Abstract: A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, a, is the s-wave scattering length, and the latter, b, is related to a by b=a-m(partial derivativea/partial derivativem), where m stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest “from scratch.” The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.

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: Transport properties of the 2DEG are studied in the presence of a normal magnetic field B and of a weak, two-dimensional periodic potential modulation. A tight-binding treatment has shown that each Landau level splits into several subbands with exponentially small gaps between them. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies the evaluation of the magnetoresistance tensor p(muv) The relative phase of the oscillations in p(xx) and p(yy) depends on the modulation strengths and periods. For short periods less than or equal to 100 nm, in addition to the Weiss oscillations, the collisional contribution to the conductivity and the corresponding resistivity contribution show prominent peaks when one flux quantum h/e passes through an integral number of unit cells in good agreement with experiments. For periods 300-400 nm long used in early experiments, these peaks occur at fields 10-25 times smaller than those of the Weiss oscillations and are not resolved. (C) 2003 Elsevier B.V. All rights reserved.

Abstract: A microscopic Hamiltonian for interacting manganese impurities in dilute magnetic semiconductors (DMS) is derived. It is shown that in p-type III-V DMS, the indirect exchange between Mn impurities has similarities with the Zener mechanism in transition metal oxides. Here the mobile and localized holes near the top of the valence band play the role of unoccupied p-orbitals which induce ferromagnetism. T-C estimated from the proposed kinematic exchange agrees with experiments on (Ga,Mn)As. The model is also applicable to the p-doped (Ga,Mn)P system. The magnetic ordering in n-type (Ga,Mn)N is due to exchange between the electrons localized on the levels lying deep in the forbidden energy gap. This mechanism is even closer to the original Zener mechanism. (C) 2003 Elsevier B.V. All rights reserved.

Abstract: The behavior of nanoparticles in a low-pressure silane discharge is studied with the use of a self-consistent one-dimensional fluid model. Nanoparticles of a given (prescribed) radius are formed in the discharge by the incorporation of a dust growth mechanism, i.e., by including a step in which large anions (typically Si12H−25), produced in successive chemical reactions of anions with silane molecules, are transformed into particles. Typically a few thousand anions are used for one nanoparticle. The resulting particle density and the charge on the particles are calculated with an iterative method. While the spatial distribution and the charge of the particles are influenced by the plasma, the presence of the nanoparticles will in turn influence the plasma properties. Several simulations with different particle radii are performed. The resulting density profile of the dust will greatly depend on the particle size, as it reacts to the shift of the balance of the different forces acting on the particles.