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We carry out a theoretical investigation of overpressurized superfluid phases of He-4 by means of quantum Monte Carlo (QMC) simulations. As a function of density, we study structural and superfluid properties, and estimate the energy of the roton excitation by inverting imaginary-time density correlation functions computed by QMC, using Maximum Entropy. We estimate the pressure at which the roton energy vanishes to be about 100 bars, which we identify with the spinodal density, i.e., the upper limit for the existence of a metastable superfluid phase., Comment: 6 pages, 7 figures

Formation of vortex rings around moving spherical objects in superfluid He-4 at 0 K is modeled by time-dependent density functional theory. The simulations provide detailed information of the microscopic events that lead to vortex ring emission through characteristic observables such as liquid current circulation, drag force, and hydrodynamic mass. A series of simulations were performed to determine velocity thresholds for the onset of dissipation as a function of the sphere radius up to 1.8 nm and at external pressures of zero and 1 bar. The threshold was observed to decrease with the sphere radius and increase with pressure thus showing that the onset of dissipation does not involve roton emission events (Landau critical velocity), but rather vortex emission (Feynman critical velocity), which is also confirmed by the observed periodic response of the hydrodynamic observables as well as visualization of the liquid current circulation. An empirical model, which considers the ratio between the boundary layer kinetic and vortex ring formation energies, is presented for extrapolating the current results to larger length scales. The calculated critical velocity value at zero pressure for a sphere that mimics an electron bubble is in good agreement with the previous experimental observations at low temperatures. The stability of the system against symmetry breaking was linked to its ability to excite quantized Kelvin waves around the vortex rings during the vortex shedding process. At high vortex ring emission rates, the downstream dynamics showed complex vortex ring fission and reconnection events that appear similar to those seen in previous Gross-Pitaevskii theory-based calculations, and which mark the onset of turbulent behavior., Comment: 23 pages, 7 figures

The effects of confinement, disorder, and reduced dimensionality upon quantum fluids have been studied by the adsorption of liquid helium in porous media. The effects of extreme, nanoscale confinement upon its microscopic excitations are not presently understood. Several previous experiments have suggested that at sufficiently low temperature, the roton mean free path is set by the restricted geometry. Here we show that the lifetime of the roton excitation is unaffected when superfluid helium is confined within cylindrical pores only a few nanometers in diameter. The temperature dependence of its lifetime are found to be identical to the bulk fluid, implying that the lifetime is not set by the scale of the confinement. Our results demonstrate that the rotons in the pore center propagate without being modified by the confining media, unlike the collective excitations of classical fluids.

We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results., Comment: Updated version, 17 pages, 10 figures

We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically symmetric reservoirs of liquid $^{4}\mathrm{He}$ separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the $^{4}\mathrm{He}{\ensuremath{-}}^{4}\text{He}$ interatomic potentials. We make a microscopic determination of the length scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below ${T}_{\ensuremath{\lambda}}$. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent $^{4}\mathrm{He}$ healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.

We compute the K-edge indirect resonant inelastic x-ray scattering (RIXS) spectrum of a triangular lattice antiferromagnet in its ordered coplanar 3- sublattice 120 degree magnetic state. By considering the first order self$-$energy corrections to the spin wave spectrum, magnon decay rate, bimagnon interactions within the ladder approximation Bethe-Salpeter scheme, and the effect of three-magnon contributions up to 1/S- order we find that the RIXS spectra is non-trivially affected. For a purely isotropic triangular lattice model, the peak splitting mechanism and the appearance of a multipeak RIXS structure is primarily dictated by the damping of magnon modes. At a scattering wavevector corresponding to the zone center \Gamma point and at the roton point q=M, where the magnon decay rate is zero, a stable single peak forms. At the $\Gamma$ point, the contribution is purely trimagnon at the 1/S level and occurs approximately at the trimagnon energy of 6JS. The roton peak occurs at a lower energy of 4JS. The K-edge single peak RIXS spectra at the roton momentum can be utilized as an experimental signature to detect the presence of roton excitations. A unique feature of the triangular lattice K-edge RIXS spectra is the nonvanishing RIXS intensity at both the zone center $\Gamma$ point and the antiferromagnetic wavevector K point. This result is in sharp contrast to the vanishing K-edge RIXS intensity of the collinear magnetic phases on the square lattice. We find that including XXZ anisotropy leads to additional peak splitting, including at the roton scattering wavevector where the single peak destabilizes towards a two-peak structure. The observed splitting is consistent with our earlier theoretical prediction of the effects of spatial anisotropy on the RIXS spectra of a frustrated quantum magnet [Luo, Datta, and Yao, Phys. Rev. B 89, 165103 (2014)]., Comment: 15 pages, 10 figures, please see PDF copy for full detailed abstract

