Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.     

Application of green functions to finite Fermi systems with fixed numbers of particles and strong pairing

The single-particle Green function formalism (Gor’kov’s method) is applied to calculate the energies of finite superconducting Fermi systems with a finite number of particles. It is shown that strong pairing leads to equations similar to those from the Bardeen-Cooper-Schrieffer theory.     

Fluctuations in transitional regions of finite Fermi systems

Transitional regions are investigated of models describing finite Fermi systems which give rise to phase transitions. The emphasis lies on the connection between the pattern of the exceptional points of the Hamiltonian and fluctuations induced by multiple level crossings. It is found that the Lipkin model produces no fluctuations in the transitional region. Fluctuations emerge when deviations from the Lipkin model are considered.     

Merging of single-particle levels in finite Fermi systems

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate. The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied. In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations. Implications of this finding are discussed for nuclear, solid-state, and atomic systems. The text was submitted by the authors in English.     

Competition between paramagnetism and diamagnetism in charged Fermi gases

The charged Fermi gas with a small Lande-factor g is expected to be diamagnetic, while that with a larger g could be paramagnetic. We calculate the critical value of the g-factor which separates the dia- and paramagnetic regions. In the weak-field limit, gc has the same value both at high and low temperatures, . Nevertheless, gc increases with the temperature reducing in finite magnetic fields. We also compare the gc value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels σ=±1,0, and find that gc of Bose and Fermi gases is larger and smaller than that of Boltzmann gases, respectively.     

Some problems in the generalized theory of finite Fermi systems

A realistic version of the generalization of the theory of finite Fermi systems to the case where some complex configurations involving phonons are explicitly taken into account is proposed. Secular equations describing the fragmentation of simple states in odd and even-even nuclei over complex configurations that belong to, respectively, the quasiparticle ? phonon + quasiparticle ? phonon ? phonon and the two quasiparticles ? phonon type and which are presently of greatest interest are derived on the basis of general relations for nuclei that involve pairing (nonmagic nuclei). These equations take into account effects associated with ground-state correlations due to complex configurations and with the additional quasiparticle-phonon mechanism of Cooper pairing in nuclei. The effects in question were disregarded previously, but they are of interest since they can be observed in present-day experiments.     

Exchange enhanced spin fluctuations in Fermi systems of finite thickness

The local spin susceptibility of an almost-ferromagnetic system of finite thickness is computed in the R.P.A. In contrasst to recent studies, it is shown that if one uses an exchange interaction with a finite range λ (of order λ_F), the exchange-enhancement of the magnetization is smaller at the surface than in the bulk.     

Self-consistent theory of finite Fermi systems and radii of nuclei

Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ _ch(r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.     

Merging of single-particle levels and non-Fermi-liquid behavior of finite Fermi systems

We examine the problem of finite Fermi systems having a degenerate single-particle spectrum and show that the Landau approach, applied to such a system, admits the possibility of merging single-particle levels. It is demonstrated that the opportunity for this behavior is widespread in quantum many-body systems. The salient feature of the phenomenon is the occurrence of nonintegral quasiparticle occupation numbers, leading to a radical alteration of the standard quasiparticle picture. Implications of this alteration are considered for nuclear, atomic, and solid-state systems.     

Raman coupling and cooper pairing in cold atomic Fermi gases

We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hainan coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.     

Pair fluctuations in ultra-small Fermi systems within self-consistent RPA at finite temperature

A self-consistent version of the thermal random phase approximation (TSCRPA) is developed within the Matsubara Green’s function (GF) formalism. The TSCRPA is applied to the many level pairing model. The normal phase of the system is considered. The TSCRPA results are compared with the exact ones calculated for the Grand Canonical Ensemble. Advantages of the TSCRPA over the thermal mean field approximation (TMFA) and the standard thermal random phase approximation (TRPA) are demonstrated. Results for correlation functions, excitation energies, single particle level densities, etc., as a function of temperature are presented.     

A renormalization procedure for the correlation function theory of finite Fermi systems

The quasiparticle renormalization of symmetrized correlation functions is treated in the framework of the double-time Green function theory of many body systems. The work is based on the Mori-theory of response functions transcribed for symmetrized correlation functions. For the specific example of finite Fermi systems it is shown that the physical situation assumed in the quasiparticle-quasihole renormalization of the many-time Green function theory allows to define an equivalent renormalization procedure for correlation functions. This procedure uses projection operator techniques and is therefore of purely algebraic nature.     

Competition between the Coulomb and phonon fields: superconductivity in a quiescent Fermi gas

Co-existence of and competition between the screened Coulomb and phonon fields are fundamental facts in superconductors. In the conventional superconductors the strong screening greatly suppresses the Coulomb interaction and the phonon field that mediates a given attractive interaction between electrons may thus play a leading role. A quiescent Fermi sea hence applies, as proposed by Cooper and adopted in BCS.In this model a graphical derivative technique, based on Ward's identity, is developed to consider the contributions to the interparticle interaction. This technique allows one to evaluate the effective two-particle interaction (T-matrix). It is shown that the conventional Cooper instability in a quiescent Fermi gas is only caused by agivenattractive interaction. Of more importance is that the methodology presented in this work can be extended to the investigation of the intermediate and strong coupling cases where the well-known Migdal theorem is not applicable and the vertex corrections must be evaluated.