Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion

• URL: http://arxiv.org/abs/2512.06263v2
• Date: Sun, 14 Dec 2025 01:26:19 GMT
• Title: Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion
• Authors: Tiange Xiang, Yubo Zhang, Joonas Keski-Rahkonen, Anton M. Graf, Eric J. Heller,
• Abstract summary: We introduce an acceleration-based adiabatic criterion that separates adiabatic and diabatic dynamics across the $(T,v)$ plane.<n>We identify a broad Planckian domain in which the dimensionless diffusivity $!=!Dm/hbar$ is of order unity and only weakly depends on the parameters.
• Score: 6.113393367813894
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate electron transport in one dimension from the quantum-acoustic perspective, where the coherent-state representation of lattice vibrations results in a time-dependent deformation potential whose rate is set by the sound speed, fluctuation spectrum is set by the temperature, and overall amplitude is set by the electron-lattice coupling strength. We introduce an acceleration-based adiabatic criterion, consistent with the adiabatic theorem and Landau-Zener theory, that separates adiabatic and diabatic dynamics across the $(T,v)$ plane. The discrete classification agrees with a continuous mean-squared acceleration scale and correlates with a coherence measure given by the ratio of coherence length to the initial packet width $L_φ(t)/σ_0$. We identify a broad Planckian domain in which the dimensionless diffusivity $α\!=\!Dm/\hbar$ is of order unity and only weakly depends on the parameters. This domain is more prevalent in diabatic regions and in areas of reduced phase coherence, indicating a dephasing driven crossover from Anderson localization to Planckian diffusion. Using the Einstein relation together with nearly constant $α$, we directly obtain a low temperature tendency $1/τ_{\rm tr}\propto T$, offering a insight to $T$-linear resistivity in strange metals. These results provide a unified picture that links adiabaticity, dephasing, and Planckian diffusion in dynamically disordered quantum-acoustics.

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