A nonextensive approach to Bose-Einstein condensation of trapped interacting boson gas

In the Bose-Einstein condensation of interacting atoms or molecules such as 87Rb, 23Na and 7Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy Uq and the particle number Nq of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature Tcq is derived versus Tc given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q ~ 0.1 for 87Rb atomic gas, q ~ 0.95 for 7Li and q ~ 0.62 for 23Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory

Magneto-Roton Modes of the Ultra Quantum Crystal: Numerical Study

The Field Induced Spin Density Wave phases observed in quasi-one-dimensional conductors of the Bechgaard salts family under magnetic field exhibit both Spin Density Wave order and a Quantized Hall Effect, which may exhibit sign reversals. The original nature of the condensed phases is evidenced by the collective mode spectrum. Besides the Goldstone modes, a quasi periodic structure of Magneto-Roton modes, predicted to exist for a monotonic sequence of Hall Quantum numbers, is confirmed, and a second mode is shown to exist within the single particle gap. We present numerical estimates of the Magneto-Roton mode energies in a generic case of the monotonic sequence. The mass anisotropy of the collective mode is calculated. We show how differently the MR spectrum evolves with magnetic field at low and high fields. The collective mode spectrum should have specific features, in the sign reversed "Ribault Phase", as compared to modes of the majority sign phases. We investigate numerically the collective mode in the Ribault Phase.Comment: this paper incorporates material contained in a previous cond-mat preprint cond-mat/9709210, but cannot be described as a replaced version, because it contains a significant amount of new material dealing with the instability line and with the topic of Ribault Phases. It contains 13 figures (.ps files

A nonextensive approach to Bose-Einstein condensation of trapped interacting boson gas

In the Bose-Einstein condensation of interacting atoms or molecules such as 87Rb, 23Na and 7Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy U q and the particle number N q of boson gas are given in terms of the nonextensive parameter q.q >1 (q <1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature T cq is derived versus T c given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q 0.1 for 87Rb atomic gas, q ≈ 0.95 for 7Li and q ≈ 0.62 for 23Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory. © Springer Science+Business Media, LLC 2007

Possible Triplet Electron Pairing and an Anisotropic Spin Susceptibility in Organic Superconductors (TMTSF)_2 X

We argue that (TMTSF)_2 PF_6 compound under pressure is likely a triplet superconductor with a vector order parameter d(k) \equiv (d_a(k) \neq 0, d_c(k) = ?, d_{b'}(k) = 0); |d_a(k)| > |d_c(k)|. It corresponds to an anisotropic spin susceptibility at T=0: \chi_{b'} = \chi_0, \chi_a \ll \chi_0, where \chi_0 is its value in a metallic phase. [The spin quantization axis, z, is parallel to a so-called b'-axis]. We show that the suggested order parameter explains why the upper critical field along the b'-axis exceeds all paramagnetic limiting fields, including that for a nonuniform superconducting state, whereas the upper critical field along the a-axis (a \perp b') is limited by the Pauli paramagnetic effects [I. J. Lee, M. J. Naughton, G. M. Danner and P. M. Chaikin, Phys. Rev. Lett. 78, 3555 (1997)]. The triplet order parameter is in agreement with the recent Knight shift measurements by I. J. Lee et al. as well as with the early results on a destruction of superconductivity by nonmagnetic impurities and on the absence of the Hebel-Slichter peak in the NMR relaxation rate.Comment: 4 pages, 1 eps figur

Understanding heavy Fermion from generalized statistics

Heavy electrons in superconducting materials are widely studied with the Kondo lattice t - J model. Numerical results have shown that the Fermi surface of these correlated particles undergoes a flattening effect according to the coupling degree J. This behaviour is not easy to understand from the theoretical point of view within standard Fermi - Dirac statistics and non-standard theories such as fractional exclusion statistics for anyons and Tsallis nonextensive statistics. The present work is an attempt to account for the heavy electron distribution within incomplete statistics (IS) which is developed for complex systems with interactions which make the statistics incomplete such that Σ i=1 w P i q=1. The parameter q, when different from unity, characterizes the incompleteness of the statistics. It is shown that the correlated electrons can be described with the help of IS with q related to the coupling constant J in the context of Kondo model. © Springer Science+Business Media, LLC 2007

DFT study of pressure induced phase transitions in LiYF4

An investigation of the pressure induced phase transition from the scheelite phase (I41/a, Z=4) to the fergusonite-like phase (I2/a, Z=4)/LaTaO(P21/c, Z=4) of LiYF4 is presented. Employing density functional theory (DFT) within the generalized gradient approximation, the internal degrees of freedom were relaxed for a pressure range of 0 GPa to 20 Gpa. The influence of pressure on the lattice vibration spectrum of the scheelite phase (I41/a, Z=4) was evaluated using the direct approach, i.e. using force constants calculated from atomic displacements. The transition volume is in good agreement with experiment, while the transition pressure is overestimated of 6 GPa. At 20 GPa, a P21/c structure with apentacoordinated lithium cation is found to be the most stable phase. This structure is compatible with a transition driven by a Bg zone-center soft optic mode linked to a soft-acoustic mode along the [11-1] direction as observed for the proper ferroelastic transition of BiVO4

The Dependence of the Superconducting Transition Temperature of Organic Molecular Crystals on Intrinsically Non-Magnetic Disorder: a Signature of either Unconventional Superconductivity or Novel Local Magnetic Moment Formation

We give a theoretical analysis of published experimental studies of the effects of impurities and disorder on the superconducting transition temperature, T_c, of the organic molecular crystals kappa-ET_2X and beta-ET_2X (where ET is bis(ethylenedithio)tetrathiafulvalene and X is an anion eg I_3). The Abrikosov-Gorkov (AG) formula describes the suppression of T_c both by magnetic impurities in singlet superconductors, including s-wave superconductors and by non-magnetic impurities in a non-s-wave superconductor. We show that various sources of disorder lead to the suppression of T_c as described by the AG formula. This is confirmed by the excellent fit to the data, the fact that these materials are in the clean limit and the excellent agreement between the value of the interlayer hopping integral, t_perp, calculated from this fit and the value of t_perp found from angular-dependant magnetoresistance and quantum oscillation experiments. If the disorder is, as seems most likely, non-magnetic then the pairing state cannot be s-wave. We show that the cooling rate dependence of the magnetisation is inconsistent with paramagnetic impurities. Triplet pairing is ruled out by several experiments. If the disorder is non-magnetic then this implies that l>=2, in which case Occam's razor suggests that d-wave pairing is realised. Given the proximity of these materials to an antiferromagnetic Mott transition, it is possible that the disorder leads to the formation of local magnetic moments via some novel mechanism. Thus we conclude that either kappa-ET_2X and beta-ET_2X are d-wave superconductors or else they display a novel mechanism for the formation of localised moments. We suggest systematic experiments to differentiate between these scenarios.Comment: 18 pages, 5 figure