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Recently there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response $\chi_{nn}(\bq,\omega)$ of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor $S(\bq,\omega)$ in superfluid $^4$He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second vs. first sound in the compressibility sum rule is given by the Landau--Placzek ratio $\lp\equiv (\bar{c}_p-\bar{c}_v)/\bar{c}_v$ for all temperatures below $T_c$. In contrast to superfluid $^4$He, $\lp$ is much larger in strongly interacting Fermi gases, being already of order unity for $T \sim 0.8 T_c$, thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in $S(\bq,\omega)$ (measured in pulse propagation studies) as compared to $\mathrm{Im}\chi_{nn}(\bq,\omega)$ (measured in two-photon Bragg scattering). We show that first and second sound in $S(\bq,\omega)$ in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in $S(\bq,\omega)$. We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound., Comment: 33 pages, 10 figures

Despite great efforts over many years, a truly microscopic understanding of the phonon-maxon-roton spectrum in superfluid 4He has continued to be elusive. High resolution neutron scattering studies1,2,3 of the lineshape exhibited by \(S(\vec{Q},\omega )\) have given vivid evidence of the completely different behaviour of the low Q phonon spectrum and the high Q maxon-roton spectrum as the temperature increases towards T λ. Recently, Glyde and the author have realized that recent experimental results gave the needed clues which were missing before. We have proposed a unified theory4 of the excitations in superfluid 4He which is firmly anchored in the existence of a Bose broken symmetry (see Sokol, these proceedings). We believe that a suitably parameterized version of this microscopic formulation will provide a natural starting point for detailed comparisons with the excitations observed in high resolution neutron scattering data. For further discussion of its experimental implications, we refer to the papers by Glyde and Svensson in these proceedings. The main goals of this article are to discuss the basic elements of the new picture, to review its historical development and relation to earlier ideas, and finally, to sketch how it might be brought into contact with the very successful phenomenological approach based on variational many body wavefunctions.

The phenomenon of Bose-Einstein condensation has been thought to underlie superfluidity in liquid helium since 1938. Now at last direct evidence for the condensate has been found, by knocking atoms out of the surface of liquid helium using a beam of photons. The atoms all come out at the same angle — a clear sign that they started out with zero momentum parallel to the surface. This experiment is in effect a type of atom laser.

Stimulated by recent high-resolution neutron data from ILL, we have carried out an extensive numerical study of the single-particle ϱ 1 ( Q , ω) and the two-particle ϱ 2 ( Q , ω) spectral densities within the well known Ruvalds and Zawadowski (ZS) scenario, over a wide range of wavevectors (1≲Q≲3A˚ -1 ), frequencies and temperatures. We extend the original RZ analysis (which concentrated on the two-roton spectrum) to include the multiparticle structure associated with the maxon-roton and maxon-maxon spectra. The microscopic theory of a Bose-condensed fluid shows that S ( Q , ω) involves a weighted sum of ϱ 1 ( Q , ω) and ϱ 2 ( Q , ω). As a result, multiparticle structure exhibited by S ( Q , ω) is not easily related to theoretical results for ϱ 1 ( Q , ω) and ϱ 2 ( Q , ω).

Co-discoverer of superfluidity, and one of the last of a generation of 'classical' physicists who delighted in explaining phenomena that could be seen.

Glyde and Griffin have recently given a new interpretation of the quasiparticle dispersion relation for superfluid 4He. The low Q phonon peak in S(ovrarr|Q,ω) corresponds to a zero sound mode while the high Q maxon-roton peak is a strongly-renormalized single particle excitation. We propose that Z(Q) should be viewed as the superposition of the weights of zero sound and maxon-roton excitations. We also speculate that the ratio Z(maxon)/Z(roton) may reflect the value of the condensate fraction n0.

Following Williams and Bloch, we consider the random-phase-approximation electronic response function of an array of parallel chains, treating the chains as cylindrical potentials of radius r/sub 0/. A careful discussion is given of the form-factored interchain Coulomb interaction, both in real space and in momentum space. We extend the calculations to include the Tomonaga-Luttinger model keeping only the small-momentum forward-scattering processes (g/sub 2/ and g/sub 4/). The finite chain radius is necessary in order to make the intrachain interaction well defined. The continuum approximation for the interchain interaction is examined in detail and compared to the analogous problem in type-II superconductors. We give the corrections to the plasmon frequency (for coupled chains) which depend on the ratio r/sub 0//d/sub perpendicular/, where d/sub perpendicular/ is the distance between chains.

