2205.15551_Thermalization study
Paper (No matching key was found for `Miura2022` in the references. Please make sure to provide an available ID in your `bib.json` file.) regarding thermalization
QGP dynamics not known around transition temperature towards deconfinement (?)
OQS approach has ben developed to describe heavy quarkonium in medium
Recombination of initially unpaired quarks is non negligible for charmonium (for this lindblad cant be solved ?!)
Check if it thermalizes (steady state of lindblad equation)
Quantum brownian regime $\tau_E \ll \tau_R, \tau_S$ (fast env, slow system)
System-environment coupling is weak
Weak coupling expansion of NRQCD $g \ll 1$ leads to brownian motion
Quantum optical regime $\tau_E, \tau_S \ll \tau_R$
Optical regime: rotating wave approximation
Lindblad equation for quarkonium $\rho(t)$: $$\rho(t) = \rho_s\ket{s}\bra{s} + \rho_o\ket{o}\bra{o}.$$ Singlet and octet states.
Lindblad equation contains terms with $\ket{s}\bra{s}$, $\ket{o}\bra{s}$ etc…
Terms in lindblad equation from coupling to environment
Lindblad operators $C_n(\vec{k})$ scattering with momentum transfer
Simulate lindblad with some quantum state diffusion model..
Initial conditions: Wave functions at t = 0 either only single ground state or only octett..
Look at sate occupation numbers: $N^{(i)}_s(t)$ $$N^{(i)}_s(t)=\braket{\psi^{(i)}_s|\rho(t)|\psi^{(i)}_s}$$
Claim: Thermalization Claim: Equilibration to Boltzmann distr. expected since Lindblad operators approx. satisfy detailed balance relation Limitation: Simulation only in 1D
Question: Comments about dipol approx.: Equiv. to pNRQCD?