V. P. Aleshin
The main result of this study consists in working out a microscopic description of collective motion in hot nuclei, allowing to express the parameters of a phenomenological collective model in terms of nucleonic quantities.
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A microscopic theory is presented for identifying shape-phase structures and transitions in interacting fermion systems. The method provides a microscopic description for collective shape-phases, and reveals detailed dependence of such shape-phases on microscopic interaction strengths. The theory is generally applicable to fermion systems such as nuclei, quarks, and in particular trapped cold atoms, where shape-phases may be observed and investigated in a controlled manner.
The nuclear collective excitations are studied within Landau Fermi liquid theory. By using the nucleon-nucleon interaction of the linear sigma-omega model, the nuclear collective excitation energies of different values of $l$ are obtained, which are fitted with the centroid energies of the giant resonances of spherical nuclei, respectively. In addition, it is pointed out that the isovector giant resonances except l=1 correspond to the modes that protons are in the creation state and neutrons are in the annihilation state, and vice versa. Some mixtures of the nuclear collective excitation state…
Isoscalar collective modes in a relativistic meson-nucleon system are investigated in the framework of the time-dependent Thomas-Fermi method. The energies of the collective modes are determined by solving consistently the dispersion relations and the boundary conditions. The energy weighted sum rule satisfied by the model allows the identification of the giant ressonances. The percentage of the energy weighted sum rule exhausted by the collective modes is in agreement with experimental data, but the energies come too high.
The collective excitation of nuclear matter is analyzed in a bosonized Landau Fermi liquid model. When the nonlinear self-interacting terms of scalar mesons are included in Walecka model, the collective excitation energy of nuclear matter can be obtained self-consistently, and the calculation results are consistent with the corresponding experimental data of the nucleus ${}^{208}Pb$ when the quantum number of the orientation of the total spin $m$ is zero. The cases with the nonzero $m$ values are also studied, and it is found that the collective excitation energy of nuclear matter decreases wi…
At finite temperature, the hydrodynamic collective modes of superfluid trapped Fermi gases are coupled to the motion of the normal component, which in the BCS limit behaves like a collisionless normal Fermi gas. The coupling between the superfluid and the normal components is treated in the framework of a semiclassical transport theory for the quasiparticle distribution function, combined with a hydrodynamic equation for the collective motion of the superfluid component. We develop a numerical test-particle method for solving these equations in the linear response regime. As a first applicatio…
We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas-Fermi-von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler-Lagrange equations of a Thomas-Fermi-von Weizsacker action functional. Finally, we show that this amazing Fermi ga…
We study the effects of superfluidity on the monopole and quadrupole collective excitations of a dilute ultra-cold Fermi gas with an attractive interatomic interaction. The system is treated fully microscopically within the Bogoliubov-de Gennes and quasiparticle random-phase approximation methods. The dependence on the temperature and on the trap frequency is analyzed and systematic comparisons with the corresponding hydrodynamic predictions are presented in order to study the limits of validity of the semiclassical approach.
We compute the shear viscosity of a two dimensional Fermi gas interacting via a short range potential with scattering length $a_{2d}$ in kinetic theory. We find that kinetic theory predicts that the shear viscosity to entropy density ratio of a strongly interacting two dimensional gas is comparable to that of the three dimensional unitary gas. We use our results to compute the damping of collective modes in a trapped Fermi gas, and compare to experimental data recently obtained in E. Vogt et al., arXiv:1111.1173.
Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Representative results showing the convergence of Kohn-Sham calculations at zero temperature in the…
We consider the low energy collective mode spectrum of a superfluid Fermi gas in a spherical trap in the collisionless regime. Using a self-consistent random-phase approximation, the effects of superfluidity on modes of dipole and quadrupole symmetries are systematically examined. The spectrum is calculated for varying pairing strength and temperature and we identify several spectral features such as the emergence of Goldstone modes that can be used to detect the onset of superfluidity. Our analysis is relevant for present experiments aimed at observing a superfluid phase transition in trapped…
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