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Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model

Subject:Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model

Speaker:Prof. Andreas Klümper(Wuppertal University)

Time:10:00am,20th Sept.,2016

Place:lecture hall,4F, Pinbiao Building of Institute,WIPM

   

 

Lectures:

10:00am,19th Sept.,2016 Thermodynamic Bethe Ansatz

10:00am,21th Sept.,2016 Qauntum tramsfer matrix method

10:00am,22th Sept.,2016 T-Y systems

10:00am,23th Sept.,2016 Two-component Bosons

 

 

Abstract:

We address the problem of computing the thermodynamic properties of the repulsive one-dimensional two-component Fermi gas with contact interaction (Gaudin-Yang model). We derive an exact system of only two non-linear integral equations for the thermodynamics of the homogeneous model. This system allows for an easy and extremely accurate calculation of thermodynamic properties circumventing the difficulties associated with the truncation of the thermodynamic Bethe ansatz system of equations. We present extensive results for the densities, polarization, magnetic susceptibility, specific heat, interaction energy, Tan contact and local correlation function of opposite spins. Our results show that at low and intermediate temperatures the experimentally accessible contact is a non-monotonic function of the coupling strength. As a function of the temperature the contact presents a pronounced local minimum in the Tonks-Girardeau regime which signals an abrupt change of the momentum distribution in a small interval of temperature. The density profiles of the system in the presence of a harmonic trapping potential are computed using the exact solution of the homogeneous model coupled with the local density approximation. At finite temperature the density profile presents a double shell structure (partially polarized centre and fully polarized wings) only when the polarization in the center of the trap is above a critical value.

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