On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

On the dynamics of itinerant electron magnets in the paramagnetic state

It is shown how disordered local-moment states, in a metal such as Fe, may be stabilized by constraining magnetic fields. Effective interaction parameters between moments are defined in terms of spin density functional theory. On removing the constraints the moments initially precess but then decay rapidly, the latter process leading to an energy width of S(q, ω) at large q of order $\text{(k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{C}}\text{W)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where T_C is the Curie temperature and W is the width of the d-band. T he consequences for neutron scattering experiments are discussed and the rather different case of Ni is considered.     

Magnetovolume effect in transition metal-metalloid amorphous alloys

The thermal expansion, spontaneous volume magnetostriction ω_s, forced volume magnetostriction $\text{(}\text{?ω}\text{?H}\text{)}$ and Young's modulus of amorphous Fe-B, Fe-P, Co-B and (Fe-M)₇₇Si₁₀B₁₃ (M = Cr, Mn, Co, Ni) alloys have been measured to make clear the magnetovolume effect in transition metal-metalloid amorphous alloys. The thermal expansion coefficient α, ω_s and $\text{(}\text{?ω}\text{?H}\text{)}$ are dependent on the number of d-electrons per transition metal atom n_eff calculated based on the charge transfer model. The n_eff vs. α, ω_s and $\text{(}\text{?ω}\text{?H}\text{)}$ curves are quite similar to the corresponding curves in fcc alloys. The maxima in those curves are, however, found at n_eff ≈ 8.2 for the amorphous alloys in contrast with n_eff ≈ 8.7 for the fcc Fe-Ni alloys. On the other hand, Young's modulus measured under the saturation of magnetization is governed by the molar volume, irrespective of n_eff. The magnetovolume effect in transition metal-metalloid amorphous alloys is discussed in connection with the instability of ferromagnetism of amorphous Fe.     

Dispersion of empty surface states on Ni(1 1 0)

We have used k-resolved bremsstrahlung isochromat spectroscopy at $\text{h}\text{?}\text{ω=9.5eV}$ to investigate Ni(1 1 0) along the ΓKL bulk mirror plane. Empty surface states of both the crystal-induced and image-potential-induced type have been detected besides two bulk direct transitions. We studied their different behaviour against oxygen contamination and mapped their energy dispersion E(k_∥) along the ΓY direction of the surface Brillouin zone.     

Low wavenumber wall pressure measurements using a rectangular membrane as a spatial filter

The response of a rectangular membrane to a convecting random pressure field is interpreted to reveal the inherent wavenumber filtering characteristics of the device. After experimental determination of its resonant response characteristics, one such membrane is used to measure the low wavenumber components of the wall pressure fluctuations beneath a plane turbulent boundary layer. The measurements were made at wavenumbers far below the convective region (k₁ = ω/U_c) but above the acoustic region (k₁ ? ω/c_o). Possible contamination by acoustic and convective ridge effects is considered. The low wavenumber measurements are also compared with values of the wavenumber-frequency pressure spectral density $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{,ω)}$ obtained by Fourier transforming cross-spectral density data obtained by Blake in the same wind tunnel. From this comparison it is seen that this transformation of Blake's data (based on a Corcos model) grossly overestimates the magnitude of $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{,ω)}$ in the low-wavenumber region. The measured values of $\text{Φ}{}_{\mathrm{p}}\text{(}\text{k}\text{, c}{}_{\mathrm{o}}\text{)}$ are about 36 dB down from convective ridge levels at the same frequency. The data are also compared with earlier results obtained by Jameson. In a similar frequency range the current data levels are approximately 10 dB higher than those of Jameson.     

Inverse solutions to the inelastic scattering problem

Exact inverse solutions to the integral equation $\text{φ(r}{}_{\mathrm{s}}\text{|r}{}_0\text{, k) = ?}{}_{\mathrm{D}}{}^3\text{f (r, ω)g(r|r}{}_0\text{, k)g(r|r, k)d}{}^3\text{r}$, where g(r|r_j, k); j = 0 or s is the free space Green function, are derived in plane and cylindrical coordinates for fixed ω. These solutions allow an inelastic scattering potential f(r, ω) which is of compact support r ? $\text{D}$³ to be recovered from scattering data collected over the surfaces of a plane and cylinder respectively.     

