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The formation of an equilibrium quantum state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of non-equilibrium many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously-generated defects, whose emergence obeys a universal scaling law with the quench duration. Much less is known about the ensuing re-equilibrating or "coarse-graining" stage, which is governed by the evolution and interactions of such defects under system-specific and external constraints. In this work we perform a detailed numerical characterization of the entire non-equilibrium process, addressing subtle issues in condensate growth dynamics and demonstrating the quench-induced decoupling of number and coherence growth during the re-equilibration process. Our unique visualizations not only reproduce experimental measurements in the relevant regimes, but also provide valuable information in currently experimentally-inaccessible regimes., Comment: Supplementary Movie Previes: SM-Movie-1: https://youtu.be/3q7-CvuBylg SM-Movie-2: https://youtu.be/-Gymaiv9rC0 SM-Movie-3: https://youtu.be/w-O2SPiw3nE SM-Movie-4: https://youtu.be/P4xGyr4dwKI

Boundaries strongly affect the behavior of quantized vortices in Bose-Einstein condensates, a phenomenon particularly evident in elongated cigar-shaped traps where vortices tend to orient along a short direction to minimize energy. Remarkably, contributions to the angular momentum of these vortices are tightly confined to the region surrounding the core, in stark contrast to untrapped condensates where all atoms contribute $\hbar$. We develop a theoretical model and use this, in combination with numerical simulations, to show that such localized vortices precess in an analogous manner to that of a classical spinning top. We experimentally verify this spinning-top behavior with our real-time imaging technique that allows for the tracking of position and orientation of vortices as they dynamically evolve. Finally, we perform an in-depth numerical investigation of our real-time expansion and imaging method, with the aim of guiding future experimental implementation, as well as outlining directions for its improvement., Comment: 10 pages, 7 figures

We present numerical calculations of the snake instability in a Fermi superfluid within the Bogoliubov-de Gennes theory of the BEC to BCS crossover using the random phase approximation complemented by time-dependent simulations. We examine the snaking behaviour across the crossover and quantify the timescale and lengthscale of the instability. While the dynamic shows extensive snaking before eventually producing vortices and sound on the BEC side of the crossover, the snaking dynamics is preempted by decay into sound due to pair breaking in the deep BCS regime. At the unitarity limit, hydrodynamic arguments allow us to link the rate of snaking to the experimentally observable ratio of inertial to physical mass of the soliton. In this limit we witness an unresolved discrepancy between our numerical estimates for the critical wavenumber of suppression of the snake instability and recent experimental observations with an ultra-cold Fermi gas., Comment: Accepted for publication in PRA

We investigate the response of superfluid Fermi gases to rapid changes of the three-dimensional s-wave scattering length a by solving the time-dependent Bogoliubov-de Gennes equations. In general the magnitude of the order parameter |\Delta| performs oscillations, which are sometimes called the "Higgs" mode, with the angular frequency 2 \Delta_{gap}/ \hbar, where \Delta_{gap} is the gap in the spectrum of fermionic excitations. Firstly, we excite the oscillations with a linear ramp of 1/a and study the evolution of |\Delta|. Secondly, we continously drive the system with a sinusoidal modulation of 1/a. In the first case, the oscillations in |\Delta| damp according to a power law. In the second case, the continued driving causes revivals in the oscillations. In both cases, the excitation of the oscillations causes a reduction in the time-averaged value of |\Delta|. We propose two experimental protocols, based around the two approaches, to measure the frequency and damping of the oscillations, and hence \Delta_{gap}., Comment: 7 pages, 7 figures

We study soliton collisions and the decay of solitons into sound in superfluid Fermi gases across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover by performing numerical simulations of the time-dependent Bogoliubov-de Gennes equations. This decay process occurs when the solitons are accelerated to the bulk pair-breaking speed by an external potential. A similar decay process may occur when solitons are accelerated by an inelastic collision with another soliton. We find that soliton collisions become increasingly inelastic as we move from the BEC to BCS regimes, and the excess energy is converted into sound. We interpret this effect as being due to evolution of Andreev bound states localized within the soliton., Comment: 9 pages, 5 figures

