Abstract
We develop new gauge-covariant implicit numerical schemes for classical real-time lattice gauge theory. A new semi-implicit scheme is used to cure a numerical instability encountered in three-dimensional classical Yang-Mills simulations of heavy-ion collisions by allowing for wave propagation along one lattice direction free of numerical dispersion. We show that the scheme is gauge covariant and that the Gauss constraint is conserved even for large time steps.
Highlights
Color Glass Condensate (CGC) effective theory [1] applies classical Yang-Mills theory to the area of high energy heavyion collisions
The treatment of these color charges is closely related to the colored particle-in-cell (CPIC) method [24,25], which is a nonAbelian extension of the particle-in-cell (PIC) method [26] commonly used in (Abelian) plasma simulations
It turns out that using a discrete variational principle to derive numerical schemes for equations of motion is a very powerful tool: the use of time-averaged expressions in the discrete action yields implicit and semi-implicit schemes depending on how exactly the time-averaging is performed and what terms are replaced by their averages
Summary
Color Glass Condensate (CGC) effective theory [1] applies classical Yang-Mills theory to the area of high energy heavyion collisions. The numerical scheme in these simulations is based on the standard Wilson gauge action with the fields coupled to external color currents The treatment of these color charges is closely related to the colored particle-in-cell (CPIC) method [24,25], which is a nonAbelian extension of the particle-in-cell (PIC) method [26] commonly used in (Abelian) plasma simulations. Improving the resolution postpones the problem at the cost of much higher computational resources We realize that this instability is due to numerical dispersion on the lattice inherent to the leapfrog scheme, which renders the dispersion relation of plane waves non-linear.
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