Memorization of short-range potential fluctuations in Landau levels

We calculate energy spectra; of a two-dimensional electron system in a perp endicular magnetic field and periodic potentials of short periods. The Coul omb interaction is included within a screened Hartree-Fock approximation. T he electrostatic screening is poor, and the exchange interatcion amplifies the energy dispersion We obtain, by numerical iterations, self-consistent s olutions that have a hysteresislike property. With increasing amplitude of the external potential, the energy dispersion and the electron density beco me periodic, and they remain stable when the external potential is reduced to zero. We explain this property in physical terms, and speculate that a r eal system could memorize short-range potential fluctuations after the pote ntial has been turned off.