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arXiv:1110.1203

Stochastic Potential and the Fate of Heavy Quarkonium in the Quark-Gluon Plasma

Yukinao Akamatsu, Alexander Rothkopf

Published Oct 6, 2011• 2 citations
arXivHTMLPDF

Abstract

Fakult¨at fu ¨r Physik, Universit t Bielefeld, D-33615 Bielefeld, Germany(Dated: November 15, 2011)We propose an open quantum systems approach to the physics of heavy quarkonia in a thermalmedium, based on stochastic quantum evolution. This description emphasizes the importance ofcollisions with the environment and focuses on the concept of spatial decoherence of the heavyquarkonium wave function. It is shown how to determine the parameters of the dynamical evolution,i.e. the real potential and the noise strength, from a comparison with quantities to be obtained fromlattice QCD. Furthermore the imaginary part of the lattice QCD heavy quark potential is found tobe naturally related to the strength of the noise correlations. We discuss the fate of QQ¯ analyticallyin a limiting scenario for the spatial decoherence and provide a qualitative 1-dimensional numericalsimulation of the real-time dynamics.

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Fakult¨at fu ¨r Physik, Universit t Bielefeld, D-33615 Bielefeld, Germany(Dated: November 15, 2011)We propose an open quantum systems approach to the physics of heavy quarkonia in a thermalmedium, based on stochastic quantum evolution. This description emphasizes the importance ofcollisions with the environment and focuses on the concept of spatial decoherence of the heavyquarkonium wave function. It is shown how to determine the parameters of the dynamical evolution,i.e. the real potential and the noise strength, from a comparison with quantities to be obtained fromlattice QCD. Furthermore the imaginary part of the lattice QCD heavy quark potential is found tobe naturally related to the strength of the noise correlations. We discuss the fate of QQ¯ analyticallyin a limiting scenario for the spatial decoherence and provide a qualitative 1-dimensional numericalsimulation of the real-time dynamics.
\nIn recent years, a significant theoretical effort has been made towards a dynamical description of quarkonia inside the Quark-Gluon Plasma (QGP), using the open quantum systems formalism. In this framework, one can get a real-time description of a quantum system (here the quarkonium) in interaction with a thermal bath (the QGP) by integrating out the bath degrees of freedom and studying the system reduced density matrix. We investigate the real-time dynamics of a correlated heavy quark-antiquark pair inside the QGP using a quantum master equation previously derived from first QCD principles in [4]. The full equation is directly resolved in 1D to lessen computing costs and is used for the first time to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution.\n
In recent years, a significant theoretical effort has been made towards a dynamical description of quarkonia inside the Quark-Gluon Plasma (QGP), using the open quantum systems formalism. In this framework, one can get a real-time description of a quantum system (here the quarkonium) in interaction with a thermal bath (the QGP) by integrating out the bath degrees of freedom and studying the system reduced density matrix. We investigate the real-time dynamics of a correlated heavy quark-antiquark pair inside the QGP using a quantum master equation previously derived from first QCD principles in [4]. The full equation is directly resolved in 1D to lessen computing costs and is used for the first time to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution.
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 nonequilibrium 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 nonlinear Schr\"odinger equation. This for the first time provides a direct link from quantum chromodynamics to phenomenological models based on nonlinear Schr\"odinger 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.
Accurate modelling and understanding of quarkonium production in ultrarelativistic heavy ion collisions requires a formalism that preserves the quantum properties of microscopic QˉQ\bar{Q}QQˉ​Q systems while treating the interaction of such pairs with the quark-gluon plasma (QGP). The open quantum system approach has recently emerged as one of the most fruitful schemes to meet such requirements. However, the quantum master equations obtained so far in this context are derived assuming a strict ordering between the QGP temperature TTT and the QˉQ\bar{Q}QQˉ​Q energy gaps (ΔEΔEΔE) of the quarkonia bound states. This limits their predictive power since, as the QGP expands and cools down, the system traverse all regimes between the quantum Brownian motion (QBM) regime for T≳ΔET\gtrsim ΔET≳ΔE to the quantum optical (QO) regime for ΔE≳TΔE\gtrsim TΔE≳T. In this paper, we derive and present a more general non-abelian quantum master equation of the Lindblad type, which does not suffer from these limitations and thus allows to faithfully describe the quantum evolution of the QQˉQ\bar{Q}QQˉ​ pairs during the whole QGP-evolution. We also provide some illustration of the key quantities governing this equation.
Abstract We treat heavy quark as an open quantum system in a hot medium and rederive the stochastic Schrödinger equation (SSE) from the full Schrödinger equation for both heavy quarks and the medium. We apply the SSE to the dynamical evolutions of a heavy quark (as a system) in the static hot medium (as an environment). Heavy quarks interact with the medium via random scatterings, which exchange the momentum and phase factor randomly between two wave functions of the system and the environment. The exchange of momentum and phase factor results in the transition between different eigenstates of the system. These are included via an external stochastic potential in the Hamiltonian of SSE. Stochastic wave functions of a heavy quark are evolved with the stochastic external potential. The mean wave functions and corresponding momentum distributions of heavy quarks are obtained after the ensemble average over a large set of stochastic wave functions. We present the thermalization of heavy quarks in the static medium with different coupling strengths.
Description théorique de la dynamique des quarkonia dans le plasma de quarks et de gluons au moyen d'une approche de type équation maîtresse quantique La Chromodynamique Quantique (QCD) prédit l'existence d'un état de la matière appelé Plasma de Quarks et de Gluons (PQG) dans des conditions extrêmes de température et de pression, qui peut être produit lors de collisions d'ions lourds. Une observable du PQG est la suppression des quarkonia (états liés de quark-antiquark lourds), qui est définie par une plus faible production de ces états en présence de PQG par rapport à la production en l'absence de plasma.Ces dernières années, un effort significatif a été réalisé d'un point de vue théorique vers une description dynamique des quarkonia au sein du Plasma de Quarks et de Gluons, à l'aide du formalisme des systèmes quantiques ouverts. Dans ce cadre, il est possible d'obtenir une description en temps réel d'un système quantique (ici un quarkonium) en interaction avec un bain thermique (le PQG) en étudiant la matrice densité réduite du système.Cette thèse étudie la dynamique d'états quarkonium en résolvant une équation maîtresse quantique basée sur l'approche de Blaizot & Escobedo. Plus précisément, cette équation est résolue numériquement directement pour la première fois dans le cas d'un PQG statique et dans le cas d'un PQG se refroidissant. Les populations d'états quarkonium sont étudiées et la validité d'approximations semi-classiques amenant à des équations de Langevin est examinée.