Inclusive electron scattering in a relativistic Green function approach

A relativistic Green function approach to the inclusive quasielastic (e,e') scattering is presented. The single particle Green function is expanded in terms of the eigenfunctions of the nonhermitian optical potential. This allows one to treat final state interactions consistently in the inclusive and in the exclusive reactions. Numerical results for the response functions and the cross sections for different target nuclei and in a wide range of kinematics are presented and discussed in comparison with experimental data.Comment: 12 pages, 7 figures, REVTeX

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.Comment: 16 pages, 7 figures, revtex

Collective excitations of a trapped boson-fermion mixture across demixing

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.Comment: revtex4, 9 pages, 8 postscript file

Finite temperature effects on the collapse of trapped Bose-Fermi mixtures

By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture.Comment: 5 pages, 4 figures; minor changes, proof version, to appear in Phys. Rev. A (Nov. 1, 2003

Shortcuts to adiabaticity for trapped ultracold gases

We study, experimentally and theoretically, the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose-Einstein condensate which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the atomic sample goes through strongly out-of-equilibrium states while the external confinement is modified until the system reaches the desired stationary state. The scheme is theoretically based on the invariants of motion and scaling equations techniques and can be generalized to decompression trajectories including an arbitrary deformation of the trap. It is also directly applicable to arbitrary initial non-equilibrium states.Comment: 36 pages, 14 figure

Finite temperature excitations of a trapped Bose-Fermi mixture

We present a detailed study of the low-lying collective excitations of a spherically trapped Bose-Fermi mixture at finite temperature in the collisionless regime. The excitation frequencies of the condensate are calculated self-consistently using the static Hartree-Fock-Bogoliubov theory within the Popov approximation. The frequency shifts and damping rates due to the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas are also taken into account by means of the random phase approximation and linear response theory. In our treatment, the dipole excitation remains close to the bare trapping frequency for all temperatures considered, and thus is consistent with the generalized Kohn theorem. We discuss in some detail the behavior of monopole and quadrupole excitations as a function of the Bose-Fermi coupling. At nonzero temperatures we find that, as the mixture moves towards spatial separation with increasing Bose-Fermi coupling, the damping rate of the monopole (quadrupole) excitation increases (decreases). This provides us a useful signature to identify the phase transition of spatial separation.Comment: 10 pages, 8 figures embedded; to be published in Phys. Rev.

Thermodynamics of a Trapped Bose-Fermi Mixture

By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive Bose-Fermi interaction we find a sizable enhancement of the condensate fraction and of the critical temperature of Bose-Einstein condensation with respect to the predictions for a pure interacting Bose gas. Conversely, the influence of the repulsive Bose-Fermi interaction is less pronounced. The possible relevance of our results in current experiments on trapped $^{87}{\rm Rb}-^{40}${\rm K} mixtures is discussed.Comment: 5 pages + 4 figures; minor changes, final version to appear in Phys. Rev. A; the extension work on the finite-temperature low-lying excitations can be found in cond-mat/030763

Analysis of exchange terms in a projected ERPA Theory applied to the quasi-elastic (e,e') reaction

A systematic study of the influence of exchange terms in the longitudinal and transverse nuclear response to quasi-elastic (e,e') reactions is presented. The study is performed within the framework of the extended random phase approximation (ERPA), which in conjuction with a projection method permits a separation of various contributions tied to different physical processes. The calculations are performed in nuclear matter up to second order in the residual interaction for which we take a (pi+rho)-model with the addition of the Landau-Migdal g'-parameter. Exchange terms are found to be important only for the RPA-type contributions around the quasielastic peak.Comment: 29 pages, 6 figs (3 in postscript, 3 faxed on request), epsf.st