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation relating the phase jump across the soliton to its energy, and hence obtain an expression for the soliton period. Our analytic approach is supported by simulations of the time-dependent Bogoliubov-de Gennes equations, which show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions., Comment: 5 pages, 4 figures

We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow expansion with a subdiffusive behavior when a controlled repulsive interaction is added. The measured features of the subdiffusion are compared to numerical simulations and a heuristic model. The observations confirm the nature of subdiffusion as interaction-assisted hopping between localized states and highlight a role of the spatial correlation of the disorder., Comment: 8 pages, to be published on Physical Review Letters

We investigate the problem of an ultracold atomic gas in the superfluid phase flowing in the presence of a potential barrier or a periodic potential. We use a hydrodynamic scheme in the local density approximation (LDA) to obtain an analytic expression for the critical current as a function of the barrier height or the lattice intensity, which applies to both Bose and Fermi superfluids. In this scheme, the stationary flow becomes energetically unstable when the local superfluid velocity is equal to the local sound velocity at the point where the external potential is maximum. We compare this prediction with the results of the numerical solutions of the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We discuss the role of long wavelength excitations in determining the critical velocity. Our results allow one to identify the different regimes of superfluid flow, namely, the LDA hydrodynamic regime, the regime of quantum effects beyond LDA for weak barriers and the regime of tunneling between weakly coupled superfluids for strong barriers. We finally discuss the relevance of these results in the context of current experiments with ultracold gases., Comment: 10 pages, 6 figures; appendix extended, to appear in Phys. Rev. A

The small oscillations of solitons in 2D Bose-Einstein condensates are investigated by solving the Kadomtsev-Petviashvili equation which is valid when the velocity of the soliton approaches the speed of sound. We show that the soliton is stable and that the lowest excited states obey the same dispersion law as the one of the stable branch of excitations of a 1D gray soliton in a 2D condensate. The role of these states in thermodynamics is discussed., Comment: 6 pages, 2 figures, minor corrections, Proceedings of QFS 2006, to be published in JLTP

We theoretically investigate the dynamic properties of a Bose-Einstein condensate in a toroidal trap. A periodic modulation of the transverse confinement is shown to produce a density pattern due to parametric amplification of phonon pairs. By imaging the density distribution after free expansion one obtains i) a precise determination of the Bogoliubov spectrum and ii) a sensitive detection of quantized circulation in the torus. The parametric amplification is also sensitive to thermal and quantum fluctuations., Comment: 4 pages, 4 figures; new figures, revised version to appear as a Rapid Communication in Physical Review A

A Bose-Einstein condensate in an optical lattice exhibits parametric resonances when the intensity of the lattice is periodically modulated in time. These resonances correspond to an exponential growth of the population of counter-propagating Bogoliubov excitations. A suitable linearization of the Gross-Pitaevskii (GP) equation is used to calculate the stability diagram and the growth rates of the unstable modes. The results agree with the ones extracted from time-dependent GP simulations, supporting our previous claim (M. Kraemer et al., Phys. Rev. A (2005) in press) concerning the key role of parametric resonances in the response observed by Stoeferle et al. (Phys. Rev. Lett. 92, 130403 (2004)) in the superfluid regime. The role of the seed excitations required to trigger the parametric amplification is discussed. The possible amplification of the quantum fluctuations present in the quasiparticle vacuum, beyond GP theory, is also addressed, finding interesting analogies with similar processes in nonlinear quantum optics and with the dynamic Casimir effect. Our results can be used in exploiting parametric instabilities for the purpose of spectroscopy, selective amplification of a particular excitation mode and for establishing a new type of thermometry., Comment: 13 pages, 9 figures, Phys. Rev. A, in press