Basing our analysis on the Anderson-Newns model for H chemisorption, we develop a systematic method of calculating the adatom self-energy arising from the effect of substrate charge fluctuations. Using the method of functional derivatives, we generate a Dyson equation for the adatom Green's function and evaluate the self-energies due to the hopping and Coulomb interactions between metal and atom to second order. The latter involves the substrate density response function, and this allows us to include the effect of surface plasmons, bulk plasmons, and the particle-hole continum of the metal surface on an equal footing. The latter become increasingly important close to the surface, where simple image-potential arguments are no longer adequate. We formulate our theory treating the adatom Coulomb repulsion $U$ perturbatively (Newns, Hertz and Handler) as well as in the atomic limit (Brenig and Sch\"onhammer, Bell and Madhukar). Keeping only surface plasmons, we discuss the relaxation shifts and surface-plasmon satellites of the H-atom spectral density within the context of the Brenig-Sch\"onhammer approximation. In particular, we show how the effective Coulomb repulsion $U$ is reduced to $U\ensuremath{-}2{V}_{I}$. We also prove that the substrate-induced self-energy term which gives rise to the above changes on the spectral density has no effect on the net chemisorption energy. The small image-potential energy shift of the main resonance is canceled by the large shift associated with the weak surface-plasmon satellite. Much of our theoretical analysis is applicable to the core-level spectrum, and not just the valence electrons involved in chemisorption.

It is shown that the Woods-Svensson decomposition of the dynamic structure factor $S(Q,\ensuremath{\omega})$ into superfluid and normal-fluid components implies relationships between $S(Q)$ and the superfluid fraction ${n}_{s}=\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}$ and between $g(r)$ and ${n}_{s}$, which are very well borne out by experiment. Combining our new relationship between $g(r)$ and ${n}_{s}$ with that between $g(r)$ and the condensate fraction ${n}_{0}$ proposed by Hyland, Rowlands, and Cummings then gives an explicit relationship between ${n}_{0}$ and ${n}_{s}$ for all temperatures in the superfluid phase.

The new high-${T}_{c}$ oxide superconductors appear to be superlattice structures with a basis composed of metallic sheets as well as metallic chains. Using a simple free-electron-gas model for the sheets and chains, we obtain the dielectric function $\ensuremath{\epsilon}(\mathbf{q},\ensuremath{\omega})$ of such a multilayer system within the random-phase approximation (RPA). We give results valid for arbitrary wave vector $\mathbf{q}$ appropriate to sheets and chains (as in the orthorhombic phase of Y-Ba-Cu-O) as well as for two different kinds of sheets (such as may be present in the Bi-Sr-Ca-Cu-O superconductors). The occurrence of acoustic plasmons is a general phenomenon in such superlattices, as shown by an alternative formulation based on the exact response functions for the individual sheets and chains, in which only the intersheet (chain) Colomb interaction is treated in the RPA. These results generalize the long-wavelength expressions recently given in the literature. We also briefly discuss the analogous results for two arrays of mutually perpendicular chains, such as found in Hg chain compounds.

The low-frequency long-wavelength spin fluctuation modes make a major contribution to the free energy near the ferromagnetic instability of an itinerant-electron model. These fluctuations renormalize the static spin susceptibility and depress the transition temperature predicted by Stoner theory. Moriya and Kawabata (MK) have suggested a simple way of computing the depression self-consistently, by making sure the spin fluctuations go soft at the renormalized temperature ${T}_{c}$ rather than at the Stoner value. We extend the discussion of MK to include both longitudinal and transverse spin fluctuations, and find a ${T}_{c}$ which is only slightly smaller than ${T}_{c}^{\mathrm{MK}}$. We also discuss the relation between ${T}_{c}$ determined from the condition that the paramagnons go soft and that obtained by considering the softening of the spin waves. We argue that our new results give evidence that the basic MK procedure is internally consistent and somewhat less ad hoc than it appeared in its original presentation.