We have performed a microscopic study of a straight quantized vortex line in three dimensions in condensed $^{4}\mathrm{He}$ at zero temperature using the shadow path integral ground state method and the fixed phase approximation. We have characterized the energy and the local density profile around the vortex axis in superfluid $^{4}\mathrm{He}$ at several densities, ranging from below the equilibrium density up to the overpressurized regime. For the Onsager-Feynman (OF) phase our results are exact and represent a benchmark for other theories. The inclusion of backflow correlations in the phase improves the description of the vortex with respect to the OF phase by a large reduction of the core energy of the topological excitation. At all densities the phase with backflow induces a partial filling of the vortex core and this filling slightly increases with density. The core size slightly decreases for increasing density and the density profile has well defined density dependent oscillations whose wave vector is closer to the wave vector of the main peak in the static density response function rather than to the roton wave vector. Our results can be applied to vortex rings of large radius $R$ and we find good agreement with the experimental value of the energy as a function of $R$ without any free parameter. We have studied also $^{4}\mathrm{He}$ above the melting density in the solid phase using the same functional form for the phase as in the liquid. We found that off-diagonal properties of the solid are not qualitatively affected by the velocity field induced by the vortex phase, both with and without backflow correlations. Therefore we find evidence that a perfect $^{4}\mathrm{He}$ crystal is not a marginally stable quantum solid in which rotation would be able to induce off-diagonal long-range coherence.

We investigate the effect of roton backflow on the scattering of atoms, rotons and phonons at the free surface of superfluid 4 He at T=0 K by including backflow semi-phenomenologically in the form of a backflow potential in the theory of Sobnack et al. [M. B. Sobnack, J. C. Inkson, and J. C. H. Fung, Phys. Rev. B 60, 3465 (1999)]. We assume that all the surface scattering processes are elastic and that the quasiparticles and atoms are incident obliquely to the free surface. We calculate probabilities for the various one-to-one surface scattering processes allowed for a range of energies and compare the scattering rates with those obtained when backflow is neglected.

Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802(February 1, 2008)A major obstacle toward a quantitative verification, by comparison to experiment, of the theory ofthe excitations of the fractional quantum Hall effect has been the lack of a proper understandingof disorder. We circumvent this problem by studying the neutral magneto-roton excitations, whoseenergy is expected to be largely insensitive to disorder. The calculated energies of the roton at1/3, 2/5 and 3/7 fillings of the lowest Landau level are in good agreement with those measuredexperimentally.PACS numbers:71.10.Pm,73.40.Hm

Auger relaxation in 2D strongly correlated electron gas can be represented as an Auger-like process for neutral magnetoplasmon excitations. The case of "dielectric" state with lack of free electrons (i.e. at integer filling $\nu$) is considered. Really the Auger-like process is a coalescence of two magnetoplasmons which are converted into a single one of a different plasmon mode with zero 2D wave-vector. This event turns out to be energetically allowed for magnetoplasmons near their roton minima where the spectrum has the infinite density of states. As a result the additional possibility appears for indirect observation of the magnetorotons by means of anti-Stokes Raman scattering. We find the rate of this process employing the technique of Excitonic Representation for the relevant matrix element calculation., Comment: 4 pages

We report high-resolution neutron inelastic-scattering measurements of the roton energy and linewidth of superfluid {sup 4}He confined in 95{percent} porosity aerogel glass for temperatures 0.08{lt}T{lt}1.2 K. The confined roton line shape can be described well by a damped harmonic oscillator (DHO) function, as in the bulk. The energy of the confined roton is essentially temperature independent over this temperature range. The roton linewidth does not exhibit a finite width of greater than 0.1 {mu}eV at low temperature. This result is in contrast to previous measurements carried out at lower resolution. {copyright} {ital 1999} {ital The American Physical Society}

We calculate microscopically the properties of the dilute He-3 component in a He-3/--He-4 mixture. These depend on both, the dominant interaction between the impurity atom and the background, and the Fermi liquid contribution due to the interaction between the constituents of the He-3 component. We first calculate the dynamic structure function of a He-3 impurity atom moving in He-3. From that we obtain the excitation spectrum and the momentum dependent effective mass. The pole strength of this excitation mode is strongly reduced from the free particle value in agreement with experiments; part of the strength is distributed over high frequency excitations. Above k > 1.7$\AA$^{-1}$ the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. Next we determine the Fermi--Liquid interaction between He-4 atoms and calculate the pressure-- and concentration dependence of the effective mass, magnetic susceptibility, and the He-3--He-3 scattering phase shifts. The calculations are based on a dynamic theory that uses, as input, effective interactions provided by the Fermi hypernetted--chain theory. The relationship between both theories is discussed. Our theoretical effective masses agree well with recent measurements by Yorozu et al. (Phys. Rev. B 48, 9660 (1993)) as well as those by R. Simons and R. M. Mueller (Czekoslowak Journal of Physics Suppl. 46, 201 (1996)), but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured Landau parameter F_0^a.