Dynamical properties of colloidal systems: III. Collective and self-diffusion of interacting charged particles

The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient D_s are calculated. Using S(k) for an actual system, $\text{D}{}_{\mathrm{s}}\text{≈}\text{1}\text{3}\text{D}{}_0$ is obtained, where D₀ is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles.     

A scaling property in critical spectra of discrete systems

Power spectra of discrete dynamical systems at the threshold of chaos contain line series obeying S_ω ∞ ω$\text{μ}$ for small ω. We explain $\text{μ}$ in terms of the Feigenbaum rescaling parameter α. Another parameter β related to the noise strength of states of periodic chaos and recently numerically determined by Huberman and Zisook is related to α as well.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

Study of two-phonon excitations in superfluid 4He

We explain the second branch of excitations in superfluid ⁴He observed by Cowley and Woods, by accounting for two-phonon contributions to the dynamic structure function, S(k, ω). Our theory gives a good fit with the experimental data in the high energy region for several values of momentum transfer. It is observed that the contribution to S(k, ω) due to two-phonon excitations is of the order of k² as against its k⁴ dependence reported in earlier theories.     

Derivation of the classical theory of correlations in fluids by means of functional differentiation

The k-particle, infinite-volume distribution functions $\text{n}\text{?}{}_{\mathrm{k}}\text{(}\text{r}{}_1\text{, …,}\text{r}{}_{\mathrm{k?1}}\text{, γ)}$ and modified Ursell correlation functions $\text{U}\text{?}{}_{\mathrm{k}}\text{(}\text{r}{}_1\text{, …,}\text{r}{}_{\mathrm{k?1}}\text{, γ)}$ of a classical system of particles with the two-body potential $\text{q(}\text{r}\text{) + γ}{}^{\mathrm{\nu }}\text{K(γ}\text{r}\text{)}$ are considered. The limiting values of the functions $\text{n}\text{?}{}_{\mathrm{k}}\text{(}\text{r}{}_1\text{, …,}\text{r}{}_{\mathrm{k?1}}\text{, γ),}\text{n}\text{?}{}_{\mathrm{k}}\text{(}\text{S}{}_1\text{/γ, …,}\text{S}{}_{\mathrm{k?1}}\text{/γ, γ)}$ and $\text{γ(}{}^{\mathrm{1?k}}\text{)ν}\text{U}\text{?}{}_{\mathrm{k}}\text{(}\text{S}{}_1\text{/γ, …,}\text{S}{}_{\mathrm{k?1}}\text{/γ, γ)}$ in the limit γ → 0 are calculated, under fairly weak conditions on q and K, by a method involving functional differentiation. These limiting functions are used to describe the molecular structure of the various states of the system both in the range of the potential q(r) and in the rage of the potential γ^νK(γr). The direct correlation function c? (r, γ) is also considered and it is shown that for $\text{S}\text{≠ 0}$, $\text{lim}{}_{\mathrm{\gamma \to 0}}\text{γ}{}^{\mathrm{?\nu }}\text{c}\text{?}\text{(}\text{S}\text{γ}\text{, γ) = ?βK (}\text{S}\text{)}$, for all one-phase states, where β is the reciprocal temperature. Special cases of our results confirm those of other authors, including the well-known results of Ornstein and Zernike.     

Predictions on the couplings of f- and ϱ- trajectories to mesons from chiral symmetry

We employ a chiral saturation scheme involving 15, $\text{L = 0,}\text{and}\text{15}\text{, L = 1}$ mesons in a classification according to SU(4) ? O(3) (i.e. the mesonns π, ?, ω, A₁, A₂, f, A₀ (δ), B, D and σ) and calculate all f and ? Regge couplings between these mesons via a matrix version of finite-energy sum rules. In addition the size of exotic exchanges is evaluated and found to be small. The results are compared with experimental numbers and other models as far as available.     