A density functional theory is used to investigate the instability arising in superfluid $^4$He as it flows at velocity u just above the Landau critical velocity of rotons v_c. Confirming an early theoretical prediction by one of us [JETP Lett. 39, 511 (1984)], we find that a stationary periodic modulation of the density occurs, with amplitude proportional to (u-v_c)^{1/2} and wave vector equal to the roton wave vector. This density pattern is studied for supercritical flow both in bulk helium and in a channel of nanometer cross-section., Comment: 4 pages, 6 figures. Submitted to Phys. Rev. B

We study the response of a Bose-Einstein condensate to a periodic modulation of the depth of an optical lattice. Using Gross-Pitaevskii theory, we show that a modulation at frequency Omega drives the parametric excitation of Bogoliubov modes with frequency Omega/2. The ensuing nonlinear dynamics leads to a rapid broadening of the momentum distribution and a consequent large increase of the condensate size after free expansion. We show that this process does not require the presence of a large condensate depletion. Our results reproduce the main features of the spectrum measured in the superfluid phase by Stoeferle et al., Phys. Rev. Lett. 92, 130403 (2004)., Comment: 4 pages, 4 figures, more results added, to appear in PRA Rapid Communications

The occurrence of energetic and dynamical instabilities in a Bose-Einstein condensate moving in a one-dimensional (1D) optical lattice is analyzed by means of the Gross-Pitaevskii theory. Results of full 3D calculations are compared with those of an effective 1D model, the nonpolynomial Schrodinger equation, pointing out the role played by transverse degrees of freedom. The instability thresholds are shown to be scarcely affected by transverse excitations, so that they can be accurately predicted by effective 1D models. Conversely, transverse excitations turn out to be important in characterizing the stability diagram and the occurrence of a complex radial dynamics above the threshold for dynamical instability. This analysis provides a realistic framework to discuss the dissipative dynamics observed in recent experiments., Comment: 9 pages, 11 figures; typos corrected, references updated, new Figure 7

We study low momentum excitations of a Bose-Einstein condensate using a novel matter-wave interference technique. In time-of-flight expansion images we observe strong matter-wave fringe patterns. The fringe contrast is a sensitive spectroscopic probe of in-trap phonons and is explained by use of a Bogoliubov excitation projection method applied to the rescaled order parameter of the expanding condensate. Gross-Pitaevskii simulations agree with the experimental data and confirm the validity of the theoretical interpretation. We show that the high sensitivity of this detection scheme gives access to the quantized quasiparticle regime., Comment: 5 pages, 5 figures, author list updated

The particle flux through a two micron diameter orifice into vacuum from a source chamber filled with solid He exhibits a striking periodic behavior similar to that of a geyser. This phenomenon is attributed to a periodic collapse of the solid inside the source induced by the accumulation of excess vacancies injected at the orifice. The flux-time curves agree well with a kinetic model and provide direct information on the diffusivity of vacancies in solid He.

We measure the response of an elongated Bose-Einstein condensate to a two-photon Bragg pulse. If the duration of the pulse is long, the total momentum transferred to the condensate exhibits a nontrivial behavior which reflects the structure of the underlying Bogoliubov spectrum. It is thus possible to perform a spectroscopic analysis in which axial phonons with different number of radial nodes are resolved. The local density approximation is shown to fail in this regime, while the observed data agrees well with the results of simulations based on the numerical solution of the Gross-Pitaevskii equation.

Helium nanodroplets and trapped Bose-Einstein condensates in dilute atomic gases offer complementary views of fundamental aspects of quantum many-body systems. We discuss analogies and differences, stressing their common theoretical background and peculiar features. We briefly review some relevant concepts, such as the meaning of superfluidity in finite systems, the behavior of elementary excitations and collective modes, as well as rotational properties and quantized vorticity., Comment: 15 pages, 1 eps figure, review article for J. Chem. Phys., thematic issue on Helium Nanodroplets

