Logarithmic, noise-induced dynamics in the Anderson insulator

Abstract

We study the dynamical behavior of the Anderson insulator in the presence of a local noise. We show that the noise induces logarithmically slow energy and entanglement growth, until the system reaches an infinite-temperature state, where both quantities saturate to extensive values. The saturation value of the entanglement entropy approaches the average entanglement entropy over all possible product states. At infinite temperature, we find that a density excitation spreads logarithmically with time, without any signs of asymptotic diffusive behavior. In addition, we provide a theoretical picture which qualitatively reproduces the phenomenology of particle transport.

7 pages, 4 figures; added references and discussion of the entanglement entropy asymptotic value

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• Thermalization propagation front and robustness against avalanches in localized systems
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Relaxation of imbalance in a disordered XX model with on-site dephasing
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Dynamical control in a prethermalized molecular ultracold plasma: Local dissipation drives global relaxation
• Resonant dynamics of spin cluster in a periodically driven one-dimensional Rydberg lattice
• Quantum transport under oscillatory drive with disordered amplitude
• Numerical Study of Disordered Noninteracting Chains Coupled to a Local Lindblad Bath