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We study the electron transport in a deformable lattice modeled in thesemiclassical approximation as a discrete nonlinear elastic chain whereacoustic phonons are in thermal equilibrium at temperature T. We reveal that aneffective dynamic disorder induced in the system due to thermalized phonons isnot strong enough to produce Anderson localization. However, for weaknonlinearity we observe a transition between ballistic (low T) and diffusive(high T) regimes, while for strong nonlinearity the transition occurs betweenthe localized soliton (low T) and diffusive (high T) regimes. Thus, theelectron-phonon interaction results in weak temperature-dependent dynamiclocalization.

Disorder-free weak dynamic localization in deformable lattices