Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

Spin susceptibility of cuprates in the model of a 2D frustrated antiferromagnet: Role of renormalization of spin fluctuations in describing neutron experiments

Experimental data on the spin susceptibility of HTSC cuprates are reproduced on the basis of a spherically symmetric approach in the frustrated Heisenberg model. The inclusion of real and imaginary renormalizations in spin Green’s functions makes it possible to explain the evolution of spin excitation spectrum ω(q) and susceptibility spectrum χ(q, ω) in the range from insulator to optimal doping. In the low-frustration limit corresponding to the weakly doped mode, the saddle singularity of ω(q) and scaling of χ_2D(ω) =∫d q Im χ(q, ω) are reproduced and an analytic expression is derived for the scaling function. In the strong frustration (optimal doping) mode, the stripe scenario is demonstrated; this leads to a peak of χ_2D (ω) in the region of ω～60 meV.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Structural features and the microscopic dynamics of the three-component Zr<Subscript>47</Subscript>Cu<Subscript>46</Subscript>Al<Subscript>7</Subscript> system: Equilibrium melt,supercooled melt,and amorphous alloy

The structural and dynamic properties of the three-component Zr₄₇Cu₄₆Al₇ system are subjected to a molecular dynamics simulation in the temperature range T = 250–3000 K at a pressure p = 1.0 bar. The temperature dependences of the Wendt–Abraham parameter and the translation order parameter are used to determine the glass transition temperature in the Zr₄₇Cu₄₆Al₇ system, which is found to be T_c ≈ 750 K. It is found that the bulk amorphous Zr₄₇Cu₄₆Al₇ alloy contains localized regions with an ordered atomic structures. Cluster analysis of configuration simulation data reveals the existence of quasi-icosahedral clusters in amorphous metallic Zr–Cu–Al alloys. The spectral densities of time radial distribution functions of the longitudinal (C?_L(k, ω)) and transverse (C?_T(k, ω)) fluxes are calculated in a wide wavenumber range in order to study the mechanisms of formation of atomic collective excitations in the Zr₄₇Cu₄₆Al₇ system. It was found that a linear combination of three Gaussian functions is sufficient to reproduce the (C?_L(k, ω)) spectra, whereas at least four Gaussian contributions are necessary to exactly describe the (C?_T(k, ω)) spectra of the supercooled melt and the amorphous metallic alloy. It is shown that the collective atomic excitations in the equilibrium melt at T = 3000 K and in the amorphous metallic alloy at T = 250 K are characterized by two dispersion acoustic-like branches related with longitudinal and transverse polarizations.     

Feynman-Diagrammatic Description of the Asymptotics of the Time Evolution Operator in Quantum Mechanics

We describe the “Feynman diagram” approach to nonrelativistic quantum mechanics on \({\mathbb{R}^n}\), with magnetic and potential terms. In particular, for each classical path γ connecting points q ₀ and q ₁ in time t, we define a formal power series V _γ (t, q ₀, q ₁) in \({\hbar}\), given combinatorially by a sum of diagrams that each represent finite-dimensional convergent integrals. We prove that exp(V _γ ) satisfies Schrödinger’s equation, and explain in what sense the \({t \to 0}\) limit approaches the δ distribution. As such, our construction gives explicitly the full \({\hbar\to 0}\) asymptotics of the fundamental solution to Schrödinger’s equation in terms of solutions to the corresponding classical system. These results justify the heuristic expansion of Feynman’s path integral in diagrams.     

The effect of the spatial variation of the order parameter on the tunneling density of states of superconducting alloys

In the first part of the paper we derive expressions of the Ginzburg-Landau (GL) type for the local tunneling density of states of superconducting alloys. These expressions are quite generally applicable at high excitation energies. One can see immediately that the density of states,N(r, ω), at any positionr and high energiesω is always larger than the local BCS density of states if the space dependence of the order parameter is governed by the GL-equation. This effect is largest for long mean free pathsl. In the second part of the paper we calculate the spatial average of the density of states,¯N, at all energiesω for a lattice of vortex lines in a magnetic field slightly below the upper critical field. The resulting curve of [¯N? N(0)]/N(0) versus co shows no gap and has a zero at about the gap value in zero field. Its value at ω=0 depends onl like ln(ξ₀/l) for l?ξ₀ [N(0) denotes the normal density of states, and ξ₀ is the BCS coherence length].     

