Quantum dissipation of a heavy quark from a nonlinear stochastic Schr\"odinger equation

TL;DR

This paper models the quantum dissipation of a heavy quark in quark-gluon plasma using a nonlinear stochastic Schrödinger equation derived from a Lindblad master equation, revealing relaxation to thermal equilibrium and the importance of quantum effects.

Contribution

It introduces a novel application of the quantum state diffusion approach to simulate heavy quark dynamics in plasma, providing new insights into quantum dissipation and decoherence effects.

Findings

Density matrix relaxes to Boltzmann distribution

Quantum dissipation affects early and long-time behavior

Numerical solutions in one spatial dimension support the model

Abstract

We study the open system dynamics of a heavy quark in the quark-gluon plasma using a Lindblad master equation. Applying the quantum state diffusion approach by Gisin and Percival, we derive and numerically solve a nonlinear stochastic Schr\"odinger equation for wave functions, which is equivalent to the Lindblad master equation for the density matrix. From our numerical analysis in one spatial dimension, it is shown that the density matrix relaxes to the Boltzmann distribution in various setups (with and without external potentials), independently of the initial conditions. We also confirm that quantum dissipation plays an essential role not only in the long-time behavior of the heavy quark but also at early times if the heavy quark initial state is localized and quantum decoherence is ineffective.