We determine the critical Zeeman energy splitting for Fermi superfluidity at infinite s-wave scattering length according to the Monte Carlo and experimental results of the equations of state. Based on the universality hypothesis, we show that there e
xist two critical fields $H_{c1}$ and $H_{c2}$, between which a superfluid-normal mixed phase is energetically favored, and model-independent formulae for $H_{c1}$, $H_{c2}$ and the critical population imbalance $P_c$ are derived. Using recent Monte Carlo and experimental results of $P_c$, $H_{c1}$ and $H_{c2}$ are determined. It is found $H_{c1}=0.41epsilon_{text F}$ and $H_{c2}=0.50epsilon_{text F}$, with $epsilon_{text F}$ being the Fermi energy of non-interacting gas.
Applying the Hellmann-Feynman theorem to a charged pion gas, the quark and gluon condensates at low isospin density are determined by precise pion properties. At intermediate density around $ f_pi^2m_pi$, from both the estimation for the dilute pion
gas and the calculation with Nambu--Jona-Lasinio model, the quark condensate is strongly and monotonously suppressed, while the gluon condensate is enhanced and can be larger than its vacuum value. This unusual behavior of the gluon condensate is universal for Bose condensed matter of mesons. Our results can be tested by lattice calculations at finite isospin density.
We investigate fermionic superconductivity with mismatched Fermi surfaces in a general two-band system. The exchange interaction between the two bands changes significantly the stability structure of the pairing states. The Sarma state with two gaple
ss Fermi surfaces which is always unstable in single-band systems, can be the stable ground state in two-band systems. To realize a visible mismatch window for the stable Sarma state, two conditions should be satisfied: a nonzero inter-band exchange interaction and a large asymmetry between the two bands.
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean field theory, the transition from unpolarized superfluid phase to normal ph
ase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local density approximation exhibits a shell structure, a superfluid core at the center and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is totally in fully polarized state with a density profile depending only on the global population imbalance. The di-fermion bound states can survive in the whole highly imbalanced normal phase.
Based on the analogy between the Nambu--Jona-Lasinio model of chiral symmetry breaking and the BCS theory of superconductivity, we investigate the effect of $bar q q$ pair fluctuations on the chiral phase transition. We include uncondensed $bar q q$
pairs at finite temperature and chemical potential in a self-consistent T-matrix formalism, the so-called $G_0 G$ scheme. The pair fluctuations reduce significantly the critical temperature and make quarks massive above the critical temperature.
