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Noise-induced transport in the Aubry-Andr\'e-Harper model
Disordered Systems and Neural Networks · Submitted 12 Jul 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase.
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The abstract, sentence by sentence
We study quantum transport in a quasiperiodic Aubry-Andr\'e-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study quantum transport in a quasiperiodic Aubry-Andr\'e-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. | contribution 0.95 | 0.84 | 0.04 | asserted 0.85 |
| s1 | We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. | result 1.00 | 0.96 | 0.44 | asserted 1.00 |
| s2 | Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. | result 1.00 | 0.94 | 0.17 | asserted 1.00 |
| s3 | On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. | result 1.00 | 0.94 | 0.13 | asserted 1.00 |
| s4 | We propose a classical master equation, which captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. | method 0.60 | 0.95 | 0.16 | asserted 0.76 |
| s5 | Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing. | result 0.96 | 0.94 | 0.20 | asserted 1.00 |
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The paper
Original abstract
We study quantum transport in a quasiperiodic Aubry-Andr\'e-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.
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4 arXiv papers cite this in 10 sentences
Papers citing it · 8 sentences without a confident label
Cites it as background 2 papers
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Besides, decoherence and dephasing effects are known to spoil localization and to enhance transport [ref] .
Dephasing-induced mobility edges in quasicrystals · Introduction · 0.85
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Several open quantum versions of this setup have also been a subject of intense research interest [ref] .
Impact of dephasing probes on incommensurate lattices · Results for the Aubry-André-Harper (AAH) model · 0.99
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