Abstract: Transport properties of a two-dimensional electron gas (2DEG) are studied in the presence of a normal magnetic field B, of a weak one-dimensional (1D) periodic potential modulation V(x) = V(0)cos(Kx), and of the Rashba spin-orbit interaction (SOI) of strength a. For V(x) = 0 the SOI mixes the up and down spin states of neighboring Landau levels into two, unequally spaced energy branches. For V(x) not equal 0 these levels broaden into bands and their bandwidths oscillate with B. The n-th level bandwidth of each series vanishes at different values of B. Relative to the ID-modulated 2DEG without SOI and one flat-band condition, there are two flat-band conditions that depend on a and the transport coefficients can change considerably. For weak a the Weiss oscillations show beating patterns while for strong a the Shubnikov-de Haas ones axe split in two.

Abstract: The deviation effect of spinor mode from the single-mode for a spin-1 Bose gas of trapped atoms is studied beyond the mean field theory. Based on the effective Hamiltonian with nondegenerated level of the collective spin states, the splitting level of the system energy due to the deviation effect has been calculated. For the large condensates of (87)Rb and (23)Na with atom number N > 10(5), the splitting fraction of the energy, arising from the magnetization exhibited by the trapped Bose gas, is found to have a typical order of (10(-4) similar to 10(-8)), decreasing as N(-2) for (87)Rb and increasing as -N(-2) for 23 Na, respectively.