Impurities in a one-dimensional Bose gas: the flow equation approach

A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities[1,2]. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction strength as long as the phase coherence length is much larger than the healing length of the condensate. For two static impurities, we calculate impurity-impurity interactions induced by the Bose gas. We find that leading order perturbation theory fails when boson-impurity interactions are stronger than boson-boson interactions. The mean-field approximation reproduces the flow equation results for all values of the boson-impurity interaction strength as long as boson-boson interactions are weak.

The Effects on Electric Field and Hydrostatic Pressure on the Doped Properties in a Strained (In,Ga)N-GaN Coupled Quantum Wells

A variational approach is utilized to investigated the electron-impurity interaction in zinc-blende (In,Ga)N-GaN strained coupled quantum wells. The donor imputrity states are studied in consideration of the effects of hydrostatic pressure and external electric field. Our results indicate that the binding energy visibly depends on hydrostatic pressure, strain of coupled quantum wells, and applied electric field. The binding energy demonstrates a peak value with the reduction of the left-well width, and which displays a minimum value with the increment of the middle-barrier width. A decreasing behavior on the binding energy is also demonstrated when the right-well width enhances. Also the binding energy augments constantly with the increasing hydrostatic pressure. Besides, the dependency of the binding energy on variation of impurity position has been analyzed detailedly.

The k·p Interaction Calculations of Conduction Band and Valence Band of InN Materials

Thek·pinteraction of the conduction band and valence band of InN materials was calculated in this paper. The nonparabolicity of the conduction band is more pronounced, because the conduction band feels stronger perturbation from the valence bands whenEgis smaller orEPis larger. The increase in absorption edge with increasing electron concentration was calculated by the dispersion relation. In the calculation, the conduction band renormalization effects due to electron interaction and electron-ionized impurity interaction are also taken into account. A good consistent picture is established in describing the conduction band of InN based on thek·pinteraction.