Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma

Abstract

In this paper we study the real-time evolution of heavy quarkonium in the quark-gluon plasma (QGP) on the basis of the open quantum systems approach. In particular, we shed light on how quantum dissipation affects the dynamics of the relative motion of the quarkonium state over time. To this end we present a novel non-equilibrium master equation for the relative motion of quarkonium in a medium, starting from Lindblad operators derived systematically from quantum field theory. In order to implement the corresponding dynamics, we deploy the well established quantum state diffusion method. In turn we reveal how the full quantum evolution can be cast in the form of a stochastic non-linear Schrödinger equation. This for the first time provides a direct link from quantum chromodynamics (QCD) to phenomenological models based on nonlinear Schrödinger equations. Proof of principle simulations in one-dimension show that dissipative effects indeed allow the relative motion of the constituent quarks in a quarkonium at rest to thermalize. Dissipation turns out to be relevant already at early times well within the QGP lifetime in relativistic heavy ion collisions. I. INTRODUCTIONOver the past decades, properties of nuclear matter in extreme conditions have been vigorously studied both experimentally and theoretically.At modern collider facilities, such as the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), heavy nuclei are collided at ultrarelativistic energy to create a multiparticle system in the collision center, endowed with an extremely high energy density.A multitude of measurements suggest that the energy densities reached are high enough that a new phase of nuclear matter, the "quark-gluon plasma (QGP)" is realized [1-3].On the theory side significant progress has been made in understanding the thermodynamic, i.e. static properties of the QGP at the temperatures reached in heavy ion collisions at which QCD dynamics is still nonperturbative. Lattice QCD simulations have played a central role in this regard shedding light on e.g. the crossover transition temperature [4,5], the physics of static screening in QCD [6,7] and the equilibrium spectral properties of heavy *

Bottomonium suppression in an open quantum system using the quantum trajectories method

“…In the present study, we relax these approximations by using the Monte Carlo wavefunction method [38]. Other methods exist and have been used to simplify the computation of the Lindblad equation in the context of quarkonium suppression [39,40]. However, for reasons that we will explain later, we believe that the Monte Carlo wave-function method is more suitable for quarkonium studies, especially when color degrees of freedom are taken into account.…”

Coupled Boltzmann transport equations of heavy quarks and quarkonia in quark-gluon plasma

“…The derivation is based on the combination of the open quantum system framework (in which correlated recombination is taken into account) and the pNRQCD effective field theory. The application of the open quantum system framework to studying quarkonium in-medium dynamics [53][54][55][56][57][58][59][60][61][62][63][64][65] and its combination with pNRQCD [66,67] has recently drawn significant theoretical interest. A quarkonium transport coefficient has been defined in ref.…”

Bottomonium suppression and elliptic flow using Heavy Quarkonium Quantum Dynamics

“…This allowed us to extract the survival probability associated with the thermal-noise averaged quantum wave-function, however, does not fully take into account in-medium transitions between different singlet/octet and angular momentum states. There is currently ongoing work to include true stochastic noise at the level of the real-time Schrödinger equation solution, either through explicit noisy potentials [26,27,31,[84][85][86][87][88] or through solution of the Lindblad equation for the reduced density matrix [28,30,[32][33][34]. Preliminary results obtained using the quantum trajectories method to solve the Lindblad equation indicate that more accurate inclusion of noise effects including, e.g., in-medium singlet-octet transitions, will result in only small changes in R AA [Υ(1s)] [89].…”