In 1970, Hyland, Rowlands, and Cummings suggested that one could obtain the condensate fraction n/sub o/(T) from careful measurements of the static pair-correlation function g(r,T) in the superfluid and normal phases of /sup 4/He. Their arguments are critically analyzed by going back to the general structure of S(Q) and S(Q,..omega..) predicted by the field-theoretic analysis of a Bose-condensed liquid. It is shown that at low temperatures, the single-particle correlation functions, which Hyland et al. argue are negligible, in fact make a major contribution to g(r,T) in the region r> or approx. =4 A.

Using a field-theoretic formalism in terms of regular (proper, irreducible) quantities, we give a detailed analysis of the long-wavelength collisionless excitations of a weakly interacting dilute Bose-condensed gas in the intermediate-temperature region. Earlier work by Sz\'epfalusy and Kondor has shown that use of the free-Bose-gas approximation for the regular quantities leads to a phonon with a velocity equal to [${n}_{0}$(T)${V}_{0}$/m${]}^{1/2}$, where ${n}_{0}$(T) is the temperature-dependent condensate of a free Bose gas. In this paper the phonon velocity is worked out with use of the one-loop diagrams for the regular quantities. The result is [${n}_{S}$(T)${V}_{0}$/m${]}^{1/2}$[1-f(T)], where ${n}_{S}$(T) is the Landau superfluid density defined in terms of the Bogoliubov excitations and f(T) is a relatively small correction. Numerical calculations are given for spin-polarized ${\mathrm{H}}_{\mathrm{\ensuremath{\downarrow}}}$ with density n=5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{3}$. .AE

The dynamic structure factor S(Q,..omega..) for a Bose-condensed system is calculated microscopically at temperatures where there are a significant number of thermally excited quasiparticles present. Our work is based on the one-loop diagrammatic approximation, which has been used by Wong and Gould to discuss the low-temperature limit. In our numerical calculations (for Q = 0.35 and 0.8 A/sup -1/) of proper, irreducible quantities, we use the Bogoliubov approximation for the coherence factors in conjunction with the experimentally determined quasiparticle spectrum. We find that at high temperatures, the collisionless phonon resonance exhibited by S(Q,..omega..) has a width which increases with the number of thermally excited rotons, in rough agreement with the neutron scattering data of Cowley and Woods as well as those of Woods and Svensson. Our results are compared with those based on a phenomenological treatment of the phonon-roton coupling.

An explicit expression for the density response function in the hydrodynamic region has been given by Hohenberg and Martin, starting from the two-fluid equations of motion for a superfluid. We use their results to calculate the first and second sound resonances in a weakly interacting, dilute Bose-condensed gas. We only consider the intermediate temperature region, where the effect of the interactions may be treated as a small correction (nV 0«k B T). We use the transport coefficients obtained by Kirkpatrick and Dorfman. As expected for a gas, the second sound mode has appreciable weight in the density-fluctuation spectrum.

Very recently, Woods and Svensson have reported neutron-scattering experiments which indicate that the temperature-dependent weight of the elementary excitation resonance in superfluid /sup 4/He is directly proportional to the superfluid density rho/sub s/(T). We argue that this result can be easily understood within the general framework of the standard field-theoretic formulation of a Bose-condensed system and that it gives strong evidence in favor of the regularity hypothesis introduced by Hohenberg and Martin.

The spin susceptibility of an exchange enhanced metallic film is studied with the objective of determining how the paramagnetic properties are modified by the surfaces and the finite size of the system. In contrast to the usual treatments, an exchange interaction of finite range λ, comparable to the Fermi wavelength λF, is used. The exchange interactions are taken into account within a mean field theory approximation.The spin susceptibility is explicitly evaluated for a model in which the boundaries are treated as infinitely high potential barriers. It is found that the results depend sensitively on the value of λ. In particular, the large quantum oscillations in the surface magnetization found by earlier workers are significantly reduced in magnitude when a realistic value of the range is used. A generalized Stoner criterion determining the ferromagnetic instability in a film of thickness L is also derived from the spin susceptibility. The critical temperature TcF for a film is found to be depressed below the bulk value TcB for two physically distinct reasons. The first is referred to as a density-of-states effect and gives a depression proportional to L−1; in the absence of density-of-states effects the shift is proportional to L−2.

