Geodesic
Asymptotic Time Evolution of a Partitioned Infinite Two-sided Isotropic $XY$-chain
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of the modern mathematical physics, Tome 228 (2000), pp. 203-216 
T. G. Ho; H. Araki. Asymptotic Time Evolution of a Partitioned Infinite Two-sided Isotropic $XY$-chain. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of the modern mathematical physics, Tome 228 (2000), pp. 203-216. http://geodesic.mathdoc.fr/item/TM_2000_228_a15/
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     title = {Asymptotic {Time} {Evolution} of {a~Partitioned} {Infinite} {Two-sided} {Isotropic} $XY$-chain},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The system under consideration is that of a two-sided infinite isotropic $XY$-chain partitioned into two distinct regions. Each side is initially in thermal equilibrium. We investigate the situation when the partition is removed at time $t=0$. For $t\rightarrow\infty the system approaches thermal equilibrium if the two sides were at the same temperature. If initially the two sides were at different temperatures then the system approaches a steady state.

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