Scaling and front dynamics in Ising quantum chains

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We study the relaxation dynamics of a quantum Ising chain initially prepared in a product of canonical states corresponding each to an equilibrium state of part of the chain at a given temperature. We focus our attention on the transverse magnetization for which a general expression is given. Explicite results are given for the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, and for the two-temperatures initial state, where part of the chain called the system is thermalized at a temperature Tₛ and the remaining part is at a temperature Tb.