A status report is given on recent theoretical work concerning the role the Bose condensate has on the dynamical properties of superfluid 4He. A Bose broken symmetry is shown to be crucial in understanding why zero-sound-type density fluctuations play the role of quasi particles in the superfluid phase. A new unified treatment of long-range order in bulk Bose liquids and quasi-long-range order in Bose films is given. In addition, the strong evidence we now have concerning the existence and magnitude of the Bose condensate is critically reviewed. This includes (i) determination of the momentum distribution from inelastic neutron scattering and (ii) recent finite-temperature Monte Carlo calculations of the condensate fraction n0(T)and the normal-fluid density ρN(T).

In the microscopic theory of Bose-condensed liquids, the condensate wave function leads to a coupling of the density fluctuations and the single-particle excitations. A simple parametrized model of this based on coupling weakly damped zero-sound modes with strongly damped free-particle-like excitations similar to Q/sup 2//2m explains why the phonon-roton resonance in S(Q,w) for superfluid /sup 4/He exists above and below Tlambda but only pays the role of an elementary excitation below Tlambda. It is pointed out that this model also predicts that S(Q,w) should exhibit a weak, low-frequency peak centered at Q/sup 2//2m, with weight roughly proportional to the condensate fraction n/OMICRON/. As a stimulus to further experimental searches for this branch, some model calculations are given for S(Q,w) for Q similar to 1A/sup -1/.

The microscopic theory of3He-4He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure4He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density ρ N in terms of the static4He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the3He atoms make no direct contribution to the superfluid flow.

The momentum distribution ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}_{p}$ of atoms in a Bose-condensed system is computed in the long-wavelength limit $p\ensuremath{\rightarrow}0$. We use frequency-moment sum rules for the single-particle Green's function, including a generalized version of Wagner's sum rule appropriate to hard-core potentials. We show that at finite temperatures ($\mathrm{cp}\ensuremath{\ll}{k}_{B}T$) the correction to ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}_{p}=\frac{{n}_{0}{m}^{2}}{{\ensuremath{\rho}}_{s}{p}^{2}}$ involves the off-diagonal self-energy ${\ensuremath{\Sigma}}_{+\ensuremath{-}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}},\ensuremath{\omega}=0)$. In calculating ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}_{p}$ in the limit $\mathrm{cp}\ensuremath{\gg}{k}_{B}T$, we include first-sound as well as second-sound contributions.

With the availability of modern lasers, light scattering can now be used as a probe of the energy, damping, and relative weight of the various hydrodynamic collective modes in anharmonic insulating crystals. We first give a general review of the distinction between hydrodynamic and high-frequency (or dynamic) vibrational modes. We then express the intensity and spectral distribution of scattered light in terms of the Fourier transform of the displacement-displacement correlation function ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\mathrm{K}\ensuremath{\Omega})$, which is the spectral weight of the phonon propagator. This follows some work of Loudon, who has discussed first-order Raman (or Brillouin) scattering using standard quantum-mechanical perturbation theory. Next we summarize what can be said about the spectral weight ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\mathrm{K}\ensuremath{\Omega})$ in the region of low frequencies (or small energy transfer). We use the model calculations of Kwok and Martin, as well as the standard theory of an elastic medium with a nonlocal form of Fourier's law of heat diffusion. In the case of pure isotropic anharmonic crystals ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\mathrm{K}, \ensuremath{\Omega})$ has resonances corresponding to first-sound (pressure) and second-sound (temperature) waves, in addition to that from transverse or shear elastic waves. Unless fairly restrictive conditions are met, the second-sound wave does not propagate and reduces to the ordinary thermal diffusion mode of Landau and Placzek. The special nature of second sound in He II is discussed in an Appendix.

