Abstract

Relativistic hydrodynamics has been used to study collective behavior of light particles produced in heavy ion collisions. It has been shown that hydrodynamic calculations with a small shear viscosity give results that agree well with experimental data. Furthermore, a holographic calculation showed that the ratio of shear viscosity and entropy density is as small as 1/(4pi) for strongly coupled N=4 supersymmetric Yang-Mills theory, which is consistent with the value extracted from experimental data via hydrodynamic simulations. On the other hand, calculating shear viscosity in QCD is very challenging: Perturbative calculations are not applicable in the temperature range of interest and Euclidean lattice QCD calculations have uncontrolled systematic uncertainties caused by the ill-defined spectral reconstruction problem. In this talk, I will discuss the Hamiltonian lattice approach which enables nonperturbative real-time calculations. I will take the 2+1D SU(2) pure gauge theory as an example and show some results obtained on a small lattice, which include the emergence of a diffusive mode on a plaquette chain and the ratio of shear viscosity and entropy density on a honeycomb lattice. Finally I will discuss some quantum algorithms for these observables, which may help us to perform calculations on bigger lattices.