Formal solutions for response functions of superconductors and 3He(B): II. Applications to acoustic and quasihomogeneous regime

Formal solutions for the autocorrelation functions of density and the transversal current are discussed in the acoustic and quasihomogeneous regime. The poles of these functions are obtained without any restrictions imposed on Landau parameters. The formula for sound dispersion at T = 0 is generalized by the inclusion of terms of the relative order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$, (k is the wave vector, v is the Fermi velocity, Δ is the energy gap, $\text{h}\text{?}\text{≡ 1}$). The dispersion formulae for transversal and longitudinal excitations with a gap for ³He(B) are also given, with an accuracy up to the terms of the order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$, for 0 ? T ? T_c, and without any restrictions imposed on Landau parameters. Under these last assumptions our autocorrelation functions are calculated in the polar as well as non-polar regions. It is shown that if T > 0, the transversal function vanishes at some ω, such that $\text{0 ? ω}{}^2\text{? (}\text{12}\text{5}\text{)Δ}{}^2$. Moreover,the zero of the density autocorrelation function is distanced from its pole by an amount of the order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$.     

Influence of the sum frequency on optically pumped parametric amplifiers

Parametric traveling-wave interactions are calculated with the aid of a plane wave approximation, considering the 4 frequencies ω _s , ω _p , ω _I =ω _p ?ω _s and ω _Σ =ω _p +ω _s . Special attention is paid to the case where ω _p ?ω _s . Competition between parametric amplification and upconversion is studied as a function of phase matching and the results are illustrated by means of numerical examples. It is shown that parametric gain disappears if the linear combination of wave vectors, 2k _p-k_I-k_Σ, vanishes. In this situation upconversion with power gain up to about (ω _Σ /ω _s )² is possible. It is concluded that fork _p?k_s the sum frequency ω _Σ can significantly influence parametric forward amplification but does not affect backward wave amplification.     

Excitation spectrum and T=0 dynamics of the one-dimensional planar spin-12 ferromagnet

The T=0 dynamics of the one-dimensional $\text{S}\text{=}\text{1}\text{2}$ ferromagnet with planar exchange anisotropy is studied by finite-chain calculations and a Green function approach. We demonstrate that the excitation spectrum relevant for appropriate low-T inelastic neutron scattering experiments is much more complex than predicted by linear spin-wave theory. It includes two continua and a set of discrete branches. Some of the low-lying excitations predicted by rigorous calculations, on the other hand, are shown to contribute no spectral weight to the T=0 dynamic structure factor S_zz(q,ω). We provide quantitative results for the spectral-weight distribution in S_zz(q,ω) at T=0 from bound states and continuum states, including a detailed analysis of the singularity in S_zz(q,ω) at the lower band edge. Further evidence is found for the prediction that some T=0 critical properties of the planar $\text{S}\text{=}\text{1}\text{2}$ ferro- and antiferromagnet are governed by exponents which depend continuously on the planar anisotropy.     

Sound attenuation in one-dimensional magnetic systems at finite temperatures

Sound attenuattion constants are calculated for the one-dimensional ferro- and antiferromagnetic systems at finite temperatures. Their frequency dependences, in both cases, turn out to be $\text{ω}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>k</mtext>}}\text{if}\text{ω}{}_{\mathrm{<mtext>k</mtext>}}\text{? ω}{}_{\mathrm{c}}\text{and}\text{ω}{}^2{}_{\mathrm{<mtext>k</mtext>}}\text{if}\text{ω}{}_{\mathrm{<mtext>k</mtext>}}\text{?ω}{}_{\mathrm{c}}$, where ω_c is a “cut-off” frequency related to the three-dimensional anisotropic interactions.     

Crossing relations for deep-inelastic and annihilation processes

We calculate in a model field theory [φ³]_σ the structure functions $\text{F}\text{?}\text{(ω), F(ω)}$ for the processes e⁺+e^?→h+X and e^?+h→e^?+X in the next to leading logarithm approximation. We find that $\text{F}\text{(ω) and F(ω)}$ satisfy the analytic continuation relation but not the Gribov-Lipatov reciprocity relation.