The electronic thermal conductivity (${K}_{s}$) of a weakly coupled, isotropic superconductor doped with a small concentration of paramagnetic impurities is computed. The theory of such superconducting alloys has been given by Abrikosov and Gor'kov, and is based on the assumption that the static magnetic impurities are randomly distributed and that their spins are uncorrelated. Starting from a Kubo formula, ${K}_{s}$ is calculated by considering the electron-impurity interaction in the ladder approximation. A considerable simplification of the final expression for ${K}_{s}$ obtains if the exchange scattering time ${\ensuremath{\tau}}_{S}$ is much larger than the total scattering time. Numerical calculations have been made of the ratio of the thermal conductivity in the superconducting and normal states as a function of the reduced temperature ($\frac{T}{{T}_{c}}\ensuremath{\equiv}t$) for different impurity concentrations. Abrikosov and Gor'kov have shown that the energy gap function ${\ensuremath{\omega}}_{0}(T)$ is quite different from the Gor'kov order parameter $\ensuremath{\Delta}(T)$ in such alloys. It is found, however, that $\frac{{K}_{s}}{{K}_{n}}$ is less than unity even in the "gapless" region ($\ensuremath{\Delta}{\ensuremath{\tau}}_{S}l1$). Moreover $\frac{{K}_{s}}{{K}_{n}}$ as a function of $t$ decreases with the paramagnetic-impurity concentration for $t\ensuremath{\gtrsim}0.8$ and low concentrations. Some aspects of the Abrikosov-Gor'kov model are reviewed in an Appendix. The numerical values of $\ensuremath{\Delta}$, ${\ensuremath{\omega}}_{0}$, and the density of states that were used in the evaluation of $\frac{{K}_{s}}{{K}_{n}}$ are given separately.

Density fluctuations in inhomogeneous systems are treated in the RPA using the Kadanoff–Baym Green's function method. In our analysis, the Wigner distribution function plays an important role. Well-known results for surface plasmons in one- and two-component plasmas are very easy to derive. A brief discussion is given of surface modes in systems for which the interaction is of short range.

Within the framework of a linear-response correlation-function approach to the collective modes in an inhomogeneous electron gas, a theory is given of the effect of retardation on surface plasmons. The case of a sharp metal-vacuum interface is worked out in detail as an illustration of the general formalism.

We give a systematic discussion of the anomalous scattering of Bogoliubov excitations at sharp N–S and S–N boundaries as well as quasi-particle tunneling in N–S–N and S–N–S geometries. The relation between the transmission resonances (E > Δ) and the bound states (E

The local spin susceptibility of an almost-ferromagnetic system of finite thickness is computed in the R.P.A. In contrasst to recent studies, it is shown that if one uses an exchange interaction with a finite range λ (of order λ F ), the exchange-enhancement of the magnetization is smaller at the surface than in the bulk.

Making use of the finite-temperature version of Beliaev's field-theoretical description of an interacting Bose gas, we sum the self-energy diagrams which correspond to the collisionless shielded potential approximation (SPA). This generalizes Bogoliubov's first-order results by replacing the bare repulsive interaction by a dynamically shielded interaction and includes the effect of the excited atoms. This theory is completely equivalent to that of Tserkovnikov if we use the ideal Bose gas approximation for the polarization function which screens the two-particle interaction. The excitation spectrum is found to have a single resonance. We do not find any convincing evidence for the additional high frequency second sound mode obtained by Tserkovnikov.

At the critical mixing point of 3He–4He mixtures, the amplitudes of both the nonpropagating diffusion mode and second sound may become anomalously large. The damping of these two critical modes is discussed on the basis of Khalatnikov's two-fluid hydrodynamics.

We consider a degenerate system of fermions interacting via a Yukawa potential and confined within a slab of thickness $L$. Using the semiclassical random-phase approximation, we obtain the retarded density response function ${\ensuremath{\chi}}_{\mathrm{nn}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}},\ensuremath{\omega})$, which exhibits resonances corresponding to surface, as well as surface-bulk, or mixed, collective excitations. The surface and surface-bulk density fluctuations are spatially either of a symmetric or antisymmetric character. Their dispersion relations and collisionless damping are discussed, mainly in the strong-coupling limit. A symmetric surface mode which is phononlike at long wavelengths is found, but the antisymmetric surface mode ceases to exist below a certain value of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$, the wave vector parallel to the surface. The mixed modes all possess an energy gap at ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}=0$. We also evaluate the dynamic structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ which describes the inelastic scattering of particles in the Born approximation. Our calculations exhibit how crucially the nature of collisionless surface modes depends on the range of interaction between quasiparticles. We argue that our model calculations should be appropriate to liquid ${\mathrm{He}}^{3}$ in situations where the restricted dimension is of order 100 \AA{} or larger.

