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Scaling behaviour of the relaxation in quantum chains

Dragi Karevski
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Abstract

We consider the nonequilibrium time evolution of the transverse magnetization in the critical Ising and $XX$ quantum chains. For some inhomogeneously magnetized initial states we derive analytically the transverse magnetization profiles and show that they evolve into scaling forms in the long-time limit. In particular it is seen that the Ising chain exhibits some similarities with the conserved dynamics $XX$ chain. That is, after a transient regime, the total residual magnetization in the transverse direction is also conserved in the Ising case. A class of general initial states is also considered.

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Dragi Karevski. 2002-03-05. Scaling behaviour of the relaxation in quantum chains. https://doi.org/10.1140/epjb%2Fe20020139

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