Temperature dependence of the two-roton Raman spectrum of superfluid ${}^{4}\mathrm{He}$ was measured at pressures of saturated vapor pressure, $9.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ Pa, $4.9\ifmmode\times\else\texttimes\fi{}{10}^{5}$ Pa, and $1.96\ifmmode\times\else\texttimes\fi{}{10}^{6}$ Pa from the lowest temperature of 0.75 K to temperatures above the \ensuremath{\lambda} point. The temperature dependence of both the spectral shape and intensity of the two-roton peak has been found to be simulated well by a model, where the temperature effect is simply broadening of the spectrum with small variation of the roton minimum energy. Spectral shape and peak height at elevated temperatures have been found to be reproduced by convolution integrals of the spectrum at the lowest temperature with Lorentzian functions which take into account the temperature broadening effect at each temperature, where also small temperature dependence of the roton minimum energy had to be taken into account in order to fit the spectrum position. The fact verifies that the Raman spectral shape of superfluid ${}^{4}\mathrm{He}$ does not change qualitatively at elevated temperatures and also even crossing the \ensuremath{\lambda} point. By the model analysis, temperature dependence of the roton minimum energy and the roton half width (inverse of the roton lifetime) have been determined at each pressure as a function of temperature. The results have been compared with theories.

We apply an efficient optimization scheme to shadow wave functions (SWF's) for the ground state of liquid and solid ${}^{4}\mathrm{He}$. Results improve on previous variational energies in both phases. In the liquid, the gain over a wave function with only pair and triplet correlations increases with density, providing a quantitative estimate of the increasing effect of higher-order correlations. The discrepancy with the exact ground-state energy is nearly constant over a wide range of densities, yielding excellent estimates for the equilibrium, freezing, and melting densities. The optimal SWF's can be represented with high precision by density-independent sets of variational parameters for the liquid and the solid phases. An extensive study of ground-state properties demonstrates the uniformly good quality of the variational description afforded by the optimized SWF's. Based on such an accurate representation of the ground state, and including the correct long-range correlations due to the zero-point motion of phonons, we compute the excitation spectrum and the strength of the single quasiparticle excitation peak. While the use of optimized SWF's confirms the accuracy of previous studies in the maxon-roton region, the proper treatment of long-range correlations allows us to extend to the phonon region the agreement between theory and experiment. We simulate relatively large systems in order to explore the long-wavelength regime in detail. Even down to wave vectors where the excitation energy exhibits a highly linear dispersion, which would suggest a harmonic phonon mode, the kinetic and potential energies of the excitation are far from verifying equipartition. This result is supported by additional diffusion Monte Carlo simulations within the fixed node approximation. We locate the onset of the harmonic regime for the long-wavelength excitations at an extremely small value of the wave vector, $k\ensuremath{\lesssim}0.05 {\mathrm{\AA{}}}^{\ensuremath{-}1}$.

The phonon-roton excitations of liquid ${}^{4}\mathrm{He}$ immersed in aerogel of 95% porosity have been measured using inelastic neutron scattering. Excitations having wave vectors at the phonon $(Q=0.2 {\mathrm{\AA{}}}^{\ensuremath{-}1}),$ maxon, roton, and beyond the roton $(Q=2.4 {\mathrm{\AA{}}}^{\ensuremath{-}1})$ regions of the dispersion curve were investigated at temperatures between $T=0.5 \mathrm{K}$ and $T=2.25 \mathrm{K}.$ Aerogel grown with deuterated materials not exposed to air was used and measurements in bulk liquid ${}^{4}\mathrm{He}$ were made under the same conditions for direct comparison. $S(Q,\ensuremath{\omega})$ in ${}^{4}\mathrm{He}$ in aerogel is very similar to that in bulk ${}^{4}\mathrm{He}.$ There is no evidence for any low-energy excitations below the phonon-roton curve or of an energy gap in the dispersion curve ${\ensuremath{\omega}}_{Q}$ at small $Q$ values. At $T=0.5 \mathrm{K}$ and at the maxon, roton, and at $Q=2.4 {\mathrm{\AA{}}}^{\ensuremath{-}1}$, the ${}^{4}\mathrm{He}$ excitation energies ${\ensuremath{\omega}}_{Q}$ in aerogel lie a few $\ensuremath{\mu}\mathrm{eV}$ below the bulk values and the width ${\ensuremath{\Gamma}}_{Q}$ of $S(Q,\ensuremath{\omega})$ has a small finite value $({\ensuremath{\Gamma}}_{Q}\ensuremath{\sim}5 \ensuremath{\mu}\mathrm{eV}).$ The temperature dependence of the energies ${\ensuremath{\omega}}_{Q}$ and widths ${\ensuremath{\Gamma}}_{Q}$ are similar, but not identical, to those in the bulk.

The structure of one- and two-particle currents in liquid ${}^{4}\mathrm{He}$ in the region of the phonon, maxon, and roton excitations is calculated using linear-response theory. A set of continuity equations is derived from the minimal-action principle. The two-particle current describes the motion of the ${}^{4}\mathrm{He}$ atoms with respect to each other and thus enables us to identify topological structures. The optimized functional space makes no assumptions on the patterns and we show how a simple sound wave of the phonon excitation develops into an atomic-size backflow roll above the roton minimum at wave numbers $kg~2.5$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. The roll gets elongated in the direction of the center-of-mass motion and forms a tubelike structure of atomic diameter when $kg~3.0$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. The roton minimum itself is a resonance effect where the wavelength of the excitation matches with the wavelength of the oscillations caused by the two-particle correlations.

