On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

A New Model in the Calogero–Ruijsenaars Family

Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of SU(n, n), to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses BC _n symmetry and is shown to be equivalent to the standard three-parameter BC _n hyperbolic Sutherland model in the cotangent bundle limit.     

Differential-geometric structures associated with Lagrangians corresponding to scalar physical fields

The paper is devoted to the investigation, using the method of Cartan–Laptev, of the differential-geometric structure associated with a Lagrangian L, depending on a function z of the variables t, x ¹,...,x ⁿ and its partial derivatives. Lagrangians of this kind are considered in theoretical physics (in field theory). Here t is interpreted as time, and x ¹,...,x ⁿ as spatial variables. The state of the field is characterized by a function z(t, x ¹,..., x ⁿ ) (a field function) satisfying the Euler equation, which corresponds to the variational problem for the action integral. In the present paper, the variables z(t, x ¹,..., x ⁿ are regarded as adapted local coordinates of a bundle of general type M with n-dimensional fibers and 1-dimensional base (here the variable t is simultaneously a local coordinate on the base). If we agree to call t time, and a typical fiber an n-dimensional space, then M can be called the spatiotemporal bundle manifold. We consider the variables t, x ¹,...,x ⁿ , z (i.e., the variables t, x ¹,...,x ⁿ with the added variable z) as adapted local coordinates in the bundle H over the fibered base M. The Lagrangian L, which is a coefficient in the differential form of the variational action integral in the integrand, is a relative invariant given on the manifold J ¹ _H (the manifold of 1-jets of the bundle H). In the present paper, we construct a tensor with components Λ⁰⁰, Λ⁰ⁱ , Λ ^ij (Λ ^ij = Λ ^ji ) which is generated by the fundamental object of the structure associated with the Lagrangian. This tensor is an invariant (with respect to admissible transformations the variables t, x ¹,...,x ⁿ , z) analog of the energy-momentum tensor of the classical theory of physical fields. We construct an invariant I, a vector G ⁱ , and a bivalent tensor G ^jk generated by the Lagrangian. We also construct a relative invariant of E (in the paper, we call it the Euler relative invariant) such that the equation E = 0 is an invariant form of the Euler equation for the variational action integral. For this reason, a nonvariational interpretation of the Euler equation becomes possible. Moreover, we construct a connection in the principal bundle with base J ² H (the variety of 2-jets of the bundle H) and with the structure group GL(n) generated by the structure associated with the Lagrangian.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

Diminishing blocking interval in particle-conveying channel bundles

We consider a channel bundle consisting of N_c parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and exit after a fixed transit time, τ. An individual channel blocks if N particles are simultaneously present. When a channel is blocked the flux previously entering it is redistributed evenly over the remaining open channels. We perform event driven simulations to examine the behaviour of an initially empty channel bundle with a total entering flux of intensity Λ. The mean blockage time of the kth channel is denoted by ? t_k ? ,k = 1,...,N_c. For N = 1, as shown previously, the interval between successive blockages is constant, while for N> 1 an accelerating cascade, i.e. one in which the interval between successive blockages decreases, is observed. After an initial transient regime we observe a well-defined universal regime that is characterized by\hbox{$\Delta_k^{(N)} = (-1)^{N-1}\frac{[(N-1)!]^2}{(\Lambda\tau)^N}$}Δk(N)=(?1)N?1[(N?1)!]2(Λτ)Nwhere \hbox{$\Delta_k^{(1)}=\langle t_k \rangle-\langle t_{k-1}\rangle$}Δk(1)=?tk???tk?1? and \hbox{$\Delta_k^{(j)}=\Delta_k^{(j-1)}-\Delta_{k-1}^{(j-1)}$}Δk(j)=Δk(j?1)?Δk?1(j?1) denotes the jth order difference.     

Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

Triadic Closure in Configuration Models with Unbounded Degree Fluctuations

The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded degree fluctuations. For this setting, we study the local clustering c(k), i.e., the probability that two neighbors of a degree-k node are neighbors themselves. We show that c(k) progressively falls off with k and the graph size n and eventually for \(k=\varOmega (\sqrt{n})\) settles on a power law \(c(k)\sim n^{5-2\tau }k^{-2(3-\tau )}\) with \(\tau \in (2,3)\) the power-law exponent of the degree distribution. This fall-off has been observed in the majority of real-world networks and signals the presence of modular or hierarchical structure. Our results agree with recent results for the hidden-variable model and also give the expected number of triangles in the configuration model when counting triangles only once despite the presence of multi-edges. We show that only triangles consisting of triplets with uniquely specified degrees contribute to the triangle counting.     