The response of a trapped Bose-Einstein condensed gas to a density perturbation generated by a two-photon Bragg pulse is investigated by solving the time-dependent Gross-Pitaevskii equation. We calculate the total momentum imparted to the condensate as a function of both the time duration of the pulse and the frequency difference of the two laser beams. The role of the dynamic response function in characterizing the time evolution of the system is pointed out, with special emphasis to the phonon regime. Numerical simulations are compared with the predictions of local density approximation. The relevance of our results for the interpretation of current experiments is also discussed., Comment: 7 pages, 3 postscript figures

Angular momentum can be transferred to a trapped Bose-Einstein condensate by distorting its shape with an external rotating field, provided the rotational frequency is larger than a critical frequency fixed by the energy and angular momentum of the excited states of the system. By using the Gross-Pitaevskii equation and sum rules, we explore the dependence of such a critical frequency on the multipolarity of the excitations and the asymmetry of the confining potential. We also discuss its possible relevance for vortex nucleation in rotating traps., Comment: 4 pages revtex, 2 figures included

We propose an experiment, based on two consecutive Bragg pulses, to measure the momentum distribution of quasiparticle excitations in a trapped Bose gas at low temperature. With the first pulse one generates a bunch of excitations carrying momentum $q$, whose Doppler line is measured by the second pulse. We show that this experiment can provide direct access to the amplitudes $u_{q}$ and $v_{q}$ characterizing the Bogoliubov transformations from particles to quasiparticles. We simulate the behavior of the nonuniform gas by numerically solving the time dependent Gross-Pitaevskii equation., Comment: 12 pages, 4 figures included

We study the dynamics of two interacting Bose-Einstein condensates, by numerically solving two coupled Gross-Pitaevskii equations at zero temperature. We consider the case of a sudden transfer of atoms between two trapped states with different magnetic moments: the two condensates are initially created with the same density profile, but are trapped into different magnetic potentials, whose minima are vertically displaced by a distance much larger than the initial size of both condensates. Then the two condensates begin to perform collective oscillations, undergoing a complex evolution, characterized by collisions between the two condensates. We investigate the effects of their mutual interaction on the center-of-mass oscillations and on the time evolution of the aspect ratios. Our theoretical analysis provides a useful insight into the recent experimental observations by Maddaloni et al., cond-mat/0003402., Comment: 8 pages, 7 figures, RevTex

We present a superfluid hydrodynamic model for the increase in moment of inertia, $\Delta I$, of molecules rotating in liquid $^4$He. The static inhomogeneous He density around each molecule (calculated using the Orsay-Paris liquid $^4$He density functional) is assumed to adiabatically follow the rotation of the molecule. We find that the $\Delta I$ values created by the viscousless and irrotational flow are in good agreement with the observed increases for several molecules [ OCS, (HCN)$_2$, HCCCN, and HCCCH$_3$ ]. For HCN and HCCH, our model substantially overestimates $\Delta I$. This is likely to result from a (partial) breakdown of the adiabatic following approximation., Comment: 4 pages, 1 eps figure, corrected version of published paper. Erratum has been submitted for changes

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach., Comment: revtex, 69 pages, 38 eps figures, new version with more references, new figures, various changes and corrections, for publ. in Rev. Mod. Phys., available also at http://www-phys.science.unitn.it/bec/BEC.html

A two-photon transition is used to convert an arbitrary fraction of the 87Rb atoms in a |F=1,m_f=-1> condensate to the |F=2,m_f=1> state. Transferring the entire population imposes a discontinuous change on the condensate's mean-field repulsion, which leaves a residual ringing in the condensate width. A calculation based on Gross-Pitaevskii theory agrees well with the observed behavior, and from the comparison we obtain the ratio of the intraspecies scattering lengths for the two states, a_|1,-1> / a_|2,1> = 1.062(12)., Comment: 4 pages, 3 figures

