Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Atomic collective excitations in liquid lead

The atomic dynamics of liquid lead at the temperature T = 600 K has been simulated on the basis of the embedded atom model potential (the “embedded” atom model making it possible to effectively take into account the many-particle interactions) in order to study the mechanisms of formation of the atomic collective excitations. Spectra of the dynamic structure factor S(k, ω) and the spectral densities of the time correlation functions of the longitudinal \(\tilde C_L\) (k, ω) and transverse \(\tilde C_T\) (k, ω) currents have been calculated for the wavenumber region 0.11 Å^?1 ≤ k ≤ 2.01 Å^?1. It has been established that the dynamics of density fluctuations is characterized by two dispersion “acoustic-like” branches of the longitudinal and transverse polarization.     

An explanation of the structure in the dynamic structure factor of an electron liquid

We explain the recently observed interesting structure in the dynamic structure factor S(k, ω) of various metallic systems by considering processes that involve single-particle and multi-particle excitations.     

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.     

Neutron inelastic scattering study of transverse spin fluctuations in CsNiF3: A soliton-only central peak

We have observed a quasi-elastic contribution to the spectrum of the transverse spin fluctuations S^perp;(Q, ω), perpendicular to an applied magnetic field in the easy plane of the one-dimensional ferromagnet CsNiF₃. According to the present theoretical understanding this contribution is due solely to soliton quasi-particles and it should not contain two-magnon scattering. The observed dependence on momentum transfer is as expected for soliton scattering with zero intensity at q_c = 0 rising through a maximum with increasing q_c.     

Dynamic structure function of liquid 3He

The dynamic structure function S(Q, ω) of liquid ³He is evaluated in the impulse approximation, based on a theoretically calculated momentum distribution n(k). The gap of n(k) at the Fermi surface gives rise to discontinuities in the slope of S(Q = const., ω) which may be detectable in neutron- or γ-ray scattering experiments.     

Vibrational relaxation in liquids

A new theory is presented for vibrational energy relaxation in a liquid. It is shown that a vibrationally excited probe molecule relaxes through interaction with the density fluctuations in the surrounding solvent fluid. This interaction occurs through a potential V(k), which is expressed in terms of the intermolecular force between the excited probe molecule and the surrounding fluid molecules. By assuming spherically symmetric solvent particles the T ₁ energy relaxation time for direct V-T processes is related to the translational dynamic structure factor for the fluid S(k, ω_v), evaluated at the vibrational resonance frequency. It is shown that this is described by gas-like particle motions on a very short distance scale corresponding to k vectors lying well beyond the first or second peaks of the fluid structure factor S(k). Such motions can be pictured as high-frequency, short-distance distortions of the local equilibrium configuration of the solvent particles around the probe. T ₁ ^-1 is found to be proportional to ρ_e T ^1/2 ω_v ^-3. The V-V energy exchange relaxation time is also calculated. This is found to be proportional to S(k, ω′) evaluated at a frequency ω′, corresponding to the vibrational energy missmatch. An energy gap law for the V-V process is derived.     

Pseudogap in the spin-polaron approach for the carrier spectrum of a two-dimensional doped antiferromagnet

In the Kondo model of the two-dimensional lattice with a strong spin-hole antiferromagnetic exchange, the pseudogap behavior of the carrier spectral function A(k, ω) is considered in the optimal and almost dielectric doping limits. A distinctive feature of the analysis is the introduction of the spin polaron even in the mean-field approximation that leads to the formation of two bands (the analogs of the upper and lower Hubbard bands) and makes it possible to immediately take into account the main rearrangement of A(k, ω). The inclusion of the scattering of the mean-field polaron (within the irreducible Green’s functions) describes the further rearrangement of A(k, ω), in particular, the unusual appearance of the pseudogap near the points N = (±π/2, ±π/2).     

Color dipole phenomenology of diffractive electroproduction of light vector mesons at HERA

We develop the color dipole phenomenology of diffractive photo- and electroproduction γ* N → V(V′)N of light vector mesons (V(1S) = ?⁰, ω⁰, ρ⁰) and their radial excitations (V′(2S) ?′, ω′, ρ′). The node of the radial wave function of the 2S states in conjunction with the energy dependence of the color dipole cross section is shown to lead to a strikingly different Q ² and ν dependence of diffractive production of the V(1S) and V′(2S) vector mesons. We discuss the restoration of flavor symmetry and universality properties of production of different vector mesons as a function of Q ² + m _V ² . The color dipole model predictions for the ρ ⁰ and ? ⁰ production are in good agreement with the experimental data from the EMC, NMC, ZEUS and H1 collaborations. We present the first direct evaluation of the dipole cross section from these data.     

