Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

Constraining conformal field theories with a slightly broken higher spin symmetry

We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual large N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one gets in the Vasiliev theories. Namely, the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of order 1/N. Using the slightly broken higher spin symmetry we constrain the three point functions of the theories to leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern-Simons gauge field, the other as a N bosons plus the Chern-Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points we get the critical O(N) models, both the Wilson-Fisher one and the Gross-Neveu one. Our analysis also fixes the on shell three point functions of Vasiliev's theory on AdS_4 or dS_4.Comment: 54 pages, 3 figure

Interactions and Scaling in a Disordered Two-Dimensional Metal

We show that a non-Fermi liquid state of interacting electrons in two dimensions is stable in the presence of disorder and is a perfect conductor, provided the interactions are sufficiently strong. Otherwise, the disorder leads to localization as in the case of non-interacting electrons. This conclusion is established by examining the replica field theory in the weak disorder limit, but in the presence of arbitrary electron-electron interaction. Thus, a disordered two-dimensional metal is a perfect metal, but not a Fermi liquid.Comment: 4 pages, RevTe

A progressive diagonalization scheme for the Rabi Hamiltonian

A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and full matrix diagonalization.Comment: 8pages, 1 figure, LaTeX. Accepted for publication in J. Phys. B: At. Mol. Opt. Phy

Oxygen Electromigration and Energy Band Reconstruction Induced by Electrolyte Field Effect at Oxide Interfaces

Electrolyte gating is a powerful means for tuning the carrier density and exploring the resultant modulation of novel properties on solid surfaces. However, the mechanism, especially its effect on the oxygen migration and electrostatic charging at the oxide heterostructures, is still unclear. Here we explore the electrolyte gating on oxygen-deficient interfaces between SrTiO3 (STO) crystals and LaAlO3 (LAO) overlayer through the measurements of electrical transport, X-ray absorption spectroscopy (XAS) and photoluminescence (PL) spectra. We found that oxygen vacancies (Ovac) were filled selectively and irreversibly after gating due to oxygen electromigration at the amorphous LAO/STO interface, resulting in a reconstruction of its interfacial band structure. Because of the filling of Ovac, the amorphous interface also showed an enhanced electron mobility and quantum oscillation of the conductance. Further, the filling effect could be controlled by the degree of the crystallinity of the LAO overlayer by varying the growth temperatures. Our results reveal the different effects induced by electrolyte gating, providing further clues to understand the mechanism of electrolyte gating on buried interfaces and also opening a new avenue for constructing high-mobility oxide interfaces.Comment: 5 figures; Supplementary materials included at the end of the main tex

Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics

Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schroedinger equation lead in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the effective S-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the S-state wave function becomes simply proportional to the D-state wave function and dips sharply to zero at the origin, unlike the usual S-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCD vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large pi-rho splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.Comment: 23 pages, 4 figure

Studying complex interventions : reflections from the FEMHealth project on evaluating fee exemption policies in West Africa and Morocco

Peer reviewedPublisher PD

Black holes in three dimensional higher spin gravity: A review

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the AdS/CFT correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Human interaural time difference thresholds for sine tones: The high-frequency limit

[EN] The smallest detectable interaural time difference (ITD) for sine tones was measured for four human listeners to determine the dependence on tone frequency. At low frequencies, 250 700 Hz, threshold ITDs were approximately inversely proportional to tone frequency. At mid-frequencies, 700 1000 Hz, threshold ITDs were smallest. At high frequencies, above 1000 Hz, thresholds increased faster than exponentially with increasing frequency becoming unmeasurably high justabove 1400 Hz. A model for ITD detection began with a biophysically based computational model for a medial superior olive (MSO) neuron that produced robust ITD responses up to 1000 Hz, and demonstrated a dramatic reduction in ITD-dependence from 1000 to 1500 Hz. Rate-ITD functions from the MSO model became inputs to binaural display models both place based and rate-differ-ence based. A place-based, centroid model with a rigid internal threshold reproduced almost all fea- tures of the human data. A signal-detection version of this model reproduced the high-frequence divergence but badly underestimated low-frequency thresholds. A rate-difference model incorporat- ing fast contralateral inhibition reproduced the major features of the human threshold data except for the divergence. A combined, hybrid model could reproduce all the threshold data.We are grateful to Dr. Les Bernstein for a useful discussion about the centroid display and to Dr. Steve Colburn for discussions about modeling. Zane Crawford provided valuable statistical help. This research was supported by The Vicerectorado de Profesorado y Ordenacion Academica of the Universitat Politecnica de Valencia (Spain), which brought L. D. to Michigan State, by the NIDCD Grant No. DC-00181 and the AFOSR Grant No. 11NL002. A. B. was supported by NIDCD Grant Nos. DC-00100 (H. S. Colburn) and P30-DC04663 (Core Center).Brughera, A.; Dunai ., L.; Hartmann, WM. (2013). Human interaural time difference thresholds for sine tones: The high-frequency limit. The Journal of the Acoustical Society of America. 133(5):2839-2855. https://doi.org/10.1121/1.4795778S28392855133