Almost One Bit Violation for the Additivity of the Minimum Output Entropy

In a previous paper, we proved that, in the appropriate asymptotic regime, the limit of the collection of possible eigenvalues of output states of a random quantum channel is a deterministic, compact set K_k,t. We also showed that the set K_k,t is obtained, up to an intersection, as the unit ball of the dual of a free compression norm. In this paper, we identify the maximum of \({\ell^p}\) norms on the set K_k,t and prove that the maximum is attained on a vector of shape (a, b, . . . , b) where a > b. In particular, we compute the precise limit value of the minimum output entropy of a single random quantum channel. As a corollary, we show that for any \({\varepsilon > 0}\), it is possible to obtain a violation for the additivity of the minimum output entropy for an output dimension as low as 183, and that for appropriate choice of parameters, the violation can be as large as \({\log 2 -\varepsilon}\). Conversely, our result implies that, with probability one in the limit, one does not obtain a violation of additivity using conjugate random quantum channels and the Bell state, in dimension 182 and less.     

Temperature dependences of the strengths of a carbon fiber and a three-dimensional reinforced carbon-carbon composite

At a fixed tension rate, the ultimate tensile strength of a carbon fiber decreases nonlinearly with increasing temperature T. This nonlinearity is caused by a change in the statistics of atomic vibrations from quantum (at T < 2250 K) to classical (at T > 2250 K) statistics. To take into account the quantum statistics, quantum function F _q is introduced into Zhurkov’s equation instead of temperature; the value of this function is calculated from the temperature dependence of the specific heat of carbon. This equation gives the values of the fracture activation energy (≈16 eV) and parameter γ (≈0.15 nm³). The strength of the three-dimensional reinforced carbon-carbon composite decreases up to ≈1800 K and increases as the temperature grows further. The decrease in the strength is explained by an increase in the rate of fiber and matrix fracture with increasing temperature, and the increase in the strength is explained by a decrease in the strength of the fiber-matrix adhesion bonds at high temperatures. As a result of this decrease, fibers begin to move with respect to each other under load, and the stresses applied to them level off. Although the fiber strength continues to decrease with increasing temperature, this effect increases the composite strength.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. II. Distributions with Heavy Tails

We study the asymptotic structure of the first K largest eigenvalues λ _k,V and the corresponding eigenfunctions ψ(?;λ _k,V ) of a finite-volume Anderson model (discrete Schrödinger operator) \(\mathcal{H}_{V}= \kappa \Delta_{V}+\xi(\cdot)\) on the multidimensional lattice torus V increasing to the whole of lattice ? ^ν , provided the distribution function F(?) of i.i.d. potential ξ(?) satisfies condition ?log(1?F(t))=o(t ³) and some additional regularity conditions as t→∞. For z∈V, denote by λ ⁰(z) the principal eigenvalue of the “single-peak” Hamiltonian κΔ _V +ξ(z)δ _z in l ²(V), and let \(\lambda^{0}_{k,V}\) be the kth largest value of the sample λ ⁰(?) in V. We first show that the eigenvalues λ _k,V are asymptotically close to \(\lambda^{0}_{k,V}\). We then prove extremal type limit theorems (i.e., Poisson statistics) for the normalized eigenvalues (λ _k,V ?B _V )a _V , where the normalizing constants a _V >0 and B _V are chosen the same as in the corresponding limit theorems for \(\lambda^{0}_{k,V}\). The eigenfunction ψ(?;λ _k,V ) is shown to be asymptotically completely localized (as V↑?) at the sites z _k,V ∈V defined by \(\lambda^{0}(z_{k,V})=\lambda^{0}_{k,V}\). Proofs are based on the finite-rank (in particular, rank one) perturbation arguments for discrete Schrödinger operator when potential peaks are sparse.     

Obliquely Propagating Electron Acoustic Shock Waves in Magnetized Plasma

Obliquely propagating electron acoustic shock waves in plasma with stationary ions, cold and superthermal hot electrons are investigated in magnetized plasma. Employing reductive perturbation method, Korteweg-de Vries-Burgers equation (KdVB) is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdVB equation show the variation of shock waves structure (amplitude, velocity, and width) with different plasma parameters. Particle density (α), superthermal parameter (κ), electron temperature ratio (??), kinetic viscosity (η₀), obliqueness (k_z), and strength of magnetic field (ω_c) significantly modify the properties of the shock waves structures. The present investigation is useful to understand dissipative structures observed in space or laboratory plasma where multielectrons population with superthermal electrons are prevalent.     

Long Time,Large Scale Limit of the Wigner Transform for a System of Linear Oscillators in One Dimension

We consider the long time, large scale behavior of the Wigner transform W _? (t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile et al. in Phys. Rev. Lett. 96 (2006) to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile et al. in Arch. Rat. Mech. 195(1):171–203 (2009). In the present paper we prove that in the unpinned case there exists γ ₀>0 such that for any γ∈(0,γ ₀] the weak limit of W _? (t/? ^3/2γ ,x/? ^γ ,k), as ??1, satisfies a one dimensional fractional heat equation \(\partial_{t} W(t,x)=-\hat{c}(-\partial_{x}^{2})^{3/4}W(t,x)\) with \(\hat{c}>0\). In the pinned case an analogous result can be claimed for W _? (t/? ^2γ ,x/? ^γ ,k) but the limit satisfies then the usual heat equation.     

