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Fluctuation-dissipation relations, i.e., the relation between two-timecorrelation and linear response functions, were successfully used to search forsigns of equilibration and to identify effective temperatures in thenon-equilibrium behavior of a number of macroscopic classical and quantumsystems in contact with thermal baths. Among the most relevant cases in whichthe effective temperatures thus defined were shown to have a thermodynamicmeaning one finds the stationary dynamics of driven super-cooled liquids andvortex glasses, and the relaxation of glasses. Whether and under whichconditions an effective thermal behavior can be found in quantum isolatedmany-body systems after a global quench is a question of current interest. Wepropose to study the possible emergence of thermal behavior long after thequench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. Ifthermalization within the Gibbs ensemble eventually occurs these parametersshould be constant and equal for all pairs of observables in "partial" or"mutual" equilibrium. We analyze these relations in the paradigmatic quantumsystem, i.e., the quantum Ising chain, in the stationary regime after a quenchof the transverse field. The lack of thermalization to a Gibbs ensemble becomesapparent within this approach.

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain