Energy weighted sum rules for mesons in hot and dense matter

We study energy weighted sum rules of the pion and kaon propagator in nuclear matter at finite temperature. The sum rules are obtained from matching the Dyson form of the meson propagator with its spectral Lehmann representation at low and high energies. We calculate the sum rules for specific models of the kaon and pion self-energy. The in-medium spectral densities of the K and anti-K mesons are obtained from a chiral unitary approach in coupled channels which incorporates the S- and P-waves of the kaon-nucleon interaction. The pion self-energy is determined from the P-wave coupling to particle-hole and Delta-hole excitations, modified by short range correlations. The sum rules for the lower energy weights are fulfilled satisfactorily and reflect the contributions from the different quasi-particle and collective modes of the meson spectral function. We discuss the sensitivity of the sum rules to the distribution of spectral strength and their usefulness as quality tests of model calculations.Comment: 19 pages, 6 figures; one figure added, enhanced discussion, version to appear in PR

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

Microscopic calculation of the phonon-roton branch in superfluid 4^4He

Diffusion Monte Carlo results for the phonon-roton excitation branch in bulk liquid $^4$He at zero temperature are presented. The sign problem associated to the excited wave function has been dealt both with the fixed-node approximation and the released-node technique. The upper bounds provided by the fixed-node approximation are shown to become exact when using the released-node method. An excellent agreement with experimental data is achieved both at the equilibrium and near the freezing densities.Comment: 12 pages, RevTex, 3 ps figures include

Ground state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\sim 0.001$. The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same $x$.Comment: Submitted to PRA. 7 pages and 8 figure

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

Bose-Einstein Condensation in liquid 4^4He near the liquid-solid transition line

We present precision neutron scattering measurements of the Bose-Einstein condensate fraction, n0(T), and the atomic momentum distribution, n\star(k), of liquid 4He at pressure p =24 bar. Both the temperature dependence of n0(T) and of the width of n\star(k) are determined. The n0(T) can be represented by n0(T) = n0(0)[1-(T/T{\lambda}){\gamma}] with a small n0(0) = 2.80\pm0.20% and large {\gamma} = 13\pm2 for T < T{\lambda} indicating strong interaction. The onset of BEC is accompanied by a significant narrowing of the n\star(k). The narrowing accounts for 65% of the drop in kinetic energy below T{\lambda} and reveals an important coupling between BEC and k > 0 states. The experimental results are well reproduced by Path Integral Monte Carlo calculations.Comment: 4 Pages, 5 Figure

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