Principles of generalized spin-echo spectroscopy

The concept is proposed for determining the total dynamic scattering function of an object under study, representing a sum of odd and even parts measured by the generalized neutron spin-echo method in the form of the signals S _odd(q, t) ～ ΣS(ω, q)sin(ωt)dω and S_even(q, t) ～ ΣS(ω,q)cos(ωt)dω as functions of the momentum q transferred to the neutron and the time t corresponding to the frequency ω and the transferred energy ?ω. The principle of the generalized spin echo and the results of mathematical modeling are confirmed in experiments on inelastic scattering on magnetic fluids and polymer solutions. The developed method makes it possible to study the features of the dynamics of atomic and molecular systems, e.g., to analyze soft vibrational spectra of nanoparticle ensembles against the background of intense relaxation processes, which is inaccessible for classical spin-echo spectrometry.     

The correlation function of the Ising model in the MFA and their sum rule

It is shown that in the correctly performed molecular field approximation the correlation function 〈S(q) S(-q)〉 fulfills the sum rule N^-1Σ_q〈S(q) S(-q)〉 = 1. This can be proved for ferro- and antiferromagnets and the disordered phases of o-hydrogen.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

Asymptotic perturbation expansion in theP(φ)2 quantum field theory

In theP(φ)₂ model it is proved that the perturbation series for the infinite volume Schwinger functionsS(λ) are asymptotic in the limit as the coupling constant λ goes to zero. We also give conditions which imply smoothness ofS(λ) at arbitrary λ.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Spectral changes of partially coherent flat topped beam in turbulent atmosphere

Spectral characteristics of partially coherent flat-topped (PCFT) beams propagated in a turbulent atmosphere are investigated and an analytical formula for the spectrum S(ω) is derived. It is shown that, if the scaling law is valid, the normalized spectrum S(ω) of PCFT beams propagating through turbulent atmosphere is the same as the normalized source spectrum S⁽⁰⁾(ω), this similarity is valid for any arbitrary order of the circular flat-topped “N”. It is proved that if the scaling law is not valid, S(ω) of PCFT is different from S⁽⁰⁾(ω). Also spectral behavior of PCFT beams in free space and turbulence media is investigated in detail.     

Changes in the spectrum of Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of Gaussian Schell-model (GSM) beams propagating through turbulent atmosphere is derived analytically. It is shown that, if the scaling law is valid, the normalized spectrum S(ω) of GSM beams propagating through turbulent atmosphere is the same as the normalized source spectrum S⁽⁰⁾(ω), whether GSM source is quasi-homogenous or not. On the other hand, if the scaling law fails, S(ω) of GSM is different from S⁽⁰⁾(ω). The structure constant of the refractive index, transverse coordinate of observation point and spatial correlation length of the source affect the spectrum, which is illustrated numerically.     

Kinetic theory of classical liquids. II. Numerical results on the density fluctuations in liquid argon

Based on a general theory given in an earlier paper, we present results of extensive calculations of the dynamical structure factor S(qω) for liquid argon. Detailed comparison is made with experimental and molecular dynamics data. Good agreement is found except for the smallest wavevectors, where temperature fluctuations are important.     

Quantum integrable systems related to lie algebras

Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g²v(q) of the following 5 types: v_I(q) = q^?2, v_II(q) = sinh^?2q, v_III(q) = sin^?2q, $\text{v}{}_{\mathrm{<mtext>IV</mtext>}}\text{(q) =}\text{P}\text{(q)}$, v_V(q) = q^?2 + ω²q². Here $\text{P}\text{(q)}$ is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp(q_jq_{j+ 1}) is moreover considered.This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.     

Streuung an Kristallen mit Ionenspin-Gitter-Kopplung

The dependence of the Heisenberg exchange interaction on the ion positions couples the lattice with the ion spins. The resulting phonon damping depends on the magnetic order of the crystal. We calculate the Phonon Greens Function (PGF) by solving the equation of motion of the coupled spin-phonon system. The scattering functionsS(q,ω) andS(q) of the crystal can be determined with the PGF. In the region of great spin fluctuations an additional diffuse scattering intensity appears. This determines spin-lattice coupling parameters at least in the case of scattering of X-rays which do not interact directly with magnetism. The ordering temperature is assumed to be small compared to the Debye temperature. The magnetic influence on the diffuse scattering intensity is then of the order of a few per cent.     

Representation of osp (2, 2) q (2) andS-matrix of super sine-Gordon theory

We investigate the representations of the osp (2, 2) _q ⁽²⁾ algebra, which leads to theS-matrix of super sine-Gordon theory. TheS-matrix has been derived from supersymmetric conformal field theory with some assumptions. We show that the conjecturedS-matrix can be derived from the representation theory using a correspondence between the representations of osp (1, 2) _q and those of sl(2) _q .     

