Abstract
We solve the coupled Wong Yang–Mills equations for both U(1) and SU(2) gauge groups and anisotropic particle momentum distributions numerically on a lattice. For weak fields with initial energy density much smaller than that of the particles we confirm the existence of plasma instabilities and of exponential growth of the fields which has been discussed previously. Also, the SU(2) case is qualitatively similar to U(1), and we do find significant “abelianization” of the non-Abelian fields during the period of exponential growth. However, the effect nearly disappears when the fields are strong. This is because of the very rapid isotropization of the particle momenta by deflection in a strong field on time scales comparable to that for the development of Yang–Mills instabilities. This mechanism for isotropization may lead to smaller entropy increase than collisions and multiplication of hard gluons, which is interesting for the phenomenology of high-energy heavy-ion collisions.
Highlights
We solve the coupled Wong Yang-Mills equations for both U (1) and SU (2) gauge groups and anisotropic particle momentum distributions numerically on a lattice
If the presence of the soft classical field is neglected, which amounts to assuming that Qs ∼ ΛQCD, the timeevolution of the hard partons after they come on-shell can be studied by means of the Boltzmann equation with a collision kernel, which is the so-called parton-cascade approach [3, 4]
Because of abelianization, non-Abelian effects should not cause instabilities to saturate; rather, to the Abelian case, the fields should continue to grow until their energy density becomes comparable to that of the hard modes [13, 14, 15], i.e. until the growing fields begin to have a significant effect on the dynamics of the particles
Summary
We solve the coupled Wong Yang-Mills equations for both U (1) and SU (2) gauge groups and anisotropic particle momentum distributions numerically on a lattice. Because of abelianization, non-Abelian effects should not cause instabilities to saturate; rather, to the Abelian case, the fields should continue to grow until their energy density becomes comparable to that of the hard modes [13, 14, 15], i.e. until the growing fields begin to have a significant effect on the dynamics of the particles. [25] for a study of particle production and propagation in Abelian fields, including back-reaction and collisions in the relaxation time approximation.
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