Onset of hydrodynamics in the hot medium created in relativistic heavy-ion collisions is a crucial theoretical question. A first principle calculation requires a real-time, non-perturbative simulation of the quantum system. In the current study, we perform quantum (many body) simulations to study the onset of thermal equilibrium and hydrodynamics. We focus on the massive Schwinger model which is a low-dimension analog of quantum chromodynamics (QCD), as it shares the important properties such as confinement and chiral symmetry breaking.
We first compute the real-time evolution of the Wigner function, which is the Wigner—Weyl transformation of the gauge-invariant two-point correlation function and it serves as the quantum analogy of the quark distribution function in phase space. Starting from a non-equilibrium initial state, the real time evolution of the Wigner functions, as well as the entanglement entropy, both demonstrate that thermalization of the quantum system is approachable. In particular, relaxation to the thermalized state depends on coupling strength, in the presence of quantum fluctuations. The system tends to thermalize in the strong-coupling case, but not the weak-coupling ones. We also study the connection of the Wigner function thermalization to the Eigenstate Thermalization (ETH). The ETH is a well-known postulation that explains the thermalization of observables in isolated quantum many-body systems without processing quantum ergodicity. The satisfaction of ETH sheds light on the rapid thermalization of QGP created in heavy-ion collisions.
We also perform quantum simulation using the Tensor Network method, which enables simulations of large scale quantum many-body systems by keeping only the most essential quantum states in the Hilbert space.
Starting from an initial quantum state that mimics hard particle collisions, we observe the onset of hydrodynamic behavior that is consistent with the Bjorken-flow in all hydrodynamic degrees of freedom: energy density, fluid velocity, and bulk pressure. The time scale for the onset of hydrodynamics is found to be consistent with the thermalization time of the quantum distribution function. Both time scales are of the same order as the hydrodynamization time determined by fitting the experimental data, upon a physical matching that extrapolates the 1+1 dimensional Schwinger model to the 3+1 dimension QCD.
Refs:
Shile Chen, Shuzhe Shi, Li Yan, 2412.00662
Haiyang Shao, Shile Chen, Shuzhe Shi, in preparation
Dr. Hadi Mehrabpour