ± 1.     

Multichanel localization and magnetic impurities

The behaviour of an electron in N-coupled conducting chains of the length L is studied in the presence of magnetic impurities. The electron flow can be expanded in an orthonormal set of 2N channels. Each channel has its own transmission coefficient T_n(L). Spontaneous breaking of the symmetry between channels results in 2N different exponential dependences T_n(L) ～ exp (—L/l¹_n) where l¹_n is a localization length in the nth channel. Low frequency kinetic behaviour depends on the channel with the maximum localization length l¹₀.     

Experimental and theoretical analyses on the microwave backscattering ability and differential radar reflectivity of non-spherical hydrometeors

This paper experimentally and theoretically examines the scattering properties of simulated non-spherical hydrometeors including water oblates, ice oblates and ice sphere-cone-oblates, in terms of the backscattering cross-section and the differential reflectivity. The experimental measurements of the backscattering cross-sections of non-spherical hydrometeor samples were performed in the Electromagnetic Scattering Laboratory of China National Space Industrial Corporation. Meanwhile, the backscattering cross-sections have been computed with the transition (T) matrix method. The theoretical results are compared with the experimental data, showing that the calculations are consistent with the observations in general. Experimental and theoretical analyses indicate that the backscattering cross-section of non-spherical particles increases as the particle size parameter increases, and fluctuates when the sizes are larger under the effect of resonance scattering. Differential reflectivity Z_DR of water oblates in natural rainfall is always greater than 0 dB whereas Z_DR of hailstones may be negative. There is a good linear relationship between differential reflectivity and aspect ratio of a particle. These derivations agree with the literature and can be used to identify the presence of hail particles and distinguish between plate-type and columnar-type hydrometeors. In this study, the measuring experiment and the T-matrix method calculations for the scattering of simulated raindrop and ice particles are also briefly described.     

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

We consider m spinless Bosons distributed over l degenerate single-particle states and interacting through a k-body random interaction with Gaussian probability distribution (the Bosonic embedded k-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as l→∞ or as m→∞. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit l→∞ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as m→∞ with both k and l fixed. Here we show that the ensemble is not ergodic and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency toward picket-fence-type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization.     

Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

Angular momentum mixing in single flavor color superconductivity with transverse pairing

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity (CSC) cannot be restricted in a single non-s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC of massless quarks with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only, though the amount of the free energy drop is numerically small. Consequently the most stable pairing state in the ultra-relativistic limit remains the spherical color-spin-locked state (CSL).     

Ericson fluctuations in dissipative collisions

We generalize Ericson's theory of fluctuations to deep inelastic reactions. Following Ericson we assume that theS-matrixS _βα(E, l) can be written as a sum of pole terms in the complex energy plane, but the dependence ofS _βα (E, l) on the angular momentuml is assumed to be coherent. Semi-classical approximations for the summation of the angular momenta lead to a simple formula for the energy autocorrelation function. It contains the average widthΓ(l) describing the lifetimeτ(l) of the intermediate dinuclear system and the numberN _eff of unresolved primary channels. These quantities can be determined from a measurement of the autocorrelation function.     

Topologic distance in the Lucena network

The Lucena network (LN) is the dual of a multifractal partition of the square. We analyzethe relation between the typical topologic distance l and the number ofvertices Nof the LN. The multifractal partition has one parameter ρ which controls thegeometrical asymmetry of the multifractal. In the limit of ρ → 1 the blocks of thepartition are squared, the connections amont the blocks are short range, the LN is moreregular and the relation l ∝ √N is observed. For the limit ρ → 0 the blocks arestrongly asymmetric, long range connections appear, and the topologic distance followsl ∝(log?N)^α, a weak smallworld phenomenon. For any network size we calculate analytically the size of the minimumdistance l_min (ρ → 0) and the maximaldistance l_max (ρ → 1). The distance in theweak small world regime is calculated using the number of vertices inside a radius oflength land taking into account the network average connectivity and the exponent α.     

Ordering behaviors of the F.C.C. and B.C.C. phase alloys in the InMg,LiMg and AlZn systems

Expressions of the band-structure energy and the electrostatic energy characterized by the usual long-range and short-range order parameters are given to a binary alloy of simple metals with the f.c.c.-type or b.c.c.-type structure.The ordering energy and the local ordering energy are calculated for the InMg, LiMg and AlZn systems. The numerical results explain successfully the facts that the InMg system has the Ll₀-type and Ll₂-type ordered phases, each of which exists over a wide range of concentration and that the LiMg system has a local order with a negative short-range order parameter, while the AlZn system has that with the positive one. A lattice distortion in the Ll₀-type ordered structure of InMg is also discussed.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Limit cycle in a bound exciton recombination model in non-equilibrium semiconductors