Two different microscopic phases have been observed via inelastic neutron scattering for superfluid helium confined within highly monodisperse, smooth, and unidimensional silica pores. When the helium forms a thin film on the pore walls, it supports a dramatically modified phonon-roton spectrum as well as a 2D surface roton. The energies of these modified phonon-roton modes are consistent with predictions for a dilute, low-density film, while the energy of the 2D surface roton corresponds to that of a dense film. The relatively smooth and weak surface potential of the substrate permits the formation of a film with large dilute regions and only small compressed regions. When the pores are saturated with liquid, the modified phonon-roton spectrum disappears, and bulk-like modes coexist with the 2D surface roton. Presumably, bulk-like liquid occupies the core volume of the pores and high density liquid layers are present at the liquid-solid interface. These findings clearly connect the nature of the excitations to the local density of the liquid.

We present neutron scattering measurements of the phonon-roton (P-R) mode of superfluid ${}^{4}$He confined in 47 \AA{} MCM-41 at $T=0.5$ K at wave vectors, $Q$, beyond the roton wave vector (${Q}_{R}=1.92$ \AA{}${}^{\ensuremath{-}1}$). Measurements beyond the roton require access to high wave vectors (up to $Q=4$ \AA{}${}^{\ensuremath{-}1}$) with excellent energy resolution and high statistical precision. Only one previous measurement in porous media (in aerogel) with low statistical precision has been reported. At $T=0.5$ K, we find that the P-R mode in MCM-41 extends out to wave vector $Q\ensuremath{\simeq}3.6$ \AA{}${}^{\ensuremath{-}1}$, with the same energy and zero width (within precision) as observed in bulk superfluid ${}^{4}$He. Layer modes in the roton region are also observed. Specifically, the P-R mode energy, ${\ensuremath{\omega}}_{Q}$, increases with $Q$ for $Qg{Q}_{R}$ and reaches a plateau at a maximum energy ${\ensuremath{\omega}}_{Q}=2\ensuremath{\Delta}$ where $\ensuremath{\Delta}$ is the roton energy, $\ensuremath{\Delta}=0.74$ $\ifmmode\pm\else\textpm\fi{}$ 0.01 meV in MCM-41. This upper limit means the P-R mode decays to two rotons if its energy exceeds 2$\ensuremath{\Delta}$. It also means that the P-R mode does not decay to two-layers modes. If the P-R could decay to two-layer modes, ${\ensuremath{\omega}}_{Q}$ would plateau at a lower energy, ${\ensuremath{\omega}}_{Q}=2{\ensuremath{\Delta}}_{L}$, where ${\ensuremath{\Delta}}_{L}=0.60$ meV is the energy of the roton-like minimum of the layer mode. Rather the P-R mode and the layer modes observed in porous media appear to be quite different modes with little interaction between them.

Optimized variational calculations have been carried out for pure and doped clusters of $^{4}\mathrm{He}$ atoms up to a cluster size of N=1000 particles. For small cluster sizes with less than or equal to 112 particles, where comparisions with existing diffusion Monte Carlo results are possible, we find excellent agreement for the ground-state energy, correlation, and structure functions. For larger clusters our ground-state energies extrapolate smoothly toward a bulk limit of -7.2 K with a surface energy of 0.272 K A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}2}$. The resulting ground-state densities show unmistakable oscillations, confirming our earlier conclusions based on diffusion Monte Carlo studies. The present study of large clusters allows us to bridge the gap between finite systems and the bulk limit. Specifically, we show how the bulk limit of collective energies is reached as well as how the bulk Feynman spectrum is reproduced in the S-wave component of the dynamic structure function in large droplets. By plotting the collective excitation energy of higher multipole modes as a function of an effective wave number k=\ensuremath{\surd}scrl(scrl+1)/R, we show that the resulting spectrum can be directly compared with experimental excitation energies determined for plane liquid surfaces and films. By summing up to scrl=50 partial wave components, we show that the full dynamic structure function simultaneously displays the phonon-roton and the ripplon excitation spectrum. In the case of helium droplets doped with impurities such as rare gas atoms or the ${\mathrm{SF}}_{6}$ molecule, we show that the dipole collective mode becomes unstable with increased droplet size, strongly indicating that these impurities are delocalized inside large droplets. The microscopic character of the instability is revealed in the excitation functions and transition densities of the dipole mode. The introduction of impurities also profoundly alters the dynamic structure function, severely ``fragments'' the Feynman spectrum, and obliterates landmark structures such as the maxon and the roton.

The stability of the flow of superfluid helium II between two corotating cylinders is investigated. The result is compared with the corresponding classical flow of helium I. The validity of Rayleigh`s stability criterion and the relation between a superfluid and a classical inviscid fluid are discussed.

