Solitons in relativistic mean field models David Augaitis Fogaça and Fernando S. Navarra

Introduction and Motivation Hydrodynamics gives a good description of nuclear matter in many situations Fast particles traversing nuclear matter may have supersonic motion : ex. 1: hard parton (jet starter) in hot and dense matter at RHIC ex. 2: fast proton hitting and entering a heavy nucleus They may generate shockwaves and ,under certain conditions Korteweg de-Vries Solitons ! G.N. Fowler, S.Raha, N. Stelte, R.M. Weiner, PLB (1982) Experimental signature: nuclear transparency at low energies in p-A collisions Very difficult to observe: outgoing p (in p-A collisions) coincides with the beam

Supersonic flow in hot and dense matter at RHIC J. Casalderrey-Solana, E.V. Shuryak, D. Teaney, hep-ph/0411315

Supersonic flow in hot and dense matter at RHIC Away side jet measured by STAR shockwave ? (maybe a soliton in the middle?) If the shockwave is real, then there may be a soliton too ! To be checked in the future...

Conditions for soliton formation Euler equation Continuity equation Using: we have: EOS The combination of Euler and Continuity equation gives the KdV equation which has a solitonic solution. If then

Equation of state The search for the EOS is given by using a phenomenological description of the nuclear matter: Quantum Hadrodynamics (QHD) QHD + non-linear terms + derivative coupling Mean field approx. and keeping the spatial derivatives

Derivation of the KdV equation The combination of Euler and continuity equations using dimensionless variables: In the - space, given by the “stretched coordinates” : with the following expansion: Gives two equations that contain power series in  up to  !

with the analytical solution: Since the coefficients in these series are independent we get a set of equations, which, when combined, lead to the KdV equation for : with the analytical solution:

speed of sound is not << 1 relativistic corrections ? Numerical results Soliton width: speed of sound is not << 1 relativistic corrections ?

Relativistic Fluid Dynamics where Thermodynamical relations:

Ansatz for the energy density: can also be found in the following works: Following the same procedure we find the KdV equation: Non-relativistic limit : 3 >> speed of sound

The analytical solution: With the condition for : and of course:

Conclusions and Perspectives The nucleus can be treated as a perfect fluid, we have investigated the possibility of formation and propagation of KdV solitons in nuclear matter. We have updated the early estimates of the soliton properties, using more reliable equations of state. The KdV equation may be found in Relativistic Fluid Dynamics, and also depends on energy density. Future numerical approach. Study systems at finite temperatures. Thank you!