We present a lattice QCD calculation of the charge diffusion coefficient, the electrical conductivity and various susceptibilities of conserved charges, for a range of temperatures below and above the deconfinement crossover. The calculations include the contributions from up, down and strange quarks. We find that the diffusion coefficient is of the order of 1/(2πT ) and has a dip around the crossover temperature. Our results are obtained with lattice simulations containing 2+1 dynamical flavours on anisotropic lattices. The Maximum Entropy Method is used to construct spectral functions from correlators of the conserved vector current.

A lattice calculation is presented for the electrical conductivity σ of the QCD plasma with 2+1 dynamical flavors at nonzero temperature. We employ the conserved lattice current on anisotropic lattices using a tadpole-improved clover action and study the behavior of the conductivity over a wide range of temperatures, both below and above the deconfining transition. The conductivity is extracted from a spectral-function analysis using the maximal entropy method, and a discussion of its systematics is provided. We find an increase of σ/T across the transition.

We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential µ and temperature T . We find evidence of a superfluid phase at intermediate µ and low T where the quark number density and diquark condensate are both very well described by a Fermi sphere of nearly-free quarks disrupted by a BCS condensate. Our results suggest that the quark contribution to the energy density is negative (and balanced by a positive gauge contribution), although this result is highly sensitive to details of the energy renormalisation. We also find evidence that the chiral condensate in this region vanishes in the massless limit. This region gives way to a region of deconfined quark matter at higher T and µ, with the deconfinement temperature, determined from the renormalised Polyakov loop, decreasing only very slowly with increasing chemical potential. The quark number susceptibility χq does not exhibit any qualitative change at the deconfinement transition. We argue that this is because χq is not an appropriate measure of deconfinement for 2-color QCD at high density.

Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker-Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected. *