We investigate the behavior of large amplitude oscillations of a trapped Bose-condensed gas of alkali atoms at zero temperature, by solving the equations of hydrodynamics for collective modes. Due to the atom-atom interaction, the equations of motion are nonlinear and give rise to significant frequency shift and mode coupling. We provide analytic expressions for the frequency shift, pointing out the crucial role played by the anisotropy of the confining potential. For special values of the anisotropy parameter the mode coupling is particularly strong and the frequency shift becomes large, revealing a peculiar behavior of the Bose-condensed gas. Consequences on the theory of collapse and revival of collective excitations are also discussed., Comment: 10 pages, RevTeX, 9 figures, more info at http://www-phys.science.unitn.it/bec/BEC.html

The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with the ones of Hartree-Fock theory and of the hydrodynamic model. We show that the Hartree-Fock scheme provides an excellent description of the excitation spectrum in a wide range of energy, revealing a major role played by single-particle excitations in these confined systems. The crossover from the hydrodynamic regime, holding at low energies, to the independent particle regime is explicitly explored by studying the frequency of the surface mode as a function of their angular momentum. The applicability of the semiclassical approximation for the excited states is also discussed. We show that the semiclassical approach provides simple and accurate formulae for the density of states and the quantum depletion of the condensate., Comment: 16 pages, REVTeX, 6 figures; misprints corrected; some clarifying remarks included

We investigate the dynamic behavior of a Bose-condensed gas of alkali atoms interacting with repulsive forces and confined in a magnetic trap at zero temperature. Using the Thomas-Fermi approximation, we rewrite the Gross-Pitaevskii equation in the form of the hydrodynamic equations of superfluids. We present solutions describing large amplitude oscillations of the atomic cloud as well as the expansion of the gas after switching off the trap. We compare our theoretical predictions with the recent experimental data obtained at Jila and MIT., Comment: 5 pages, REVTeX, 4 postscript figures, available also at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

We study the scattering of atoms, rotons and phonons at the free surface of $^4$He at normal incidence and calculate the evaporation, condensation and reflection probabilities. Assuming elastic one-to-one processes and using general properties of the scattering matrix, such as unitarity and time reversal, we argue that all nonzero probabilities can be written in terms of a single energy-dependent parameter. Quantitative predictions are obtained using linearized time dependent density functional theory., Comment: 12 pages, REVTeX, 2 postscript figures, available also at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed., Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

The scattering of atoms and rotons at the free surface of superfluid 4He is studied in the framework of linearised time dependent mean field theory. The phenomenological Orsay-Trento density functional is used to solve numerically the equations of motion for the elementary excitations in presence of a free surface and to calculate the flux of rotons and atoms in the reflection, condensation, and evaporation processes. The probability associated with each process is evaluated as a function of energy, for incident angles such that only rotons and atoms are involved in the scattering. The evaporation probability for R+ rotons is predicted to increase quite rapidly from zero, near the roton minimum, to 1 as the energy increases. Conversely the evaporation from R- rotons remains smaller than 0.25 for all energies. Close to the energy of the roton minimum the mode-change process is the dominant one. The consistency of the results with general properties of the scattering matrix, such as unitarity and time reversal, is explicitly discussed. The condensation of atoms into bulk excitations is also investigated., Comment: Uuencoded file including: REVTEX (35 pages) and 7 figures, also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions., Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

The probability of evaporation induced by $R^+$ and $R^-$ rotons at the surface of superfluid helium is calculated using time dependent density functional theory. We consider excitation energies and incident angles such that phonons do not take part in the scattering process. We predict sizable evaporation rates, which originate entirely from quantum effects. Results for the atomic reflectivity and for the probability of the roton change-mode reflection are also presented., Comment: 11 pages, REVTEX, 3 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

A novel density functional, which accounts correctly for the equation of state, the static response function and the phonon-roton dispersion in bulk liquid helium, is used to predict static and dynamic properties of helium droplets. The static density profile is found to exhibit significant oscillations, which are accompanied by deviations of the evaporation energy from a liquid drop behaviour in the case of small droplets. The connection between such oscillations and the structure of the static response function in the liquid is explicitly discussed. The energy and the wave function of excited states are then calculated in the framework of time dependent density functional theory. The new functional, which contains backflow-like effects, is expected to yield quantitatively correct predictions for the excitation spectrum also in the roton wave-length range., Comment: 15 pages, REVTEX, 10 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

The sum rule approach is used to derive upper bounds for the dispersion law $\omega_0(q)$ of the elementary excitations of a Bose superfluid. Bounds are explicitly calculated for the phonon-roton dispersion in superfluid $^4$He, both at equilibrium ($\rho=0.02186$ \AA$^{-3}$) and close to freezing ($\rho=0.02622$ \AA$^{-3}$). The bound $\omega_0(q) \le 2S(q)\mid\chi(q)\mid^{-1}$, where $S(q)$ and $\chi(q)$ are the static structure factor and density response respectively, is calculated microscopically for several values of the wavevector $q$. The results provide a significant improvement with respect to the Feynman approximation $\omega_F(q)= q^2(2mS(q))^{-1}$. A further, stronger bound, requiring the additional knowledge of the current correlation function is also investigated. New results for the current correlation function are presented., Comment: 13 pages, REVTEX, 7 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.html

We present a novel density functional for liquid 4He, properly accounting for the static response function and the phonon-roton dispersion in the uniform liquid. The functional is used to study both structural and dynamical properties of superfluid helium in various geometries. The equilibrium properties of the free surface, droplets and films at zero temperature are calculated. Our predictions agree closely to the results of ab initio Monte Carlo calculations, when available. The introduction of a phenomenological velocity dependent interaction, which accounts for backflow effects, is discussed. The spectrum of the elementary excitations of the free surface and films is studied., Comment: 37 pages, REVTeX 3.0, figures on request at dalfovo@science.unitn.it

A detailed study of the dispersion law of surface excitations in liquid \hef at zero temperature is presented, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on thick films and explicitly reveal the occurrence of important hybridization effects between ripplons and rotons., Comment: 23 pages, REVTEX 3.0, 11 figures upon request, UTF-326/94

Variational Monte Carlo method is used to calculate ground state properties of $^4$He droplets, containing 70, 112, 168, 240, 330, and 728 particles. The resulting particle and kinetic energy densities are used as an input in the Feynman-Lekner theory for $^3$He impurities. The kinetic energy density of $^4$He atoms and the energy of the $^3$He surface states are compared with the results of previous phenomenological calculations., Comment: 12 pages, in revtex 3.0, with 5 .ps figures

A density functional theory is used to predict the binding energy of atomic and molecular impurities (Ne, Ar, Kr, Xe, Li, Na, K, Rb, Cs, and SF$_6$) in the center of $^4$He clusters, in the limit of zero temperature and for zero angular momentum states. The size dependence of the binding energy, from small clusters to the bulk liquid limit, is investigated. The behaviour of the $^4$He density near the impurity is also studied., Comment: 16 pages (plain TeX), 6 figures (not included), UTF-298

Relevant features of the dynamic structure function $S(q,\omega)$ in $^3$He-$^4$He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to $S(q,\omega)$, coming from $^3$He and $^4$He elementary excitations, as well as to explore the role of the cross term $S^{(3,4)}(q,\omega)$. Both the low-$q$ (phonon-roton $^4$He excitations and 1p-1h $^3$He excitations) and high-$q$ (deep inelastic scattering) ranges are discussed., Comment: 29 pages, Plain TeX, 11 figures available by request from dalfovo@itnvax.cineca.it

The sum rule formalism is used to evaluate rigorous bounds for the density and current static response functions in superfluid helium at zero temperature. Both lower and upper bounds are considered. The bounds are expressed in terms of ground state properties (density and current correlation funtions) and of the interatomic potential. The results for the density static response significantly improve the Feynman approximation and turn out to be close to the experimental (neutron scattering) data. A quantitative prediction for the transverse current response is given. The role of one-phonon and multi-particle excitations in the longitudinal and transverse channels is discussed. (Phys.Rev.B, in press), Comment: 19 pages (plain TeX) and 3 Figures (postscript), UTF-263