Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions

摘要

We study the dependence of the electric conductivity on chemical potential in finite-density S U ( 2 ) gauge theory with N f = 2 flavors of rooted staggered sea quarks, in combination with Wilson-Dirac and domain-wall valence quarks. The pion mass is reasonably small with m π / m ρ ≈ 0.4 . We concentrate in particular on the vicinity of the chiral crossover, where we find the low-frequency electric conductivity to be most sensitive to small changes in fermion density. Working in the low-density QCD-like regime with spontaneously broken chiral symmetry, we obtain an estimate of the first nontrivial coefficient c ( T ) of the expansion of conductivity σ ( T , μ ) = σ ( T , 0 ) ( 1 + c ( T ) ( μ / T ) 2 + O ( μ 4 ) ) in powers of μ , which has rather weak temperature dependence and takes its maximal value c ( T ) ≈ 0.10 ± 0.07 around the critical temperature. At larger densities and lower temperatures, the conductivity quickly grows toward the diquark condensation phase and also becomes closer to the free-quark result. As a by-product of our study we confirm the conclusions of previous studies with heavier pion that for S U ( 2 ) gauge theory the ratio of crossover temperature to pion mass T c / m π ≈ 0.4 at μ = 0 is significantly smaller than in real QCD.