Fundamental Entangling Operators in Quantum Mechanics and Their Properties

For the first time, we introduce so-called fundamental entangling operators \(e^{iQ_{1} P_{2}}\) and \(e^{iP_{1} Q_{2} }\) for composing bipartite entangled states of continuum variables, where Q_i and P_i (i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation (q₁, q₂) → (Aq₁ + Bq₂, Cq₁ + Dq₂), where AD?BC = 1, which means even the basic coordinate transformation (Q₁, Q₂) → (AQ₁ + BQ₂, CQ₁ + DQ₂) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.     

Construction of a dynamical matrix for an HCP crystal using phonon data at the symmetry points of the Brillouin zone and elastic constants

General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants C _ik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ω _i (N) at the symmetry points of the Brillouin zone and the elastic constants C _ik . A number of relations between the values of ω _i (N) and C _ik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co.     

Propagation of electromagnetic waves in hot magnetoactive plasma

The paper derives the general form of the tensor of dielectric permittivity? _ij(ω,k), Eq. (15), of non-relativistic hot magnetoactive collisionless plasma taking into consideration the influence of spatial dispersion. The general form of the tensor? _ij(ω,k) is used to express the tensorε _ij(ω,k) in the region of weak and strong spatial dispersion and in some special cases. A general dispersion equation (30) is derived and an analysis is made of the waves propagating in hot magnetoactive plasma. The expressions derived are used to investigate the damping of a right-handed circularly polarized wave propagating in hot magnetoactive plasma in the direction of the magnetic field.     

Bilayer membrane in confined geometry: Interlayer slide and entropic repulsion

We derive the free energy functional of a bilayer lipid membrane from the first principles of elasticity theory. The model explicitly includes position-dependent mutual slide of monolayers and bending deformation. Our free energy functional of a liquid-crystal membrane allows for incompressibility of the membrane and vanishing of the in-plane shear modulus and obeys reflectional and rotational symmetries of the flat bilayer. Interlayer slide at the midplane of the membrane results in local difference of surface densities of the monolayers. The slide amplitude directly enters the free energy via the strain tensor. For small bending deformations, the ratio between the bending modulus and the area compression coefficient, K _b /K _A , is proportional to the square of monolayer thickness h. Using the functional, we perform self-consistent calculation of the entropic potential acting on a bilayer between parallel confining walls separated by distance 2d. We find that at the minimum of the confining potential, the temperature-dependent curvature α ∝ T ² /K _b d⁴ is enhanced four times for a bilayer with slide as compared with a unit bilayer. We also calculate viscous modes of a bilayer membrane between confining walls. Pure bending of the membrane is investigated, which is decoupled from area dilation at small amplitudes. Three sources of viscous dissipation are considered: water and membrane viscosities and interlayer drag. The dispersion relation gives two branches ω_{1, 2} (q).     

Evolution of surface morphology during the growth of amorphous and polycrystalline silicon films

The evolution of the surface morphology of LPCVD poly-Si films (deposition temperature 620°C), a-Si films (deposition temperature 550°C) and poly-Si films, obtained by the crystallization of a-Si is investigated in the thickness range 40–500 nm. It is found that upon an increase in the thickness from 40 to 500 nm, the surface roughness (parameters S _q , S _z , S _v ) is increased for poly-Si, while in the case of a-Si and poly-Si obtained by crystallization a-Si, on the contrary, decreases. The correlation length (S _al ) increases for all three types of silicon films. Poly-Si films, obtained by the crystallization of a-Si, as compared to LPCVD poly-Si films have a significantly lower surface roughness, respectively, S _q two times less at a thickness of 40 nm and sixteen times less at 500 nm. In contrast to thick films, thin a-Si films (at thicknesses of less than 40 nm) have a granular structure, which is especially pronounced at an average thickness of about 20 nm and there is a maximum on the dependence of the roughness S _q on the thickness.     

