@incollection{statphys23_0580,
        title = {One-Dimensional $\delta$-Function Fermi Gases with Imbalanced Spin Populations},
        address = {Genova, Italy},
        author = {T. Iida and M. Wadati},
        booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
        editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
        month = {9-13 July},
        year = 2007,
        url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=580},
        abstract = {The possibility to access the predicted crossover between
 Bardeen-Cooper-Schrieffer (BCS) superfluidity of momentum pairs and
 Bose-Einstein condensation (BEC) of molecules has been exploited in the
 ultra cold atom systems with tunable inter-atomic interaction via
 Feshbach resonance.  More recently, experimental studies of an atomic Fermi gas
 with unequal numbers of two components have attracted much 
 attention of physicists related to many fundamental problems in quantum
 physics.  

 In this presentation, we would like to report an exact analysis of
 one-dimensional integrable two-component Fermi gas with arbitrary spin
 polarization at zero temperature. Rigorously speaking, neither the BCS state nor the BEC
 state occurs in one-dimension. However, the quasi-one 
 dimensional experimental settings are possible and realized in
 laboratory, and for integrable models we have a theoretical advantage
 of analyzing the physical properties by using the Bethe ansatz
 method. 

 We discuss a one-dimensional integrable systems of $N$ spin-$1/2$
 Fermi gas with either attractive or repulsive $\delta$-function
 interaction at zero temperature. 
 The ground state with arbitrary spin
 polarization (i.e., for all $0\le S\le N/2$, where 
 $S$ is the total spin) is characterized by the sets of integral 
 equations; the Gaudin integral equation for the attractive case and the
 Yang integral equation for the repulsive case. They determine the
 distribution of quasi-momenta and that of spin rapidities. 
 We analytically investigate these integral equations with arbitrary
 spin polarization. The first few terms of the 
 asymptotic expansions of the distribution functions are calculated 
 explicitly for both strong and weak coupling cases. 
 In the weakly attractive case, BCS-like paired fermions and unpaired  
 separate in the quasi-momentum space. This property remains with a 
 weakly repulsive interaction. On the other hand, in the strongly 
 attractive case, bound pairs of fermions behave like hard core bosons.   
 We further 
 study some physical quantities, such as the ground state energy and the
 chemical potentials, as functions of the coupling constant and the
 polarization. These expressions are valid for all values of $S$. 

 The method of solution and the
 detail of the results are found in [1] and [2].   \\
 
References\\

1) T. Iida and M. Wadati, J. Phys. Soc. Jpn. \textbf{74} 1724 (2005). \\
\phantom{[1]}\  M. Wadati and T. Iida, Phys. Lett. A \textbf{360} 423 (2007).

2)  T. Iida and M. Wadati, J. Low. Temp. Phys., in press. \\
\phantom{[2]}\ T. Iida and M. Wadati, in preparation.},
	biburl = {http://www.bibsonomy.org/bibtex/2d974e36389db93c02fbb6308ddaa9b87/statphys23},
	keywords = {systems gas topic-1 yang nested gaudin equation statphys23 one-dimensional integrable integral}
}