The sum-rule approach is used to derive upper bounds for the dispersion law ${\mathrm{\ensuremath{\omega}}}_{0}$(q) of the elementary excitations of a Bose superfluid. Bounds are explicitly calculated for the phonon-roton dispersion in superfluid $^{4}\mathrm{He}$, both at equilibrium (\ensuremath{\rho}=0.021 86 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}3}$) and close to freezing (\ensuremath{\rho}=0.026 22 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}3}$). The bound ${\mathrm{\ensuremath{\omega}}}_{0}$(q)\ensuremath{\le}2S(q)\ensuremath{\Vert}\ensuremath{\chi}(q)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}1}$, where S(q) and \ensuremath{\chi}(q) are the static structure factor and density response, respectively, is calculated microscopically for several values of the wave vector q. The results provide a significant improvement with respect to the Feynman approximation ${\mathrm{\ensuremath{\omega}}}_{\mathit{F}}$(q)=${\mathit{q}}^{2}$[2mS(q)${]}^{\mathrm{\ensuremath{-}}1}$. A further, stronger bound, requiring the additional knowledge of the current correlation function is also investigated. Results for the current correlation function are presented.

We calculate the dynamical structure factor of the \nu=5/2 non-abelian quantum Hall state in the dipole approximation, valid for large momenta. Due to the fact that both quasi-particles (qps) and quasi-holes (qhs) have an internal Majorana degree of freedom, a qp-qh pair has a fermionic degree of freedom which can be either empty or occupied, and leads to a splitting of the roton mode. Observation of this splitting by means of finite wavelength optical spectroscopy could provide evidence for Majorana modes in the \nu=5/2 quantum Hall state.

We have studied static and dynamical properties of superfluid ${}^{4}$He at $T=0$ K in the pressure range from $\ensuremath{-}6$ up to 87 atm well above freezing into the metastable region. Zero temperature properties have been obtained with the exact shadow path integral ground state (SPIGS) method. Information about dynamic structure factors at different pressures have been obtained from imaginary time correlation functions via the genetic inversion via falsification of theories (GIFT) method. In the full pressure range sharp roton excitations are always present in the spectral functions. The roton energy decreases at higher pressures in good agreement with experimental data also in the metastable region. The roton energies have essentially a linear trend with pressure, going from about 7.4 K near freezing to about 4.3 K at about 87 atm. The pressure at which the linear trend would extrapolate to a zero roton energy turns out to be about 170 atm. At $T=0$ K, no sign of metastable glass phase has been found; the disordered systems studied at pressures above about 87 atm readily start homogeneous nucleation processes. Our results in the metastable phase for the condensate fractions and roton gaps differ remarkably from previous ones obtained via a diffusion Monte Carlo study.

We employ a quantitative microscopic theory of nonuniform quantum liquids to explore the excitations in thin films of $^{4}\mathrm{He}$ adsorbed onto a substrate. These liquid films studied undergo a series of structural phase transitions coinciding with the completion of individual atomic layers. A generalized Feynman ansatz is used for the wave function of the excited states; multiphonon effects are included by generalizing the Feynman theory to allow for time-dependent pair correlations. We study the dispersion relation, excitation mechanisms, transition densities, and particle currents, as a function of the surface coverage, including coverages near the phase transitions. Because of the film's layered growth, the sound velocity exhibits a series of minima and maxima. A pronounced long-wavelength softening of the lowest-energy mode is observed near the transitions. In the monolayer, the nature of the excitations undergoes a noticeable change at the coverage where the velocity of sound starts to decrease. This is a crossover from ``essentially two-dimensional'' to ``essentially three-dimensional'' behavior. At long wavelengths, below and above the crossover coverage, the lowest-energy excitation is a longitudinal phonon (propagating within the monolayer) and a surface excitation, respectively. At shorter wavelengths, a layer-phonon propagating within the liquid layers, level crosses with a surface excitation to become the lowest-energy mode. For double- and higher-layer films the excitations are complicated by multiple (layer phonon with layer phonon and layer phonon with surface excitation) level crossings. At higher coverages, a mode is identifiable that will evolve into the bulk phonon-maxon roton. Our results agree qualitatively with the available spectra obtained by neutron scattering experiments.

A spin-field model in two space and one time dimensions is proposed and investigated using a bilinearization technique. This model, which can be considered as a modified version of the Ishimori system, allows a Hamiltonian formulation, a symmetry algebra of Kac-Moody type with a loop-algebra structure, and the conformal invariance property. Many nonlinear excitations are found, which turn out to be of the helical and roton type, meronlike configurations endowed with a fractional topological charge, radially symmetric solutions, and domain walls. Our results are compared with those of the study of the O(3) nonlinear \ensuremath{\sigma} model and the Ishimori system. Finally, the physical role of both our model and the Ishimori system is discussed in the light of certain reduced equations which find applications in the theory of vortex filaments in liquid $^{4}\mathrm{He}$ and in dealing with the two spin-correlation functions of the two-dimensional Ising model in the scaling limit.

We have studied the excitation spectrum of the specific two-dimensional model of strongly interacting Bose particles via mapping of the many-body Schr\"odinger equation in imaginary time to the classical stochastic dynamics. In a broad range of coupling strengths $\ensuremath{\alpha}$, a roton-like spectrum is found, with the roton gap being extremely small in natural units. A single quantum phase transition between a strongly correlated superfluid and a quantum Berezinsky crystal is found.

