Mean-Field Approximation to the Master Equation for Sympathetic Cooling of Trapped Bosons

We use the mean-field approximation to simplify the master equation for sympathetic cooling of Bosons. For the mean single-particle occupation numbers, this approach yields the same equations as the factorization assumption introduced in an erlier paper. The stationary or equilibrium solution of the resulting master equation for the one-body density matrix shows that the mean-field approximation breaks down whenever the fraction of condensate Bosons exceeds ten percent or so of the total. Using group-theoretical methods, we also solve the time-dependent master equation for the one-body density matrix. Given the time dependence of the mean single-particle occupation numbers, this solution is obtained by quadratures. It tends asymptotically towards the equilibrium solution.Comment: submitted to PR

Distortion and orientation of fulleride ions in A(4)C(60)

A(4)C(60) compounds (A = K, Rb, Cs) are good candidates to exhibit the Mott-Jahn-Teller insulating state. We present near-IR and neutron scattering data to reflect molecular and crystal stucture changes with temperature. We show how the size of the cation affects the structural and electronic properties of these compounds

Electronic and structural properties of alkali doped SWNT

Comprehensive experiments on structural and transport properties of alkali intercalated single walled carbon nanotubes (SWNT) are presented. The increasing electron density was measured as a shift of the Drude-edge in optical reflectivity in-situ with progressive doping. In saturation-doped samples the Drude-edge shifts into the visible (to 25,000 - 30,000 cm— 1 for potassium and rubidium doped samples) and the samples have a golden-brown color, similar to stage I graphite. X-ray diffraction reveals a crystalline rope structure with expanded lattice constant, similar to results of Duclaux et al. The change in the low temperature divergence of the resistivity after degassing at high temperature and high vacuum and after K-doping is studied in-situ

Charge transfer and Fermi level shift in p-doped single-walled carbon nanotubes

The electronic properties of p-doped single-walled carbon nanotube (SWNT) bulk samples were studied by temperature-dependent resistivity and thermopower, optical reflectivity, and Raman spectroscopy. These all give consistent results for the Fermi level downshift (Delta E(F)) induced by doping. We find Delta E(F) approximate to 0.35 eV and 0.50 eV for concentrated nitric and sulfuric acid doping respectively. With these values, the evolution of Raman spectra can be explained by variations in the resonance condition as E(F) moves down into the valence band. Furthermore, we find no evidence for diameter-selective doping, nor any distinction between doping responses of metallic and semiconducting tubes

Ordered low-temperature structure in K4C60 detected by infrared spectroscopy

Infrared spectra of a K4C60 single-phase thin film have been measured between room temperature and 20 K. At low temperatures, the two high-frequency T1u modes appear as triplets, indicating a static D2h crystal-field stabilized Jahn-Teller distortion of the (C60)4- anions. The T1u(4) mode changes into the known doublet above 250 K, a pattern which could have three origins: a dynamic Jahn-Teller effect, static disorder between "staggered" anions, or a phase transition from an orientationally-ordered phase to one where molecular motion is significant.Comment: 4 pages, 2 figures submitted to Phys. Rev.

Nanosegregation in Na2C60

There is continuous interest in the nature of alkali metal fullerides containing C(4)(60) and C(2)(60), because these compounds are believed to be nonmagnetic Mott–Jahn–Teller insulators. This idea could be verified in the case of A(4)C(60), but Na(2)C(60) is more controversial. By comparing the results of infrared spectroscopy and X-ray diffraction, we found that Na(2)C(60) is segregated into 3-10 nm large regions. The two main phases of the material are insulating C(60) and metallic Na(3)C(60). We found by neutron scattering that the diffusion of sodium ions becomes faster on heating. Above 470 K Na(2)C(60) is homogeneous and we show IR spectroscopic evidence of a Jahn–Teller distorted C(2)(60) anion