Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909973070479360 |
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| author | Xiang, Tiange Zhang, Yubo Keski-Rahkonen, Joonas Graf, Anton M. Heller, Eric J. |
| author_facet | Xiang, Tiange Zhang, Yubo Keski-Rahkonen, Joonas Graf, Anton M. Heller, Eric J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion Xiang, Tiange Zhang, Yubo Keski-Rahkonen, Joonas Graf, Anton M. Heller, Eric J. Quantum Physics 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. |
| title | Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.06263 |