The local-field correction for the two-dimensional and the three-dimensional electron gas is calculated within a sum-rule version of the self-consistent approach of Singwi, Tosi, Land, and Sj\"olander. Correlation effects are studied. Results for 0.001${\mathit{r}}_{\mathit{s}}$100 are given where ${\mathit{r}}_{\mathit{s}}$ is the random-phase-approximation parameter. An analytical expression for the static structure factor, representing a generalized Feynman-Bijl spectrum, is used in the calculation. We derive analytical expressions for the density dependence of the local-field correction and we compare the results for the ground-state energy for the interacting electron gas with Monte Carlo computations. The pair-correlation function and the compressibility are studied. Exchange and correlation effects for quantum wells and heterostructures are calculated: numerical and analytical results are derived. In two dimensions and at low density a roton structure in the plasmon dispersion is found. We discuss an instability in layered structures of two-dimensional electron gases.

The collective modes of the v=1/2 state in double-quantum-well systems are analyzed within the framework of the single-mode approximation. The dependence of these modes on the interwell spacing is discussed. The derivation of the plasma sum rules for the two-component classical plasmas corresponding to the unpolarized [mmn] states is derived in the Appendixes

The difference between the specific heat of a dilute [sup 3]He-[sup 4]He mixture and the specific heat of pure superfluid [sup 4]He at temperatures below the superfluid transition temperature is usually explained by considering the [sup 3]He as an ideal gas of quasiparticles with an energy spectrum that is not quadratic in the momentum, but which is difficult to justify on a theoretical basis. On the basis of a polaron-type model, introduced by three of the present authors, the specific heat of the mixture can be calculated, taking into account the emission and absorption of the phonon-roton excitations. In a temperature range where the [sup 3]He particles follow Boltzmann statistics, we find that the model accurately explains the experimental data for the specific heat. Therefore, the difference between the specific heat of the mixture and the specific heat of pure superfluid [sup 4]He can be explained as the result of the interaction of [sup 3]He with the excitations of the superfluid. Moreover, it is one of the most clearly measured polaron'' effects.

We describe calculations of the inelastic-light-scattering spectrum for frequencies of the order of up to several times the roton frequency. The calculations are based on the two-body approximation in a theoretical description of the fluid due to Manousakis and Pandharipande. On the basis of earlier results we calculate only the contribution arising from quasiparticle anharmonicities in the spectrum and take full account of the strong dependence of the three-quasiparticle coupling on the magnitudes and directions of the momenta of the quasiparticles, which is implied by the two-body approximation. The results are compared with recent experimental results. At high energies, the calculated spectrum is in most respects consistent with the experimental one. We discuss the possible origins of the remaining discrepancies.

The equations-of-motion method has been used to calculate the collective excitation energies of an anyon gas. Both the cases with and without Coulomb interactions are considered. This method provides corrections to the random-phase approximation (RPA) in the calculations of the anyon excitation energies. Our calculations indicate that the RPA results are only valid in the long-wavelength limit. The superfluidity of anyons still exists only when the Coulomb interaction is weak. A roton structure, induced by the Coulomb interactions, is discovered. This roton minimum changes with the Coulomb-interaction strength. It approaches zero at some limit of the Coulomb-interaction strength, indicating that anyons are forming a Wigner crystal and the superfluidity of anyons is vanishing.

Many years ago Khalatnikov described unusual properties of the Doppler shift for the second sound in He II, first of all the ``back-entrainment'' effect: at some temperatures (at the beginning of the roton region) the center of the spreading sound moves in the direction opposite to the normal-component velocity ${\mathit{v}}_{\mathit{n}}$ [\ensuremath{\Delta}${\mathit{u}}_{2}$=\ensuremath{\gamma}(T)${\mathit{v}}_{\mathit{n}}$, \ensuremath{\gamma}(T\ensuremath{\sim}0.6 K)0]. However, the existing theory describes Doppler shift of the first and fourth sounds as a trivial, ``kinematic'' effect: the center of the spreading sound moves with the velocity of the liquid as a whole [\ensuremath{\Delta}${\mathit{u}}_{1,4}$\ensuremath{\approxeq}j/p=(1-${\mathrm{\ensuremath{\rho}}}_{\mathit{n}}$/\ensuremath{\rho})${\mathit{v}}_{\mathit{s}}$]. We show that the real situation is quite different. We find (1) the coefficient K in the Doppler-shift expression, \ensuremath{\Delta}${\mathit{u}}_{1,4}$=(1-${\mathit{K}}_{1,4}$${\mathrm{\ensuremath{\rho}}}_{\mathit{n}}$/\ensuremath{\rho})${\mathit{v}}_{\mathit{s}}$, substantially differs from the kinematic value K=1:\ensuremath{\Vert}K${\mathrm{\ensuremath{\Vert}}}_{\mathrm{max}}$ reaches some tens. (2) ${\mathit{K}}_{1}$(T) and ${\mathit{K}}_{4}$(T) have different (qualitatively opposite) nontrivial temperature dependences, in particular a high peak (modulo) at the beginning of the roton region. (3) ${\mathit{K}}_{1,4}$(T) can be negative: ${\mathit{K}}_{1}$0 in the region of the peak, ${\mathit{K}}_{4}$0 in the phonon region. This implies an ``outstripping'' effect: the center of the spreading sound moves faster than the flowing superfluid part of the liquid itself.

