Abstract
By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, m(t), of the random transverse-field Ising chain after global quenches. We observe different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by m(t) ∼ ln^a t, and in a finite sample of length L the average magnetization saturates at a size-dependent plateau m_p(L) ∼ L^-b; here the two exponents satisfy the relation b/a=ψ=1/2. Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until t=t_d with ln t_d ∼ L^ψ and then starts to increase until it saturates to an asymptotic value m_p(L) ∼ L^-b', with b'≈ 1.5. For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable ln t/L^ψ. Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.