We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the dr2−3z2 type in three dimensions and of the dx2−y2 type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the H...

It is well known that, generically, one-dimensional interacting fermions cannot be described in terms of a Fermi liquid. Instead, they present a different phenomenology, that of a Tomonaga-Luttinger liquid: the Landau quasiparticles are ill defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine tuning of the interaction between fermions c...

A phenomenological theory is presented for two-dimensional quantum liquids in terms of the Fermi surface geometry. It is shown that there is a one-to-one correspondence between the properties of an interacting electron system and its corresponding Fermi surface. By doing this, the concept of Fermi surface is generalized to include different topologies. It is shown that for a Fermi liquid the co...

It is argued that the recently observed Fermi liquids in strongly interacting ultracold Fermi gases are adiabatically connected to a projected Fermi gas. This conclusion is reached by constructing a set of Jastrow wavefunctions, following Tan’s observations on the structure of the physical Hilbert space [Annals of Physics 323, 2952 (2008)]. The Jastrow projection merely implements the BethePeie...

Fermi acceleration is a mechanism, first suggested by Enrico Fermi in 1949, to explain heating of particles in cosmic rays. Fermi studied charged particles being reflected by the moving interstellar magnetic field and either gaining or losing energy, depending on whether the ”magnetic mirror” is approaching or receding. In a typical environment, Fermi argued, the probability of a head-on collis...

1. We consider the half-filled Hubbard model with a cutoff forbidding momenta close to the angles of the square shaped Fermi surface. By Renormalization Group methods we find a convergent expansion for the Schwinger function up to exponentially small temperatures. We prove that the system is not a Fermi liquid, but on the contrary it behaves like a Marginal Fermi liquid, a behaviour observed in...

In the non relativistic case, some emphasis has been placed on the question of an appropriate choice of the coefficient λ of the gradient term connected to the kinetic energy. The non relativistic gradient correction λ(∇ρ)2/ρ was initially derived by Weizsäcker [14] with a value λ = 1, whereas the systematic gradient expansion by Kirznits [7, 6] leads to λ = 1/9. In the derivation of Tomishima ...