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Chaînes de spins quantiques hors de l'équilibre

Abstract : The work exposed in this thesis is focused on the analyze of the non-equilibrium dynamics of quantum spin chains described by the XY model. We start by considering the unitary dynamics obtained by the interaction of neighboring sub-systems thermalized at different temperatures. The initial state is inhomogeneous and the dynamics is evolving towards an homogeneous state. For a system, initially divided in two sub-systems thermalized at the temperatures T_b=\inflty and T_s, we obtain the analytic expression of the Green function associated to the evolution of the magnetization profile. This results are generalized for finite temperatures T_b. In the particular case T_b=T_s=0, we analyze the behavior of the entenglement entropy generated between sub-systems. This quantity presents a fast increase, predicted by the conformal theory, followed by a slow relaxation towards equilibrium. In the last part, the dynamics of the system is obtained by the interaction with the environment, descibed by the process of repeated interactions. We are analyzing the structure of the system density matrix and are giving the equation of evolution for the set of two-points correlators. Finally, we study the time evolution of the XX model in contact with two baths at the temperatures T_1 and T_2. For T_1=T_2, the analysis of the short time behavior reveals useful informations on the stationary state. For T_1\ne T_2 we numericaly check that the density profil is flat and propose the introduction of a dynamical disorder which lead to a linear density profile.
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Submitted on : Thursday, March 29, 2018 - 11:28:16 AM
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Thierry Platini. Chaînes de spins quantiques hors de l'équilibre. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 2008. Français. ⟨NNT : 2008NAN10150⟩. ⟨tel-01748197⟩



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