Models of spin structures in Sr<Subscript>2</Subscript>RuO<Subscript>4</Subscript>

The mean-field method is used to calculate the bands, Fermi surfaces, and spin susceptibilities of a three-band model of the RuO₄ plane of Sr₂RuO₄ rutinate for states with different spin structures. In particular, the spiral state is studied with the “incommensurate” vector Q=2π(1/3, 1/3) corresponding to the nesting of bands with the population n=4. This state proves to be the lowest with respect to energy among other (paramagnetic, ferromagnetic, antiferromagnetic, and periodic) solutions. In the spiral state, in addition to the main α, β, and γ sheets of the Fermi surface, shadow Fermi boundaries along the Γ(0, 0)-M(π, 0) line (previously observed in the ARPES experiments) are revealed and explained. This may change the interpretation of the data on dispersionless peaks in photoemission, previously ascribed to surface states. The spin susceptibilities of the spiral state exhibit peaks in the dependence Im?(q, ω) at q=Q in accordance with the observed magnetic peak in neutron scattering. The hypothesis of the presence of spin structures with q=Q in the normal state of Sr₂RuO₄ and the methods of checking this hypothesis are discussed.     

Influence of the probe sizes on the parameters of the surface morphology of hemispherical-grain polysilicon films: Estimation via atomic-force microscopy

The influence of probe sizes on the basic surface-morphology parameters of hemispherical-grain polysilicon films which possess substantial surface roughness and non-Gaussian height distribution functions with appreciable negative skewness is studied. The dependences between the basic surface morphology parameters S _dr , S _q , S _al , S _z , S _v , S _p , and S _sk defined by the ISO 25178-2:2012 standard and the probe width-to-tip height (W/L) ratio are determined. It is ascertained that the relative increase S _dr in the surface area is most sensitive to the “degree of sharpness” (W/L ratio) and, on the contrary, the autocorrelation length S _al is least sensitive. Hemispherical-grain silicon films with considerable parameter S _dr can be employed as test samples in estimating the degree of sharpness of a probe.     

Phenomenology of light- and strange-quark simultaneous production at high energies

This letter presents an extension of EPL116(2017)62001 to light- and strange-quark nonequilibrium chemical phase-space occupancy factors (γ_q,s). The resulting damped trigonometric functionalities relating γ_q,s to the nucleon-nucleon center-of-mass energies (\(\sqrt {{s_{NN}}} \)) looks very similar except different coefficients. The phenomenology of the resulting γ_q,s(\(\sqrt {{s_{NN}}} \)) describes a rapid decrease at \(\sqrt {{s_{NN}}} \) ? 7GeV followed by a faster increase up to ~20 GeV. Then, both γ_q,s become nonsensitive to \(\sqrt {{s_{NN}}} \). Although these differ from γ _s (\(\sqrt {{s_{NN}}} \))obtained at γ _q (\(\sqrt {{s_{NN}}} \))=1, various particle ratios including K⁺/π⁺, K^?/π^?, Λ/π^?, Λ?/π^?, Ξ⁺/π⁺, and Ω/π^?, can well be reproduced, as well. We conclude that γ_q,s(\(\sqrt {{s_{NN}}} \)) should be instead determined from fits of various particle yields and ratios but not merely from fits to the particle ratio K⁺/π⁺.     

New forms of the Cauchy operator and some of their applications

In this paper, we first construct the Cauchy q-shift operator T(a, b;D _xy ) and the Cauchy q-difference operator L(a, b; θ _xy ). We then apply these operators in order to represent and investigate some new families of q-polynomials which are defined in this paper. We derive some q-identities such as generating functions, symmetry properties and Rogers-type formulas for these q-polynomials. We also give an application for the q-exponential operator R(bD _q ).     