Surface modes in a homogeneous system with a sharp boundary are discussed using the collisionless Boltzmann equation for the Wigner distribution function. In a one-component system of fermions interacting via a Yukawa potential, we show that there is an acoustic surface mode. In the limit of long wavelengths, it becomes indistinguishable from the analogous bulk zero-sound mode. For a system of electrons and ions, we find a low-frequency in-phase surface mode, in addition to a high-frequency out-of-phase optical surface mode. For long wavelengths, the low-frequency mode is phononlike with a speed identical to that given by the Bohm-Staver expression.

At room temperature, the mercury chains in Hg/sub 3-delta/AsF/sub 6/ exhibit phonons characteristic of a one-dimensional lattice. We calculate the screening of the Hg ion-ion interaction in a single chain by electrons moving in a cylindrical potential of finite radius, within the random-phase approximation. The resulting Bohm-Staver-type expression for the phonon velocity is (Z/sup 2/mN/sub I//MN/sub e/)/sup 1/2/v/sub F/, where Z is the Hg ionic charge and N/sub I/ (N/sub e/) is the number of ions (electrons) per unit length. Use of the Tomonaga-Luttinger solution for the electronic response function (keeping only the small-momentum scattering processes) just renormalizes the Fermi velocity in this expression.

If the temperature in an insulating crystal decreases in the z-direction, there are more phonons with momentum qz > 0 than with qz < 0. The resulting difference between the Stokes and anti-Stokes Brillouin intensities is proportional to the mean free path of the phonon involved and to the temperature gradient. The effect should be observable by either neutron or photon scattering.

There is considerable evidence that the electronic behavior of orthorhombic ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ is dominated by energy bands associated with Cu-O sheets and chains. We discuss the long-wavelength plasmon modes expected in an array of parallel metallic sheets and chains, coupled by the Coulomb interaction and using the random-phase approximation. We show that in the a-b plane, there is a low-energy acoustic plasmon mode, in addition to the usual high-energy bulk plasmon. This new acoustic plasmon does not arise in an array of coupled layers or in an array of parallel chains. Depending as it does on electronic motion in the chains along the b axis, the frequency of the mode is highly anisotropic in the a-b plane.

Recently it is been argued that the plasmon modes expected in the oxide superconductors should be characteristic of a superlattice with a basis of several metallic sheets. We extend this work by including the exchange-correlation effects in a given CuO sheet via local-field corrections (the generalized random-phase approximation). In addition, the effective interaction between electrons in a given CuO sheet is worked out for a superlattice with a basis of several sheets, separating out the effects of the various kinds of plasmons. Numerical results are given for the superlattice plasmon dispersion relations for two and three sheets/unit cell. If the spacing of the sheets is small compared to the superlattice period (as it is in the 2:2:1:2 and 2:2:2:3 superconductors), we find that the low-frequency plasmon branches (/ital n//minus/1 of them, where /ital n/ is the number of sheets/unit cell) are essentially identical to those of an isolated bilayer or trilayer.

In dealing with density oscillations near a planar boundary, one must make some choice on how one deals with the static part of the problem and the dynamic part of the problem. In the present model calculations we are interested in relatively high-frequency collisionless modes and we argue that one may treat the boundary (whether a wall or a free liquid surface) in terms of a high potential barrier which gives rise to simple specular scattering. For the dynamics we will use the well-known self-consistent field approximation (or RPA) appropriate to a degenerate Fermi system. More precisely, we shall use the semiclassical RPA. Thus we neglect the quantum mechanical interference effects for particles bounding off the surface.1,2

Using the RPA and specular boudary scattering, we show that a ferromagnetic mental with a surface exhibits a surface spin wave mode. It lies above the bulk spin wave spectrum and only appears when one includes the inter-atomic exchange between electrons.

A superlattice with a unit cell of n metallic sheets will exhibit n - 1 low energy plasmons can be studied by infrared optical to the usual high energy branch. We discuss how the q z = 0 low energy plasmons can be studied by infrared optical studies, electronic Raman scattering of light, EELS experiments, as well as through their coupling to LO phonons in the ab plane.