Adiabaticity Crossover: From Anderson Localization to Planckian Diffusion

TL;DR

The paper develops a quantum-acoustic framework for 1D electron transport under a time-dependent deformation potential, introducing an acceleration-based adiabatic criterion that separates adiabatic from diabatic dynamics and ties these regimes to phase coherence. By quantifying coherence through L_φ and linking it to transport via the diffusivity D, the authors map regime boundaries in the (T,v) plane and identify a broad Planckian domain with α ≈ 1 where localization is suppressed. The findings connect adiabaticity, dephasing, and Planckian diffusion, predicting T-linear relaxation and resistivity in the Planckian regime and offering experimental routes to test coherence-transport correlations in dynamically disordered low-dimensional systems. This work provides a cohesive framework for understanding how dynamic lattice fluctuations control localization-to-diffusion crossovers and strange-metal transport behavior. Extensions to polaron formation and interacting carriers are highlighted as natural next steps.

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.

Figures (8)

• Figure 1: Acceleration-based adiabatic criterion illustrated with space-time density, center-of-mass acceleration, and equal-time snapshots. The top row shows an adiabatic case and the bottom row shows a diabatic case. Panels (c) and (f) are snapshots at $t=0.750$ ps where blue curves plot $|\psi(x,t)|^{2}$ and red curves plot the instantaneous deformation potential $V(x,t)$. Panels (a)--(c) share adiabatic parameters and panels (d)--(f) share another set of diabatic parameters. (a) Adiabatic $x$--$t$ map $|\psi(x,t)|^{2}$ with discrete kinks that mark resolved channel switches between localized pockets. Red indicates the magnitude of $\vert \psi\vert^2$. (b) Adiabatic $a_{\rm cm}(t)$ with many sharp accepted peaks that pass our scale-invariant peak tests. (c) Adiabatic snapshot at $t=0.750$ ps showing a compact probability profile trapped near a pocket of $V(x,t)$. (d) Diabatic $x$--$t$ map that appears smooth under our thresholds with no resolvable kinks. (e) Diabatic $a_{\rm cm}(t)$ dominated by broad undulations that fail the peak tests. (f) Diabatic snapshot at $t=0.750$ ps showing a more extended and asymmetric probability profile relative to $V(x,t)$.
• Figure 2: Adiabatic--diabatic regime map in the $(T,v)$ plane at fixed $g$ from the acceleration-based adiabatic criterion. Red symbols denote adiabatic points, blue symbols denote diabatic points, and the black staircase marks the boundary.
• Figure 3: Average number of accepted peaks $N$ along the diagonal running from the top-left to the bottom-right of Figure \ref{['fig:fig2']}. Each dot is the mean over 64 random thermal phase seeds, the gray dashed line marks the classification threshold $N=3$. Blue points lie in the diabatic sector, red points in the adiabatic sector. The sharp rise of $N$ shows a sudden onset of kink activity near the regime boundary.
• Figure 4: Mean-squared acceleration ($\mathrm{MSA}$) heat map on the $(T,v)$ grid. Color indicates $\mathrm{MSA}$ magnitude, with brighter yellow representing a more adiabatic system, and the green polyline shows a representative MSA contour.
• Figure 5: Coherence map reporting the dimensionless ratio $L_{\phi}/\sigma_{0}$ on the $(T,v)$ grid, with brighter red indicates a system with stronger coherence. Color encodes $L_{\phi}/\sigma_{0}$ and the green polyline marks a reference threshold.