We calculate the probability of the creation of a circular phonon (c-phonon) in He II by a c-photon of the resonator. It is shown that this probability has sharp maxima at frequencies, where the effective group velocity of the c-phonon is equal to zero. For He II, these frequencies correspond to a roton and a maxon. From the probability of the c-roton birth, we calculate the roton linewidth which is found to approximately agree with the experimental one.

We have studied the dynamic structure function of superfluid $^{3}\text{H}\text{e-}^{4}\text{H}\text{e}$ mixtures at zero temperature as a function of pressure and $^{3}\text{H}\text{e}$ concentration. Results obtained in the full random-phase approximation (RPA) plus density-functional theory and in a generalized Landau-Pomeranchuk approach are presented and compared with experiment. Analytic expressions for several sum rules of the dynamic structure functions have been determined, and have been used to obtain average energies of the collective excitations. In the RPA approach, the dispersion relation of the collective modes shows typical features of level repulsion between zero-soundlike and phonon-rotonlike excitations. The structure of the coupled RPA equations for the mixture leads in a natural way to the hybridization of the collective modes. The mixed $^{3}\text{H}\text{e-}^{4}\text{H}\text{e}$ dynamic structure function quenches the zero-soundlike mode before it crosses the phonon-roton branch, causing that the former mode only appears with enough strength after the crossing.

Excitation spectra of hard-core bosons with nearest- and next-nearest-neighbor interactions on square and triangular lattices in the superfluid phase are studied using the spin-wave theory. We go beyond the standard linear spin-wave approximation calculating corrections due to spin-wave interaction. Account for the spin-wave interaction considerably improves the quantitative description of the excitation spectra. The behavior of the spectra is analyzed in detail at different particle densities and relations between the interaction parameters. Particular attention is given to the spectrum minima with the aim to find out the conditions for instability of the superfluid phase. We show that for a triangular lattice at high enough next-nearest-neighbor repulsion there appears a true roton minimum inside the Brillouin zone located on the line connecting the zone center with the midpoint of the face of the zone boundary. The obtained analytical results are in excellent quantitative agreement with the numerical simulations known from literature.

We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.

We identify a new kind of elementary excitations, spin-rotons, in the doped Mott insulator. They play a central role in deciding the superconducting transition temperature Tc, resulting in a simple Tc formula,Tc=Eg/6, with Eg as the characteristic energy scale of the spin rotons. We show that the degenerate S=1 and S=0 rotons can be probed by neutron scattering and Raman scattering measurements, respectively, in good agreement with the magnetic resonancelike mode and the Raman A1g mode observed in the high-Tc cuprates., 10 pages, 9 figures

By way of exact microscopic considerations, we elucidate some long-standing points of contention in the literature: (i) We prove the absence of both zero sound (ZS) and the quadratic single-particle (SP) branch in He II. (ii) As to the origin and interrelation of phonons and rotons, we show that they form a unified branch of SP origin; the presence of condensate (independently of its intensity) leads to a suppression of the ZS, to a transference of some properties of ZS to the SP branch, and to the nonmonotonicity of the latter

The recent interpretation of the phonon-roton excitations in superfluid {sup 4}He as a density mode at low wave vector and a quasiparticle excitation at higher {ital Q} proposed by Glyde and Griffin is developed. When there is a condensate, {ital n}{sub 0}({ital T}), the quasiparticle response of liquid {sup 4}He, becomes a component of the observed density dynamic structure factor, {ital S}({ital Q},{omega}). The quasiparticle and density response functions also share a common denominator, due to a coupling via the condensate. At low {ital Q}, the observed {ital S}({ital Q},{omega}) is confined predominantly to a single peak. The peak broadens with temperature but remains well defined in normal {sup 4}He, where {ital n}{sub 0}({ital T})=0. This peak is interpreted as a density mode. At the maxon and higher {ital Q}, {ital S}({ital Q},{omega}) has a sharp peak plus a broad component. The sharp peak is interpreted as the quasiparticle component of {ital S}({ital Q},{omega}). As {ital T} is increased and {ital n}{sub 0}({ital T}) is decreased, the intensity in the sharp peak is reduced until it vanishes from {ital S}({ital Q},{omega}) at {ital T}{sub {lambda}}. A simple model based on uncoupled quasiparticle and density excitations with coupling via {ital n}{submore » 0}({ital T}) is proposed. For simplicity, all model parameters are held independent of {ital T}. By allowing only {ital n}{sub 0}({ital T}) to vary with {ital T}, the temperature dependence of {ital S}({ital Q},{omega}) can be quite accurately reproduced.« less

Application de l'approche de la theorie du champ quantique de la super-radiance a 4 H e liquide. On trouve des explications naturelles de: (i) la variation du gap des rotons et de la fraction de fluide normal avec la temperature; (ii) la structure microscopique a deux fluides de 4 H 2 superfluide; et (iii) le mecanisme fondamental de la formation des tourbillons et les vitesses critiques associees

Calcul des structures de bandes des bandes des phonons et des rotons par la methode Hartree-Fock dependante du temps, pour la phase commensurable (√3×√3) R30 o de p-H 2 et de O-D 2 sur du graphite. Utilisation d'une base de fonctions d'oscillateurs harmoniques tridimensionnelles pour les vibrations translationnelles et d'une base d'harmoniques spheriques pour les rotations faiblement entravees. Un potentiel anisotrope molecule-substrat est modelise de facon semi-empirique. Tous ces potentiels sont developpes explicitement par rapport aux deplacements moleculaires, avec inclusion des termes anharmoniques eleves, et par rapport a leur anisotropie

We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.

