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In analytic descriptions of quantum quenches, the overlaps between the initial pre-quench state and the eigenstates of the time evolving Hamiltonian are crucial ingredients.
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P. Calabrese, F. H. L. Essler and G. Mussardo, Introduction to “Quantum Integrability in Out of Equilibrium Systems” , Journal of Statistical Mechanics: Theory and Experiment 6
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L. Piroli, B. Pozsgay and E. Vernier, What is an integrable quench? , Nuclear Physics B 925
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J. M. Deutsch, Quantum statistical mechanics in a closed system , Physical Review A 43
2046
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