We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension.Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as a Luttinger liquid.Instead, the non-relativistic Fermi gas with infinite point-like repulsion becomes the universal model for the long-wavelength, low temperature physics of the one-dimensional electrons.This model, which we call the impenetrable electron gas, allows for a rigorous mathematical treatment.In particular, a so-called determinant representation for the two particle Green function could be derived.This determinant representation is related to an integrable classical evolution equation and to a Riemann-Hilbert problem, that enable the exact calculation of the asymptotics of the two-particle Green functions.We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension.Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as a Luttinger liquid.Instead, the non-relativistic Fermi gas with infinite point-like repulsion becomes the universal model for the long-wavelength, low temperature physics of the one-dimensional electrons.This model, which we call the impenetrable electron gas, allows for a rigorous mathematical treatment.In particular, a so-called determinant representation for the two particle Green function could be derived.This determinant representation is related to an integrable classical evolution equation and to a Riemann-Hilbert problem, that enable the exact calculation of the asymptotics of the two-particle Green functions.

arXiv:cond-mat/0007327CRM proceedings & lecture notesMar 1, 20020 citations

Bulk and collective properties of a dilute Fermi gas in the BCS-BEC crossover

Nicola Manini, Luca Salasnich

We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure, and the sound velocity. In addition, by using a time-dependent density functional approach, we determine the collective modes of the Fermi gas under harmonic confinement. The calculated collective frequencies are compared to experimental data on confined vapors of $^{6}\mathrm{Li}$ atoms and with other theoretical predictions.We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure, and the sound velocity. In addition, by using a time-dependent density functional approach, we determine the collective modes of the Fermi gas under harmonic confinement. The calculated collective frequencies are compared to experimental data on confined vapors of $^{6}\mathrm{Li}$ atoms and with other theoretical predictions.

arXiv:cond-mat/0407039Physical Review AMar 23, 2005167 citations

^{6}\mathrm{Li}

atoms and with other theoretical predictions.