Dispersive viscosity coefficient of nuclear matter

By application of Landau's kinetic theory of a Fermi liquid in non-equilibrium, we have deduced a dispersive, momentum and frequency dependent shear viscosity coefficient η(q, ω) for symmetric nuclear matter. The resulting formula for η is found to be complicated for arbitrary q, ω; however, simple interpretation is possible in the limit of small momentum q → 0. In the static limit, ω → 0, η reduces to the well known kinetic formula for the hydrodynamic viscosity coefficient η_o, while in the high frequency (zero sound) limit, ωτ ? 1, η(ω) is found proportional to (?iω)^? indicating elastic behaviour of nuclear matter. As is discussed shortly, application of these results to finite nuclei unfortunately does not seem justified.     

Bi-solitons for a class of non-linear equations with quadratic non-linearity. II

We generalize to any order q, the methods developed in a companion paper for q = 2,3 for finding bi-solitons, solutions of the class of non-integrable non-linear equations L_qK = K²; L_q = ? + Σ_i+j≤qa_ij?_xⁱ?_lⁱ, ? ≠ 0 in 1 + 1 dimensions. We call bi-solitons K(ω₁,ω₂) of the exponential type variables ω_i = exp(γ_ix + ρ_it), i = 1,2 and deal only with the so-called “non trivial” solutions which may be written as a finite sum K = Σ^lmax₀ω¹₂F_i(Z)_, F₁ rational function of Z = ω₁Z = ω₁ + ω₁. To any such polynomial K, we associate a linear transformation such that L_qK has only the power ω¹₂ of K² and we find that there are particular polynomialswhere the above restriction provide a factorization of the linear operator L_q in the product of smaller order differential operators. After this linear phase, we show in a second step that these forms yield solutions for the full non linear equation which can be derived in an intrinsic manner. Examples in the monomial and binomial cases are given.     

Ab initio results for the plasmon dispersion and damping of the warm dense electron gas

Warm dense matter (WDM) is an exotic state on the border between condensed matter and dense plasmas. Important occurrences of WDM include dense astrophysical objects, matter in the core of our Earth, and matter produced in strong compression experiments. As of late, x-ray Thomson scattering has become an advanced tool to diagnose WDM. The interpretation of the data requires model input for the dynamic structure factor S(q, ω) and the plasmon dispersion ω(q) . Recently, the first ab initio results for S(q, ω) of the homogeneous warm dense electron gas were obtained from path integral Monte Carlo simulations (Dornheim et al., Phys. Rev. Lett., 121, 255001, 2018). Here, we analyse the effects of correlations and finite temperature on the dynamic dielectric function and the plasmon dispersion. Our results for the plasmon dispersion and damping differ significantly from the random-phase approximation and from earlier models of the correlated electron gas. Moreover, we show when commonly used weak damping approximations break down and how the method of complex zeroes of the dielectric function can solve this problem for WDM conditions.     

A relaxation theory of Stark broadening by ions

A theory of Stark broadening in plasmas is presented in which the effects of broadening by ion perturbers are treated in a manner similar to the relaxation theory or unified theory for electrons. An expression is derived for Fano's broadening operator M(ω) which does not contain the projection operators or cumulants of previous forms. To obtain a calculable expression for M(ω), an approximation is made in which small, second-order fluctuation terms are replaced by their adiabatic limits. Sample calculations are presented for the first two members of the Lyman and Balmer series of hydrogen which show reasonable agreement with experiment, although the “dip” of the β-lines is still too pronounced.     

Spin dynamics of layered triangular antiferromagnets with uniaxial anisotropy

The spin dynamics of the semiclassical Heisenberg model with uniaxial anisotropy, on the layered triangular lattice with antiferromagnetic coupling for both intralayer nearest neighbor interaction and interlayer interaction is studied both in the ordered phase and in the paramagnetic phase, using the Monte Carlo-molecular dynamics technique. The important quantities calculated are the full dynamic structure function S(q,ω)$S(\mathbf{q},\omega )$, the chiral dynamic structure function _Schi(ω)$S_{\mathrm{chi}}(\omega )$, the static order parameter and some thermodynamic quantities. Our results show the existence of propagating modes corresponding to both S(q,ω)$S(\mathbf{q},\omega )$ and _Schi(ω)$S_{\mathrm{chi}}(\omega )$ in the ordered phase, supporting the recent conjectures. Our results for the static properties show the magnetic ordering in each layer to be of coplanar 3-sublattice type deviating from 120^°${120}^{°}$ structure. In the presence of magnetic trimerization, however, we find the 3-sublattice structure to be weakened along with the tendency towards non-coplanarity of the spins, supporting the experimental conjecture. Our results for the spin dynamics are in qualitative agreement with those from the inelastic neutron scattering experiments performed recently.     

Nichtsenkrechte Interbandübergänge in Graphit durch unelastische Elektronenstreuung

Characteristic energy loss measurements are carried out on natural graphite single crystals. The frequency and wave vector dependent dielectric constant ?(ω,q) forq⊥c-axis is determined by Kramers Kronig Analysis. The results are interpreted in terms of non vertical interband transitionsE(k)→E(k+q) between the π-bands within the two dimensional approximation.