Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
De Grandi, Claudia
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Citation (published version)C De Grandi, A Polkovnikov. 2011. "Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point." Quantum Quenching, Annealing and Computation (Lecture Notes in Physics), Volume 802, https://doi.org/10.1007/978-3-642-11470-0_4
Dynamics in closed systems recently attracted a lot of theoretical interest largely following experimental developments in cold atom systems (see e.g.,  for a review). Several spectacular experiments already explored different aspects of non-equilibrium dynamics in interacting many-particle systems [2–8]. Recent theoretical works in this context focused on various topics, for instance: connection of dynamics and thermodynamics [9–11 M. Rigol, unpublished], dynamics following a sudden quench in low dimensional systems [11–23, L. Mathey and A. Polkovnikov, unpublished; A. Iucci and M.A. Cazalilla,unpublished], adiabatic dynamics near quantum critical points [24–37, D. Chowdhury et al., unpublished; K. Sengupta and D. Sen, unpublished; A.P. Itin and P. Törmä, unpublished; F. Pollmann et al., unpublished] and others. Though there is still very limited understanding of the generic aspects of non-equilibrium quantum dynamics, it has been recognized that such issues as integrability, dimensionality, universality (near critical points) can be explored to understand the non-equilibrium behavior of many-particle systems in various specific situations.