Classical electromagnetic fields from quantum sources in heavy-ion collisions

Abstract

Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. We compute the electromagnetic field created by a charged particle described initially as a Gaussian wave packet of width 1 fm and evolving in vacuum according to the Klein-Gordon equation. We completely neglect the medium effects. We show that the dynamics, magnitude and even sign of the electromagnetic field created by classical and quantum sources are different.

Magnetic field in expanding quark-gluon plasma

“…Our paper paves the road to a comprehensive computation of electromagnetic field with quantum sources, whose importance was demonstrated in [56,57]. The fact that the flow of plasma and the wake effects are but small corrections is enormous simplification of the MHD equations.…”

“…Furthermore, for our arguments in this paper it is sufficient to approximate the valence electric charges as classical point particles. In a more comprehensive treatment one has to replace the classical sources by the quantum distributions [56,57].…”

Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions

“…A number of numerical simulations have revealed that the magnitudes of the magnetic fields in heavy-ion collisions can be very large [5][6][7][8][9][10][11][12][13][14][15][16]. In Fig.…”

How does the Quark-Gluon Plasma know the collision energy?

“…Unfortunately, it is very difficult to assess the precise magnitude of the magnetic fields relevant to this situation, and the question is currently under intense scrutiny. The maximal possible values of eB, those attained in the initial state of the fireball generated by a peripheral collision, were estimated in the classic work of Deng et al [21], but it has recently been suggested that these values may need to be reconsidered: in [22,23], for example, it is argued that quantum diffusion effects can significantly adjust the estimated initial magnetic field upward.…”