2014/12/31 by Pablo R. Zangara, Denise Bendersky, Horacio M. Pastawski
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Chemistry #Hamiltonian (control theory) #Mathematics #Perturbation (astronomy) #Physics #Polarization (electrochemistry) #Quantum #Quantum and electron transport phenomena #Quantum decoherence #Quantum many-body systems #Quantum mechanics #Quantum system #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physreva.91.042112
published as Phys. Rev. A 91, 042112 (2015) · 8 pages, 4 figures
arxiv created 2015/02/22 · openalex publication_date 2015/04/13 · arxiv updated 2015/04/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.