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

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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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     author = {T. G. Ho and H. Araki},
     title = {Asymptotic {Time} {Evolution} of {a~Partitioned} {Infinite} {Two-sided} {Isotropic} $XY$-chain},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     publisher = {mathdoc},
     volume = {228},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2000_228_a15/}
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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/