Heavy-Quark Diffusion in the Quark-Gluon Plasma - ResearchGate

correct equil. lim. ⇒ Einstein relation: B 1 (t, p) = T (t)E p A(t, p)Hendrik vanRelativistic Hees (Texas A&MLangevin University) simulation Heavy-Quark Diffusion for flowing the QGP medium February 13, 2008 8 / 11Heavy-Quark diffusionFokker Planck Equation∂f(t, ⃗p)∂t= ∂ [p i A(t, p) +∂ ]B ij (t, ⃗p) f(t, ⃗p)∂p i ∂p jdrag (friction) and diffusion coefficientsp i A(t, ⃗p) = 〈 p i − p ′ 〉iB ij (t, ⃗p) = 1 〈(pi − p ′2i)(p j − p ′ j) 〉(= B 0 (t, p) δ ij − p )ip jp 2 + B 1 (t, p) p ip jp 2transport coefficients defined via M〈X(⃗p ′ ) 〉 = 1 ∫1 d 3 ∫⃗q d 3 ⃗q ′ ∫d 3 ⃗p ′γ c 2E p (2π) 3 2E q (2π) 3 2E q ′ (2π) 3 2E p ′∑|M| 2 (2π) 4 δ (4) (p + q − p ′ − q ′ ) ˆf(⃗q)X(⃗p ′ )