Evaluating emission widths of giant dipole resonances in a Fermi liquid model

It is shown in the theory of finite Fermi systems that giant resonances can be considered as zero-sound excitations in concrete nuclei. Solutions to the zero-sound dispersion equation in symmetric nuclear matter, ωs(k), are obtained. Hydrodynamic models determine the wave vector k _A corresponding to giant resonance in a nucleus with atomic number A. The real and imaginary parts of ωs(k _A ) compare to the energy and escape width of giant resonance. Calculations are performed for giant dipole resonances.     

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.     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.     

Biquadratic exchange interaction between Ru5+ ions in (Ru2O9) clusters

The energy levels of a Ru₂O₉ cluster have been calculated, including a higher order spin interaction. The Ru⁵⁺-Ru⁵⁺ coupling is described by the Hamiltonian ?= -2JS₁· S₂ ?j(S₁·S₂)². The temperature dependence of the magnetic susceptibility is used to determine the values of the bilinear J and biquadratic j exchange integrals: J/k = -161K and j/k = 6.6K. The second term in the Hamiltonian corresponds to a fourth order perturbation involving low spin states.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

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.     

Spatial dispersion of the lattice polarizability and the properties of the large polaron

The polaron states are studied in crystals with optical phonon dispersion of the type ω²(k) = ω ₀ ² + u ² k ². The appearance and propagation of a local polarization in such a medium is treated as the evolution of a wave packet having a nonzero group velocity. This approach enables one to construct a consistent theory of moving self-trapped electron. The total energy and the effective mass of a slowly moving polaron are found and are shown to be strongly dependent on the dispersion parameter σ = u/ω₀.     

Investigation of 238U in the (n,n′γ) reaction

An irradiation of ²³⁸U with a beam of reactor fast neutrons permits revealing about 550 gamma transitions associated with the respective (n, n′γ) reaction and with fission fragments. The use of all known data on gamma radiation from fission fragments makes it possible to identify gamma transitions belonging to ²³⁸U with a high probability. The scheme of levels and gamma transitions is composed for ²³⁸U. New levels (including those of spin-parity J ^π = 0⁺) at excitation energies below 2 MeV are proposed. The low-lying levels in the rotational band for two-phonon octupole excitations are determined. It is found that a hybrid state is formed upon the crossing of this band and the band based on two-quasiparticle excitations. This hybrid state must involve excitations of both types. A small value of the rotational-band parameter in the isomer of energy 2559.0(4) keV is explained by the contribution to this state from two-quasiparticle configurations belonging to the 1k _17/2 subshell. The same circumstance may also be responsible for an enhanced yield of ternary fission for this isomer.     

Diffusion of vibrations in disordered systems

We consider diffusion of vibrations in random lattices with translational invariance. Above the frequency ω_IR corresponding to the Ioffe-Regel crossover (and depending on the strength of disorder), phonons cannot propagate through the lattice and transfer energy. At the same time, most of the vibrations in this range are not localized. We show that these delocalized excitations are similar to diffusons introduced by P. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten (see, e.g., Phil. Mag. B 79, 1715 (1999)) to describe heat transport in glasses. In this range the energy in the lattice is transferred by means of diffusion of vibrational excitations. We have calculated the diffusivity of the modes D(ω) using both the direct numerical solution of Newton equations and the Edwards-Thouless formula. It is nearly constant above ω_IR and goes to zero at the localization threshold.     

On the temperature behavior of second sound and Poiseuille flow

The linearized Peierls equation for the phonon densityN (k λ,r t) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants byk-dependent relaxation rates. For the normal process relaxation time the behaviorτ _N (k λ)∝|k|^?p for smallk is assumed. Taking into account thisk-dependence ofτ _N explicitly and avoiding an expansion with respect toΩτ _N (kλ) before performing the necessary integration overk yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments.