Condensate fraction in liquid 4He at zero temperature

We present results of the one-body density matrix (OBDM) and the condensate fraction n_0 of liquid 4He calculated at zero temperature by means of the Path Integral Ground State Monte Carlo method. This technique allows to generate a highly accurate approximation for the ground state wave function Psi_0 in a totally model-independent way, that depends only on the Hamiltonian of the system and on the symmetry properties of Psi_0. With this unbiased estimation of the OBDM, we obtain precise results for the condensate fraction n_0 and the kinetic energy K of the system. The dependence of n_0 with the pressure shows an excellent agreement of our results with recent experimental measurements. Above the melting pressure, overpressurized liquid 4He shows a small condensate fraction that has dropped to 0.8% at the highest pressure of p = 87 bar.Comment: 12 pages. 4 figures. Accepted for publication on "Journal of Low Temperature Physics

Path Integral Monte Carlo study of phonons in the bcc phase of 4^4He

Using Path Integral Monte Carlo and the Maximum Entropy method, we calculate the dynamic structure factor of solid $^4$He in the bcc phase at a finite temperature of T = 1.6 K and a molar volume of 21 cm$^3$. Both the single-phonon contribution to the dynamic structure factor and the total dynamic structure factor are evaluated. From the dynamic structure factor, we obtain the phonon dispersion relations along the main crystalline directions, [001], [011] and [111]. We calculate both the longitudinal and transverse phonon branches. For the latter, no previous simulations exist. We discuss the differences between dispersion relations resulting from the single-phonon part vs. the total dynamic structure factor. In addition, we evaluate the formation energy of a vacancy.Comment: 10 figure

Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated'' random--phase approximation (CRPA), our approach has the following properties: i) The CRPA is reproduced when pair fluctuations are neglected. ii) The first two energy--weighted sumrules are fulfilled implying a correct static structure. iii) No ad--hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the roton in 3He. iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug. 2006, Kyoto, Japa

A Wave Function Describing Superfluidity in a Perfect Crystal

We propose a many-body wave function that exhibits both diagonal and off-diagonal long-range order. Incorporating short-range correlations due to interatomic repulsion, this wave function is shown to allow condensation of zero-point lattice vibrations and phase rigidity. In the presence of an external velocity field, such a perfect crystal will develop non-classical rotational inertia, exhibiting the supersolid behavior. In a sample calculation we show that the superfluid fraction in this state can be as large as of order 0.01 in a reasonable range of microscopic parameters. The relevance to the recent experimental evidence of a supersolid state by Chan and Kim is discussed.Comment: final version to be published in Journal of Statistical Mechanics: Theory and Experimen

Beyond the binary collision approximation for the large-qq response of liquid 4^4He

We discuss corrections to the linear response of a many-body system beyond the binary collision approximation. We first derive for smooth pair interactions an exact expression of the response $\propto 1/q^2$, considerably simplifying existing forms and present also the generalization for interactions with a strong, short-range repulsion. We then apply the latter to the case of liquid $^4$He. We display the numerical influence of the $1/q^2$ correction around the quasi-elastic peak and in the low-intensity wings of the response, far from that peak. Finally we resolve an apparent contradiction in previous discussions around the fourth order cumulant expansion coefficient. Our results prove that the large-$q$ response of liquid $^4$He can be accurately understood on the basis of a dynamical theory.Comment: 19 p. Figs. available on reques

Layer- and bulk roton excitations of 4He in porous media

We examine the energetics of bulk and layer-roton excitations of 4He in various porous medial such as aerogel, Geltech, or Vycor, in order to find out what conclusions can be drawn from experiments on the energetics about the physisorption mechanism. The energy of the layer-roton minimum depends sensitively on the substrate strength, thus providing a mechanism for a direct measurement of this quantity. On the other hand, bulk-like roton excitations are largely independent of the interaction between the medium and the helium atoms, but the dependence of their energy on the degree of filling reflects the internal structure of the matrix and can reveal features of 4He at negative pressures. While bulk-like rotons are very similar to their true bulk counterparts, the layer modes are not in close relation to two-dimensional rotons and should be regarded as a third, completely independent kind of excitation

Theoretical study of the dynamic structure factor of superfluid 4He

We study the dynamic structure factor $S(\vec{q},\omega)$ of superfluid 4He at zero temperature in the roton momentum region and beyond using field-theoretical Green's function techniques. We start from the Gavoret-Nozi\`{e}res two-particle propagator and introduce the concept of quasiparticles. We treat the residual (weak) interaction between quasiparticles as being local in coordinate space and weakly energy dependent. Our quasiparticle model explicitly incorporates the Bose-Einstein condensate. A complete formula for the dynamic susceptibility, which is related to $S (\vec{q},\omega)$, is derived. The structure factor is numerically calculated in a self-consistent way in the special case of a momentum independent interaction between quasiparticles. Results are compared with experiment and other theoretical approaches.Comment: 17 pages, 16 figure

The free surface of superfluid 4He at zero temperature

The structure and energetics of the free surface of superfluid $^4$He are studied using the diffusion Monte Carlo method. Extending a previous calculation by Vall\'es and Schmidt, which used the Green's function Monte Carlo method, we study the surface of liquid $^4$He within a slab geometry using a larger number of particles in the slab and an updated interatomic potential. The surface tension is accurately estimated from the energy of slabs of increasing surface density and its value is close to one of the two existing experimental values. Results for the density profiles allow for the calculation of the surface width which shows an overall agreement with recent experimental data. The dependence on the transverse direction to the surface of other properties such as the two-body radial distribution function, structure factor, and one-body density matrix is also studied. The condensate fraction, extracted from the asymptotic behavior of the one-body density matrix, shows an unambiguous enhancement when approaching the surface.Comment: RevTex, 11 pages, accepted in Phys. Rev.

Dynamics of liquid 4He in Vycor

We have measured the dynamic structure factor of liquid 4He in Vycor using neutron inelastic scattering. Well-defined phonon-roton (p-r) excitations are observed in the superfluid phase for all wave vectors 0.3 < Q < 2.15. The p-r energies and lifetimes at low temperature (T = 0.5 K) and their temperature dependence are the same as in bulk liquid 4He. However, the weight of the single p-r component does not scale with the superfluid fraction (SF) as it does in the bulk. In particular, we observe a p-r excitation between T_c = 1.952 K, where SF = 0, and T_(lambda)=2.172 K of the bulk. This suggests, if the p-r excitation intensity scales with the Bose condensate, that there is a separation of the Bose-Einstein condensation temperature and the superfluid transition temperature T_c of 4He in Vycor. We also observe a two-dimensional layer mode near the roton wave vector. Its dispersion is consistent with specific heat and SF measurements and with layer modes observed on graphite surfaces.Comment: 3 pages, 4 figure