  When quantized, traces of classically chaotic single particle systems include
eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical
and experimental works have argued that classically chaotic single electron
dynamics influences and controls collective electron transport. For transport
in semiconductor superlattices under tilted magnetic and electric fields, these
theories rely on a reduction to a one-dimensional self-consistent drift model.
A two-dimensional theory based on self-consistent Boltzmann transport does not
support that single electron chaos influences collective transport. This theory
agrees with existing experimental evidence of current self-oscillations,
predicts spontaneous collective chaos via a period doubling scenario and it
could be tested unambiguously by measuring the electric potential inside the
superlattice under a tilted magnetic field.
