arXiv subjects
Publications and source records attributed to J. E. Hetrick.
We conclude our analysis of the N_t=6 equation of state for two flavor QCD, first described at last year's conference. We have obtained new runs at am_q=0.025 and improved runs at am_q=0.0125. The results are extrapolated to m_q=0, and we extract the speed of sound as well. We also present evidence for a restoration of the SU(2) X SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry.
Two-dimensional QED with $N$ flavor fermions is solved at zero and finite temperature with arbitrary fermion masses to explore QCD physics such as chiral condensate and string tension. The problem is reduced to solving a Schrödinger equation for $N$ degrees of freedom with a specific potential determined by the ground state of the Schrödinger problem itself.
The Schwinger model (QED_2) with N flavors of massive fermions on a circle of circumference L, or equivalently at finite temperature T, is reduced to a quantum mechanical system of N-1 degrees of freedom. With degenerate fermion masses (m) the chiral condensate develops a cusp singularity at $θ=\pm π$ in the limit L -> $\infty$ or T -> 0, which is removed by a large asymmetry in the fermion masses. Physical quantities sensitively depend on the parameter mL or m/T, and the m -> 0 and L -> $\infty$ (or T -> 0) limits do not commute. A detailed analysis is given for N=3.
We improve the calculation of the equation of state for two flavor QCD by simulating on $N_t=6$ lattices at appropriate values of the couplings for the deconfinement/chiral symmetry restoration crossover. For $am_q=0.0125$ the energy density rises rapidly to approximately 1 ${\rm GeV/fm^3}$ just after the crossover($m_π/m_ρ\approx 0.4$ at this point). Comparing with our previous result for $N_t=4$~\cite{eos}, we find large finite $N_t$ corrections as expected from free field theory on finite lattices. We also provide formulae for extracting the speed of sound from the measured quantities.
QED with N species of massive fermions on a circle of circumference L is analyzed by bosonization. The problem is reduced to the quantum mechanics of the 2N fermionic and one gauge field zero modes on the circle, with nontrivial interactions induced by the chiral anomaly and fermions masses. The solution is given for N=2 and fermion masses (m) much smaller than the mass of the U(1) boson with mass μ=\sqrt{2e^2/π} when all fermions satisfy the same boundary conditions. We show that the two limits m \go 0 and L \go \infty fail to commute and that the behavior of the theory critically depends on the value of mL|\cos\onehalfθ| where θis the vacuum angle parameter. When the volume is large μL \gg 1, the fermion condensate <\psibar ψ> is -(e^{4γ} mμ^2 \cos^4\onehalfθ/4π^3)^{1/3} or $-2e^γmμL \cos^2 \onehalfθ/π^2 for mL(μL)^{1/2} |\cos\onehalfθ| \gg 1 or \ll 1, respectively. Its correlation function decays algebraically with a critical exponent η=1 when m\cos\onehalfθ=0.