A non-equilibrium semiconductor model involving the processes of photogeneration of electron-hole pairs (e-h) (rate G), stimulated creation of excitons from e-h (rate constant C) and decay of excitons on recombination centres (rate constant k) is analyzed in this paper for steady states and limit cycle behaviour. Considering the exciton decay to be similar to enzymatic processes in chemical reactions obeying a Michaelis-Menten law, and choosing units such that k = 1 = N, where N is the concentration of recombination centres, the model represents a 2-parameter (C and G) 2-dimensional (exciton and electron-hole concentrations x, n) dynamical system with a unique steady state (x₀,n₀) which is unstable in the region (l ? G)³?4C, the equality sign corresponding to the bifurcation curve in parameter space. In the region (l ? G)³ > 4C the system displays a unique stable limit cycle which is obtained in analytical form by employing a two-time-scales method for parameters in the neighbourhood of the bifurcation curve. The limit cycles are tilted ellipses with angular frequency $\text{}\text{?}$gw of the order of 10⁶ s^?1. In a realistic semiconductor situation G$\text{\$}\text{?}$10^?3.     

Dynamics of ball-like flames in extremely low-speed counterflow field in near-lean limit low-Lewis number mixture

For the understanding of ball-like flame behavior in counterflow field, transient three-dimensional computations with thermal-diffusion model were conducted for a low-Lewis number mixture near lean limit. Three types of flame behaviors were confirmed: stable spherical ball-like flame (spherical BLF) in A ≤ 0.010, stable non-spherical ball-like flame (non-spherical BLF) in 0.01 < A < 0.089 and splitting ball-like flame (splitting BLF) in A ≥ 0.089, where A is ordinary stretch rate normalized with laminar burning velocity S_L and thermal diffusivity α. Analysis of flame structure for non-spherical BLF located its center at the stagnation point showed that the maximum temperature on the stagnation plane was higher than that on the counterflow axis because of the small difference between the flame curvatures on the stagnation plane and that on the counterflow axis. With the increase of stretch rate, the maximum temperature of the non-spherical BLF on the stagnation plane increased and the position of maximum temperature got away from the stagnation point. The maximum temperature on the counterflow axis decreased and the position of maximum temperature got closer to the stagnation point. Existence of unburned fuel was also confirmed near the stagnation point at A = 0.085. Thus, net fuel velocity was newly introduced to evaluate the effect of the unburned fuel diffusion. The profile of the net fuel velocity revealed two peaks in the case of A < 0.050 and four peaks in the case of A > 0.050. In the case A > 0.050, the inner two peaks were found to be due to the diffusion of unburned fuel to the outward direction. The analyses on the peak positions showed that the flame splitting occurs when the positions of the inner two peaks of the net fuel velocity are located outside of the reference flame ball radius.     

Separable interactions and liquid 3He

A rigorous expression is given for the free energy of a system of fermions in the presence of a magnetic field interacting via a pairing hamiltonian in the weak-coupling limit. Starting from this expression Landau expansions are derived in two special cases, i.e. the case of general l-wave pairing in zero field and the case of l = 1 pairing, which applies to liquid ³He, in non-zero field.     

Multichannel phase-equivalent transformation and supersymmetry

A phase-equivalent transformation of local interaction is generalized to the multichannel case in the direct-scattering problem. Generally, the transformation does not change the number of bound states in the system and their energies. For a special choice of the parameters involved, however, the transformation removes one of the bound states and is equivalent to the multichannel supersymmetry transformation recently proposed by J.M. Sparenberg and D. Baye (1997). With the aid of the transformation, it is also possible to add a bound state to the discrete spectrum of the system at a given energy E<0 if the angular momentum l≥2 in at least one of the coupled channels.     

Liquid-crystalline ordering in the solution of partially flexible macromolecules

The liquid-crystalline ordering in the solution of persistent chains which length, L, is comparable with the length of the effective Kuhn segment, l, is considered by means of a generalization of the Onsager method. The orientational entropy for this case is calculated using the method proposed by I.M. Lifshitz (for another problem) in 1968. It is shown that a slight flexibility of the persistent chain is sufficient for the complete change in the properties of the liquid-crystalline transition: for example, at $\text{L}\text{l}$～0.1 these properties are more similar to those which are characteristic for the semi-flexible limit ($\text{L}\text{l}$?1), than for the rigid rod limit ($\text{L}\text{l}$?1), although at such $\text{L}\text{l}$ the geometric form of the macromolecule is much closer to the rodlike one.     

The nonparaxial propagation of the TEM0l doughnut beam with the orbital angular momentum in the far field

The analytical expression for nonparaxial electric field amplitude of the TEM_0l^? doughnut beam with the orbital angular momentum quantum number l is derived in the far field by means of the angular spectrum representation and the stationary phase method. It is shown that the divergent angle of the far field of TEM_0l^? doughnut beam will be smaller with the decreasing of the orbital angular momentum quantum number l or the increasing of the beam waist width w of the initial beam. And the maximal radial intensity of the beam is decreased with its propagation at different rates for different l and w.