- May 2018-July 2018, VSRP Fellow at TIFR, Mumbai
- Guide: Dr. Rishi Sharma, Department of Theoretical Physics TIFR, Mumbai
Apart from it’s applications in non-relativistic regime, hydrodynamics has been quite useful in describing the flow of matter formed when heavy nuclei collide with each other at a speed approaching to that of light[1, 2]. This motivated theoretical investigations into relativistic hydrodynamics.
Amongst many other research topic, study of perturbations has been quite active owing to the fact that one cannot avoid them in real situations. Deviations from ideal models are inevitable and we must have how they affect the system. Moreover, studying perturbations gives important physical insights. A naive analysis of perturbation over a uniform background gives reveals the acausality of relativistic hydrodynamics[3]. This motivated to explore the perturbation on a different background. The physics of heavy ion collision have been influenced by Bjorken’s flow[4, 5]. Even though it is very difficult to get an analytic solution, successful attempts has been made to obtain one has been made for some particular cases. Bjorken’s solution neglects transverse motion of fluid elements, while many of these solutions happen to generalize the Bjorken’s solution to a more generic context by relaxing the assumption made by Bjorken[6, 7].
At very high energies, of the order of 100 GeV, the number of particles produced is almost equal to that of anti-particles. Hence one generally neglects the chemical potential corresponding to any conserved charges in heavy ion collision at high energy regime. Nevertheless, there is a small baryon number density which evolve with time and rapidity[8]. Also the evolution of fluctuations in fluid four-velocity and energy-density has been studied, with viscous effects taken into account.
In this project we discuss the perturbation over Bjorken background neglecting the baryon number density. This restricts our treatment to high energy regime only. Furthermore we consider only the ideal hydrodynamics and apply perturbations to the Bjorken four-velocity and obtain differential equations which describe their evolution.
This work is organised as follows. In the second chapter we introduce the basic equations of Ideal relativistic hydrodynamics. Bjorken flow and it’s characteristics have been discussed in the following chapter. Differential equations for the evolution of perturbations have been derived. Analytic solutions have been obtained making the assumption of rapidity independence of the perturbations. Also the validity of obtained solution and theoretical constraints on perturbation and background have been discussed.
References:
[1] L. D. Landau, “On the multiparticle production in high-energy collisions,” Izv. Akad. Nauk Ser. Fiz., vol. 17, pp. 51–64, 1953.
[2] J.-Y. Ollitrault, “Relativistic hydrodynamics for heavy-ion collisions,”
Eur. J. Phys., vol. 29, pp. 275–302, 2008.
[3] P. Romatschke, “New Developments in Relativistic Viscous Hydrodynamics,” Int. J. Mod. Phys., vol. E19, pp. 1–53, 2010.
[4] J. D. Bjorken, “Highly relativistic nucleus-nucleus collisions: The central
rapidity region,” Phys. Rev. D, vol. 27, pp. 140–151, Jan 1983.
[5] T. Hirano, N. van der Kolk, and A. Bilandzic, “Hydrodynamics and flow,”
pp. 139–178, 2010.
[6] T. Csorgo, M. I. Nagy, and M. Csanad, “A New family of simple solutions
of perfect fluid hydrodynamics,” Phys. Lett., vol. B663, pp. 306–311,
2008.
[7] B. Kurgyis and M. Csand, “Perturbative accelerating solutions of relativistic hydrodynamics,” Universe, vol. 3, no. 4, p. 84, 2017.
[8] S. Floerchinger and M. Martinez, “Fluid dynamic propagation of initial
baryon number perturbations on a Bjorken flow background,” Phys. Rev.,
vol. C92, no. 6, p. 064906, 2015.