Energy and structure of dilute hard- and soft-sphere gases

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, such as the variational correlated theory, the Bogoliubov model, and the uniform limit approximation, valid in the weak-interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. Jastrow-type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-sphere potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of x~0.001. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of x. The occurrence of a maximum in the radial distribution function, in the momentum distribution, and in the excitation spectrum is a natural effect of the correlations when x increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach is very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens.

New predictions for inclusive heavy-quarkonium P-wave decays

We show that some nonrelativistic quantum chromodynamics color-octet matrix elements can be written in terms of (derivatives of) wave functions at the origin and of nonperturbative universal constants once the factorization between the soft and ultrasoft scales is achieved by using an effective field theory where only ultrasoft degrees of freedom are kept as dynamical entities. This allows us to derive a new set of relations between inclusive heavy-quarkonium P-wave decays into light hadrons with different principal quantum numbers and with different heavy flavors. In particular, we can estimate the ratios of the decay widths of bottomonium P-wave states from charmonium data.

New predictions for inclusive heavy-quarkonium p-wave decays

We show that some nonrelativistic quantum chromodynamics color-octet matrix elements can be written in terms of (derivatives of) wave functions at the origin and of nonperturbative universal constants once the factorization between the soft and ultrasoft scales is achieved by using an effective field theory where only ultrasoft degrees of freedom are kept as dynamical entities. This allows us to derive a new set of relations between inclusive heavy-quarkonium P-wave decays into light hadrons with different principal quantum numbers and with different heavy flavors. In particular, we can estimate the ratios of the decay widths of bottomonium P-wave states from charmonium data.

Nonlinear Saffman-Taylor instability

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

High-Momentum Response of Liquid 3He

A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid 3He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitly through a new additive term which depends on the semidiagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for good agreement with available deep-inelastic neutron scattering data.

Effective field theories for heavy quarkonium

This article reviews recent theoretical developments in heavy-quarkonium physics from the point of view of effective-field theories of QCD. We discuss nonrelativistic QCD and concentrate on potential nonrelativistic QCD. The main goal will be to derive Schrödinger equations based on QCD that govern heavy-quarkonium physics in the weak- and strong-coupling regimes. Finally, the review discusses a selected set of applications, which include spectroscopy, inclusive decays, and electromagnetic threshold production.

External Fluctuations in Front Propagation

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Precision determination of r(0)Lambda((MS)over-bar) from the QCD static energy

We use the recently obtained theoretical expression for the complete QCD static energy at next-to-next-to-next-to leading-logarithmic accuracy to determine r(0)Lambda((MS) over bar) by comparison with available lattice data, where r(0) is the lattice scale and Lambda((MS) over bar) is the QCD scale. We obtain r(0)Lambda((MS) over bar) = 0.622(-0.015)(+0.019) for the zero-flavor case. The procedure we describe can be directly used to obtain r(0)Lambda((MS) over bar) in the unquenched case, when unquenched lattice data for the static energy at short distances becomes available. Using the value of the strong coupling alpha(s) as an input, the unquenched result would provide a determination of the lattice scale r(0).

Collective and single-particle excitations of a trapped Bose gas

The density of states of a Bose-condensed gas confined in a harmonic trap is investigated. The predictions of Bogoliubov theory are compared with those 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 formulas for the density of states and the quantum depletion of the condensate.

Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.

Off-axis vortices in trapped Bose-condensed gases: Angular momentum and frequency splitting

We consider noncentered vortices and their arrays in a cylindrically trapped Bose-Einstein condensate at zero temperature. We study the kinetic energy and the angular momentum per particle in the Thomas-Fermi regime and their dependence on the distance of the vortices from the center of the trap. Using a perturbative approach with respect to the velocity field of the vortices, we calculate, to first order, the frequency shift of the collective low-lying excitations due to the presence of an off-center vortex or a vortex array, and compare these results with predictions that would be obtained by the application of a simple sum-rule approach, previously found to be very successful for centered vortices. It turns out that the simple sum-rule approach fails for off-centered vortices.

Relevance of dynamic wetting in viscous fingering patterns

We demonstrate that wetting effects at moving contact lines have a strong impact in viscous fingering patterns. Experiments in a rotating Hele-Shaw (HS) cell, dry or prewetted, show consistent morphological differences. When the wetting fluid invades a dry region, contact angle dynamics yield a kinetic contribution to the interface pressure drop that scales with capillary number as Ca2¿3 but is significantly larger than the Park-Homsy kinetic correction. Numerical results are in very good agreement with experiments and show that standard HS equations work best for prewetted cells.

Semiclassical coupled wave theory and its application to TE waves in one dimensional crystals

A semiclassical coupled-wave theory is developed for TE waves in one-dimensional periodic structures. The theory is used to calculate the bandwidths and reflection/transmission characteristics of such structures, as functions of the incident wave frequency. The results are in good agreement with exact numerical simulations for an arbitrary angle of incidence and for any achievable refractive index contrast on a period of the structure.

Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate

We have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.