Noncompact <Emphasis Type="Italic">u</Emphasis><Subscript>q</Subscript>(2, 1) quantum algebra: Discrete series of highest weight irreducible representations

The structure of unitary irreducible representations of the noncompact u_q(2, 1) quantum algebra that are related to a negative discrete series is examined. With the aid of projection operators for the su_q(2) subalgebra, a q analog of the Gelfand-Graev formulas is derived in the basis corresponding to the reduction u_q(2, 1) → su_q(2)×u(1). Projection operators for the su_q(1, 1) subalgebra are employed to study the same representations for the reduction u_q(2, 1) → u(1)×su_q(1, 1). The matrix elements of the generators of the u_q(2, 1) algebra are computed in this new basis. A general analytic expression for an element of the transformation brackets <U∣T>_q between the bases associated with the above two reductions (the elements of this matrix are referred to as q Weyl coefficients) is obtained for a general case where the deformation parameter q is not equal to a root of unity. It is shown explicitly that, apart from a phase, the q Weyl coefficients coincide with the q Racah coefficients for the su_q(2) quantum algebra.     

A first order Tsallis theory

We investigate first-order approximations to both (i) Tsallis’ entropy S _q and (ii) the S _q -MaxEnt solution (called q-exponential functions e _q ). We use an approximation/expansion for q very close to unity. It is shown that the functions arising from the procedure (ii) are the MaxEnt solutions to the entropy emerging from (i). Our present treatment is motivated by the fact it is FREE of the poles that, for classic quadratic Hamiltonians, appear in Tsallis’ approach, as demonstrated in [A. Plastimo, M.C. Rocca, Europhys. Lett. 104, 60003 (2013)]. Additionally, we show that our treatment is compatible with extant date on the ozone layer.     

Derivation of Hamaker Dispersion Energy of Amorphous Carbon Surfaces in Contact with Liquids Using Photoelectron Energy-Loss Spectra

Hamaker interaction energies and cutoff distances have been calculated for disordered carbon films, in contact with purely dispersive (diiodomethane) or polar (water) liquids, using their experimental dielectric functions ε (q, ω) obtained over a broad energy range. In contrast with previous works, a q-averaged <ε (q, ω) >  _q is derived from photoelectron energy-loss spectroscopy (XPS-PEELS) where the energy loss function (ELF) < Im[?1/ε (q, ω)] >  _q is a weighted average over allowed transferred wave vector values, q, given by the physics of bulk plasmon excitation. For microcrystalline diamond and amorphous carbon films with a wide range of (sp³/sp² + sp³) hybridization, non-retarded Hamaker energies, A ₁₃₂ (L < 1 nm), were calculated in several configurations, and distance and wavenumber cutoff values were then calculated based on A ₁₃₂ and the dispersive work of adhesion obtained from contact angles. A geometric average approximation, H _0?CVL ?=?(H _0?CVC H _0?LVL )^1/2, holds for the cutoff separation distances obtained for carbon-vacuum-liquid (CVL), carbon-vacuum-carbon (CVC) and liquid-vacuum-liquid (LVL) equilibrium configurations. The linear dependence found for A _CVL, A _CLC and A _CLV values as a function of A _CVC, for each liquid, allows predictive relationships for Hamaker energies (in any configuration) using experimental determination of the dispersive component of the surface tension, \( {\gamma}_{CV}^d \), and a guess value of the cutoff distance H _0?CVC of the solid.

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Graphical Abstract

     

The effect of non-linear capacitances in the localization properties of aperiodic dual electric transmission lines

This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The V_C,n voltage across each capacitor is selected as a non-linear function of the electric charge q_n, i.e., V_C,n = q_n(1/C_n -ε_n|q_n|²)where C_n is the linear part of the capacitance and ε_n the amplitude of the non-linear term. We follow a binary distribution of values of ε_n, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.