Three-Body Losses in Trapped Bose-Einstein Condensed Gases

A time-dependent Kohn-Sham (KS)-like equation for N bosons in a trap is generalized for the case of inelastic collisions. We derive adiabatic equations which are used to calculate the nonlinear dynamics of the Bose-Einstein condensate (BEC) and non-mean field corrections due to the three-body recombination. We find that the calculated corrections are about 13 times larger for 3D trapped dilute bose gases and about 7 times larger for 1D trapped weakly interacting bose gases when compared with the corresponding corrections for the ground state energy and for the collective frequencies.Comment: 11 pages, 2 figure

Cold Bose Gases near Feshbach Resonances

The lowest order constrained variational method [Phys. Rev. Lett. 88, 210403 (2002)] has been generalized for a dilute (in the sense that the range of interatomic potential is small compared with inter-particle spacing) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na (F=1, m_F=1) atoms near the $B_0=907$G Feshbach resonance. It is shown that at high densities, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform con densate for the case of negative scattering length.Comment: Revised version of cond-mat/0212196. Added Eqs. (21,22) and references for section

Housing and the Great Recession : a VAR accounting exercise

We use a vector autoregression (VAR) for the components of gross domestic product (GDP) to conduct some sectoral and temporal accounting for the current recession. It is obvious that housing played an important role in the current recession, but residential investment declined for two years before GDP declined. According to the VAR, the level of GDP in the second quarter of 2009---the trough of the decline in GDP---was close to but above the level implied by the estimated sequence of VAR innovations to residential investment over the period 2006:Q1--2009:Q2. Until late 2007 other offsetting shocks kept real GDP growing roughly at trend, but after that the other shocks disappeared or reversed sign. Taking a similar approach with employment, we first observe that, as with output, employment in the housing industry began to fall well before aggregate employment. However, unlike output, the eventual decline in aggregate employment dwarfed the decline in housing-industry employment. The shock to residential construction employment can nonetheless explain a small portion of the current employment shortfall relative to trend.Labor market ; Housing ; Recessions

Flexoelectric effect in finite samples

Static flexoelectric effect in a finite sample of a solid is addressed in terms of phenomenological theory for the case of a thin plate subjected to bending. It has been shown that despite an explicit asymmetry inherent to the bulk constitutive electromechanical equations which take into account the flexoelectric coupling, the electromechanical response for a finite sample is "symmetric". "Symmetric" means that if a sensor and an actuator are made of a flexoelectric element, performance of such devices can be characterized by the same effective piezoelectric coefficient. This behavior is consistent with the thermodynamic arguments offered earlier, being in conflict with the current point of view on the matter in literature. This result was obtained using standard mechanical boundary conditions valid for the case where the polarization vanishes at the surface. It was shown that, for the case where there is the polarization is nonzero at the surface, the aforementioned symmetry of electromechanical response may be violated if standard mechanical boundary conditions are used, leading to a conflict with the thermodynamic arguments. It was argued that this conflict may be resolved when using modified mechanical boundary conditions. It was also shown that the contribution of surface piezoelectricity to the flexoelectric response of a finite sample is expected to be comparable to that of the static bulk contribution (including the material with high values of the dielectric constant) and to scale as the bulk value of the dielectric constant (similar to the bulk contribution). This finding implies that if the experimentally measured flexoelectric coefficient scales as the dielectric constant of the material, this does not imply that the measured flexoelectric response is controlled by the static bulk contribution to the flexoelectric effect