From local to global Loschmidt Echo in many-body systems

P. R. ZANGARA; D. BENDERSKY; H. M. PASTAWSKI

Dresden

Workshop; International Workshop: Echoes in Complex Systems; 2014

Inspired in Nuclear Magnetic Resonance, the Loschmidt Echo (LE) has become an important dynamical witness to assess quantum chaos, decoherence and the emergence of classicality [1]. The study of the LE in interacting many-body systems is still a major and stimulating theoretical challenge, since it provides a sort of order parameter for novel dynamical transitions [2]. Here, we evaluate numerically the LE in an interacting spin system, where uncontrolled degrees of freedom involve polarization non-conserving interactions, which as in the experiments are truncated by the effective Zeeman splitting induced by rf irradiation. We find that these interactions yields to polarization-conserving virtual processes that proliferate as a function of the number of spins involved. We also assess the role of different dynamically prepared states. Our results confirm that the more ?prepared? (i.e. correlated or entangled) the states are, the more fragile they become under perturbations [3]. Moreover, it is observed that the dynamical preparation saturates at a finite time-scale and thereafter the local LE can be mimicked by a global LE of a random superposition state [4]. Since these states already exhibit thermal properties [5], our results confirms that LE dynamics is a priviledged witness of the onset of thermalization in closed quantum systems. [1] A. Goussev, R. Jalabert, H. Pastawski and D. Wisniacki, Scholarpedia 7, 11687 (2012). [2] P. Zangara, A. Dente, A. Iucci, P. Levstein, and H. Pastawski, Phys. Rev. B 88, 195106 (2013). [3] D. Bendersky, P. Zangara, and H. Pastawski, Phys. Rev. A 88, 032102 (2013). [4] G. Alvarez, E. Danieli, P. Levstein, and H. Pastawski, Phys. Rev. Lett. 101, 120503 (2008). [5] P. Zangara, A. Dente, E. J. Torres-Herrera, H. Pastawski, A. Iucci, L. F. Santos, Phys. Rev. E 88, 032913 (2013).