Intrinsic localization of Bloch electrons in dc-ac electric fields

Exact soliton solutions describing nonlinear dynamical behavior of Bloch electrons under action of dc-ac electric fields are obtained, from which it is found that the evolution behavior of Bloch electrons is always oscillatory in time, with oscillatory frequencies depending on electric fields. A number of phenomena associated with the translational symmetry of the system, the staggered localized states, as well as the relationship between intrinsic localized states and solitons are addressed. The corresponding energy, momentum, and norm are also studied.