2017/05/22 by Yochai Werman, Steven A. Kivelson, Werman, Yochai +3 · 1 citation
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1705.07895
We calculate the scrambling rate λL and the butterfly velocity vB associated with the growth of quantum chaos for a solvable large-N electron-phonon system. We study a temperature regime in which the electrical resistivity of this system exceeds the Mott-Ioffe-Regel limit and increases linearly with temperature - a sign that there are no long-lived charged quasiparticles - although the phonons remain well-defined quasiparticles. The long-lived phonons determine λL, rendering it parametrically smaller than the theoretical upper-bound λL ≪ λmax=2πT/ℏ. Significantly, the chaos properties seem to be intrinsic - λL and vB are the same for electronic and phononic operators. We consider two models - one in which the phonons are dispersive, and one in which they are dispersionless. In either case, we find that λL is proportional to the inverse phonon lifetime, and vB is proportional to the effective phonon velocity. The thermal and chaos diffusion constants, DE and DL≡ vB2/λL, are always comparable, DE ∼ DL. In the dispersive phonon case, the charge diffusion constant DC satisfies DL≫ DC, while in the dispersionless case DL ≪ DC.