37,056 research outputs found
Universal Properties of Fermi Gases in One-dimension
In this Rapid Communication, we investigate the universal properties of a
spin-polarized two-component Fermi gas in one dimension (1D) using Bethe
ansatz. We discuss the quantum phases and phase transitions by obtaining exact
results for the equation of state, the contact, the magnetic susceptibility and
the contact susceptibility, giving a precise understanding of the 1D analogue
of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in
three dimension (3D) and the associated universal magnetic properties. In
particular, we obtain the exact form of the magnetic susceptibility at low temperatures, where is the
energy gap and is the temperature. Moreover, we establish exact upper and
lower bounds for the relation between polarization and the contact for
both repulsive and attractive Fermi gases. Our findings emphasize the role of
the pair fluctuations in strongly interacting 1D fermion systems that can shed
light on higher dimensions.Comment: 4 figures, the main pape
The Lax pair for C_2-type Ruijsenaars-Schneider model
We study the C_2 Ruijsenaars-Schneider(RS) model with interaction potential
of trigonometric type. The Lax pairs for the model with and without spectral
parameter are constructed. Also given are the involutive Hamiltonians for the
system. Taking nonrelativistic limit, we obtain the Lax pair of C_2
Calogero-Moser model.Comment: LaTeX2e, 10 pages, some misprints corrected and sections rearrange
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