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From localization to anomalous diffusion in the dynamics of coupled kicked rotors

Simone Notarnicola1,*, Fernando Iemini2, Davide Rossini3, Rosario Fazio2,4, Alessandro Silva1, and Angelo Russomanno2,4

  • 1SISSA, Via Bonomea 265, I-34136 Trieste, Italy
  • 2Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
  • 3Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
  • 4NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy

  • *Email address: simone.notarnicola@gmail.com
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Phys. Rev. E 97, 022202 – Published 2 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022202

Abstract

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N→∞, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.

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Phys. Rev. E 97, 022202– Published 2 February, 2018
  • Received 26 September 2017
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