Proliferation of effective interactions: Decoherence-induced equilibration in a closed many-body system

Pablo R. Zangara, Denise Bendersky, and Horacio M. Pastawski
Phys. Rev. A 91, 042112 – Published 13 April 2015

Abstract

We address the question of how weak perturbations, which are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid-state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by nonreversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed N spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as N increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.

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  • Received 3 January 2015
  • Revised 22 February 2015

DOI:https://doi.org/10.1103/PhysRevA.91.042112

©2015 American Physical Society

Authors & Affiliations

Pablo R. Zangara, Denise Bendersky, and Horacio M. Pastawski*

  • Instituto de Física Enrique Gaviola (IFEG), CONICET-UNC, and Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina

  • *horacio@famaf.unc.edu.ar

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Issue

Vol. 91, Iss. 4 — April 2015

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