Conformal Geometry of the Supercotangent and Spinor Bundles

We study the actions of local conformal vector fields \({X \in {\rm conf}(M,g)}\) on the spinor bundle of (M, g) and on its classical counterpart: the supercotangent bundle \({\mathcal{M}}\) of (M, g). We first deal with the classical framework and determine the Hamiltonian lift of conf (M, g) to \({\mathcal{M}}\) . We then perform the geometric quantization of the supercotangent bundle of (M, g), which constructs the spinor bundle as the quantum representation space. The Kosmann Lie derivative of spinors is obtained by quantization of the comoment map.The quantum and classical actions of conf (M, g) turn, respectively, the space of differential operators acting on spinor densities and the space of their symbols into conf (M, g)-modules. They are filtered and admit a common associated graded module. In the conformally flat case, the latter helps us determine the conformal invariants of both conf (M, g)-modules, in particular the conformally odd powers of the Dirac operator.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

Temperature Dependence of the Thermal Conductivity of a Trapped Dipolar Bose-Condensed Gas

The thermal conductivity of a trapped dipolar Bose condensed gas is calculated as a function of temperature in the framework of linear response theory. The contributions of the interactions between condensed and noncondensed atoms and between noncondensed atoms in the presence of both contact and dipole-dipole interactions are taken into account to the thermal relaxation time, by evaluating the self-energies of the system in the Beliaev approximation. We will show that above the Bose-Einstein condensation temperature (T?>?T _BEC ) in the absence of dipole-dipole interaction, the temperature dependence of the thermal conductivity reduces to that of an ideal Bose gas. In a trapped Bose-condensed gas for temperature interval k _B T?<<?n ₀ g _B , E _p ?<<?k _B T (n ₀ is the condensed density and g _B is the strength of the contact interaction), the relaxation rates due to dipolar and contact interactions between condensed and noncondensed atoms change as \( {\tau}_{dd12}^{-1}\propto {e}^{-E/{k}_BT} \) and τ _c12?∝?T ^?5, respectively, and the contact interaction plays the dominant role in the temperature dependence of the thermal conductivity, which leads to the T ^?3 behavior of the thermal conductivity. In the low-temperature limit, k _B T?<<?n ₀ g _B , E _p ?>>?k _B T, since the relaxation rate \( {\tau}_{c12}^{-1} \) is independent of temperature and the relaxation rate due to dipolar interaction goes to zero exponentially, the T ² temperature behavior for the thermal conductivity comes from the thermal mean velocity of the particles. We will also show that in the high-temperature limit (k _B T?>?n ₀ g _B ) and low momenta, the relaxation rates \( {\tau}_{c12}^{-1} \) and \( {\tau}_{dd12}^{-1} \) change linearly with temperature for both dipolar and contact interactions and the thermal conductivity scales linearly with temperature.     

Degree correlation in scale-free graphs

We obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination preferential attachment growth model, where incoming nodes at each timestep attach to β existing nodes, selected by degree-proportional probabilities. By the conditional degree distribution p(?|k), we mean the degree distribution of nodes that are connected to a node of degree k. By the joint degree distribution p(k,?), we mean the proportion of links that connect nodes of degrees k and ?. In addition to this growth model, we consider the shifted-linear preferential growth model and solve for the same quantities, as well as a closed form expression for its steady-state degree distribution.     

Hadroproduction of direct <Emphasis Type="Italic">J/ψ</Emphasis> and <Emphasis Type="Italic">ψ</Emphasis>′ mesons in the fragmentation of gluons and <Emphasis Type="Italic">c</Emphasis> quarks at high energies

The transverse-momentum spectra of direct J/ψ and ψ′ mesons in pp interactions at the Tevatron collider energy of \(\sqrt s = 1.8\) TeV are calculated on the basis of nonrelativistic QCD, the fragmentation model, the k_T-factorization approach, and the standard parton model. The contribution of gluon fragmentation is shown to exceed the contribution of c-quark fragmentation both within the parton model and within the k_T-factorization approach. Experimental data of the CDF Collaboration agree with the assumption that gluon fragmentation plays a dominant role in the \(Q\bar Q[^3 S_1 ,8]\) octet state, with the nonperturbative matrix element taking approximately equal values in the parton model and in the k_T-factorization approach.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.     

Root System of Singular Perturbations of the Harmonic Oscillator Type Operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space \({\mathcal{H}}\), i.e. of the self-adjoint operator with simple positive eigenvalues μ_k satisfying μ_k+1 ? μ_k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.