The neutron-scattering function for dilute mixtures of {sup 3}He (1% and 5%) in superfluid {sup 4}He at pressures of 0, 10, and 18 bars and temperatures in the range from 0.07 to 1.5 K has been determined for wave vectors between 0.4 and 2.2 A{sup {minus}1}. This is the first such measurement for {sup 3}He-{sup 4}He mixtures at temperatures below the Fermi temperature. The line shape of the {sup 3}He particle-hole excitation is well described by a nearly-free-Fermi-gas model at all temperatures. The {sup 3}He quasiparticle spectrum is derived for wave vectors in the range 0.9{lt}{ital Q}{lt}1.7 A{sup {minus}1}. The results deviate from the quadratic Landau-Pomeranchuk spectrum and are in good agreement with thermodynamical measurements. No rotonlike minimum is observed. We find strong indications of a crossover between the {sup 3}He particle-hole band and the {sup 4}He roton excitation. The pressure and temperature dependence of the shift and broadening of the {sup 4}He phonon-roton peak is derived. The main features are reproduced in a simple model for Landau damping.

We report high-precision neutron scattering measurements of the temperature dependence of the phonon and roton excitations in liquid $^{4}\mathrm{He}$ at saturated vapor pressure in both the superfluid and normal-fluid phases. Two wave vectors were examined in detail: Q=0.4 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$ in the phonon region and Q=1.925 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$ at the roton minimum. The goal is to understand excitations in Bose liquids by determining the dynamic structure factor S(Q,\ensuremath{\omega}) accurately in both phases. At Q=0.4 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$ the sharp peak in S(Q,\ensuremath{\omega}) broadens with temperature T, but remains sharp and well defined in the normal phase (Tg${\mathit{T}}_{\ensuremath{\lambda}}$) up to T\ensuremath{\approxeq}3 K. The rate of increase of the width of S(Q,\ensuremath{\omega}) shows a break at ${\mathit{T}}_{\ensuremath{\lambda}}$, but otherwise S(Q,\ensuremath{\omega}) is similar in the two phases and a transition could not be identified through S(Q,\ensuremath{\omega}). In contrast at Q=1.925 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$, the sharp component of S(Q,\ensuremath{\omega}) disappears at ${\mathit{T}}_{\ensuremath{\lambda}}$ and S(Q,\ensuremath{\omega}) is very different above and below ${\mathit{T}}_{\ensuremath{\lambda}}$. This behavior is documented and values of the frequencies and linewidths at several temperatures are reported.

Microwave (MW) absorption in liquid $^{4}\mathrm{He}$ is investigated in the frequency range of $40--200\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ at $T=1.4--2.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A ``whispering gallery'' of waves was generated by a dielectric disk resonator immersed into the liquid. Resonance absorption of MWs was detected at the frequency, which corresponds to the roton minimum of the liquid helium excitation spectrum. The creation of a single roton is possible because of the presence of the resonator wall which absorbs an extra momentum. The resonance frequency is shown to decrease with temperature in an excellent agreement with the temperature dependence of the roton gap obtained previously in the neutron scattering experiment.

We present neutron scattering measurements of the phonon-roton (P-R) modes of liquid {sup 4}He at saturated vapor pressure confined in 44 A mean pore diameter gelsil in the wave vector range 0.4{

We apply numerical and computational analyses to the decay of a topologically nontrivial, bundle-structured superfluid vortex tangle via mutual friction effected energy transfer to an initially stationary, viscous normal fluid. We demonstrate that, as long as the coherent superfluid vorticity structures remain intact, the induced normal-fluid vorticity acquires a similar to the superfluid vorticity morphology, and the normal-fluid energy spectrum mimics the superfluid energy spectrum presenting a low-wavenumber scaling regime. After a (smaller than the integral advective time scale) transient, the superfluid vorticity bundles disintegrate; this is followed by the decay of normal-fluid energy. The kinetic energies of the two fluids are mismatched throughout the decay period, and the dismantling of coherent vorticity destroys the low-wavenumber energy spectrum scaling in both fluids. At the point of maximum normal-fluid energy, the circulation of the induced normal-fluid vortices is comparable to the ''macroscopic'' circulation of the superfluid vorticity bundles. We show that the superfluid dynamics are dominated throughout the decay period by inertial rather than mutual friction effects, that the formation of bundlelike coherent superfluid vortices cannot be the outcome of pure (reconnecting) Biot-Savart dynamics, and that superfluid vortex length dynamics are not analogous to superfluid energy dynamics. We conjecture that themore » dynamics of fully developed, turbulent thermal superfluid flow could be described in terms of interactions of cyclic coherent vorticity patterns in both fluids.« less