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تسجيل مستخدم جديدQuantum chaos in an electron-phonon bad metal
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We calculate the scrambling rate $lambda_L$ and the butterfly velocity $v_B$ 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 $lambda_L$, rendering it parametrically smaller than the theoretical upper-bound $lambda_L ll lambda_{max}=2pi T/hbar$. Significantly, the chaos properties seem to be intrinsic - $lambda_L$ and $v_B$ 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 $lambda_L$ is proportional to the inverse phonon lifetime, and $v_B$ is proportional to the effective phonon velocity. The thermal and chaos diffusion constants, $D_E$ and $D_Lequiv v_B^2/lambda_L$, are always comparable, $D_E sim D_L$. In the dispersive phonon case, the charge diffusion constant $D_C$ satisfies $D_Lgg D_C$, while in the dispersionless case $D_L ll D_C$.
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