The nonthermal quantum relaxation of the magnetization under nonequilibrium initial conditions is studied for the transverse Ising chain and for the one-dimensional isotropic XY model. In the absence of a heat bath the transverse Ising system exhibits an oscillating relaxation with a decaying amplitude. At the critical transverse field some stationary properties become independent of the initial state. The isotropic XY chain with a spatially inhomogeneous initial state shows a slow, modulated algebraic decay of the magnetization. Analysis of the two-time autocorrelation function reveals the phenomenon of aging.
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Schütz et al. (1999) studied this question.
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