Algebraic equivalence between certain models for superfluid--insulator transition

Algebraic contraction is proposed to realize mappings between models Hamiltonians. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic $XXZ$ Heisenberg model, the Quantum Phase Model, and the Bose Hubbard Model is established as the contractions of the algebra $u(2)$ underlying the dynamics of the $XXZ$ Heisenberg model.Comment: 5 pages, revte

Algebraic Bethe Ansatz for a discrete-state BCS pairing model

We show in detail how Richardson's exact solution of a discrete-state BCS (DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz solution of the inhomogeneous XXX vertex model with twisted boundary conditions: by implementing the twist using Sklyanin's K-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe Ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the H_i as Hamiltonian, more general exactly solvable models can be constructed. -- To make the paper accessible to readers that are not Bethe Ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.

Mixed Early and Late-Type Properties in the Bar of NGC 6221: Evidence for Evolution along the Hubble Sequence?

Rotation curves and velocity dispersion profiles are presented for both the stellar and gaseous components along five different position angles (P.A.=5, 50, 95, 125 and 155 degrees) of the nearby barred spiral NGC 6221. The observed kinematics extends out to about 80" from the nucleus. Narrow and broad-band imaging is also presented. The radial profiles of the fluxes ratio [NII]/Halpha reveal the presence of a ring-like structure of ionized gas, with a radius of about 9" and a deprojected circular velocity of about 280 km/s. The analysis of the dynamics of the bar indicates this ring is related to the presence of an inner Lindblad resonance (ILR) at 1.3 kpc. NGC6221 is found to exhibit intermediate properties between those of the early-type barred galaxies: the presence of a gaseous ring at an ILR, the bar edge located between the ILR's and the corotation radius beyond the steep rising portion of the rotation curve, the dust-lane pattern, and those of the late-type galaxies: an almost exponential surface brightness profile, the presence of Halpha regions along all the bar, the spiral-arm pattern. It is consistent with scenarios of bar-induced evolution from later to earlier-type galaxies.Comment: 1 File ds7406.tar.gz which contains: one latex file (ds7406.tex), and 10 encsulated postscript figures (ds7406f**.eps). To be compiled with aa-l latex2e macro style. To be published in A&A Sup. Serie

Experiences with HPTN 067/ADAPT Study-Provided Open-Label PrEP Among Women in Cape Town: Facilitators and Barriers Within a Mutuality Framework.

Placebo-controlled trials of pre-exposure prophylaxis (PrEP) have reported challenges with study-product uptake and use, with the greatest challenges reported in studies with young women in sub-Saharan Africa. We conducted a qualitative sub-study to explore experiences with open-label PrEP among young women in Cape Town, South Africa participating in HTPN 067/Alternative Dosing to Augment Pre-Exposure Prophylaxis Pill Taking (ADAPT). HPTN 067/ADAPT provided open label oral FTC/TDF PrEP to young women in Cape Town, South Africa who were randomized to daily and non-daily PrEP regimens. Following completion of study participation, women were invited into a qualitative sub-study including focus groups and in-depth interviews. Interviews and groups followed a semi-structured guide, were recorded, transcribed, and translated to English from isiXhosa, and coded using framework analysis. Sixty of the 179 women enrolled in HPTN 067/ADAPT participated in either a focus group (six groups for a total of 42 participants) or an in-depth interview (n = 18). This sample of mostly young, unmarried women identified facilitators of and barriers to PrEP use, as well as factors influencing study participation. Cross-cutting themes characterizing discourse suggested that women placed high value on contributing to the well-being of one's community (Ubuntu), experienced a degree of skepticism towards PrEP and the study more generally, and reported a wide range of approaches towards PrEP (ranging from active avoidance to high levels of persistence and adherence). A Mutuality Framework is proposed that identifies four dynamics (distrust, uncertainty, alignment, and mutuality) that represent distinct interactions between self, community and study and serve to contextualize women's experiences. Implications for better understanding PrEP use, and non-use, and intervention opportunities are discussed. In this sample of women, PrEP use in the context of an open-label research trial was heavily influenced by underlying beliefs about safety, reciprocity of contributions to community, and trust in transparency and integrity of the research. Greater attention to factors positioning women in the different dynamics of the proposed Mutuality Framework could direct intervention approaches in clinical trials, as well as open-label PrEP scale-up

Bethe Ansatz solution of a new class of Hubbard-type models

We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the statistics is equivalent to the presence of a magnetic field produced by the particles themselves, which is present also in a ``free gas'' of these particles.Comment: 4 pages, revtex. Essentially modified versio

Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced BCS model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors that describe superconducting pairing.Comment: revised version, 5 pages, revtex, no figure

Mesoscopic BCS pairing in the repulsive 1d-Hubbard model

We study mesoscopic pairing in the one dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type, where the Cooper-pairs form an un-condensed liquid on a ``lattice'' of single particle energies provided by the Hubbard charge degrees of freedom; the condensation in the BCS ground state corresponds to Hubbard excitations constituted by a sea of spin singlets.Comment: 15 pages, 6 figures. To be published on Physical Review

Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations

We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the system; the Hamiltonian does not contain any time dependence. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state the Pfaffians in the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of refs. modifie

Connecting dissipation and phase slips in a Josephson junction between fermionic superfluids

We study the emergence of dissipation in an atomic Josephson junction between weakly-coupled superfluid Fermi gases. We find that vortex-induced phase slippage is the dominant microscopic source of dissipation across the BEC-BCS crossover. We explore different dynamical regimes by tuning the bias chemical potential between the two superfluid reservoirs. For small excitations, we observe dissipation and phase coherence to coexist, with a resistive current followed by well-defined Josephson oscillations. We link the junction transport properties to the phase-slippage mechanism, finding that vortex nucleation is primarily responsible for the observed trends of conductance and critical current. For large excitations, we observe the irreversible loss of coherence between the two superfluids, and transport cannot be described only within an uncorrelated phase-slip picture. Our findings open new directions for investigating the interplay between dissipative and superfluid transport in strongly correlated Fermi systems, and general concepts in out-of-equlibrium quantum systems.Comment: 6 pages, 4 figures + Supplemental Materia

Conserved Ising Model on the Human Connectome

Dynamical models implemented on the large scale architecture of the human brain may shed light on how function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the \it{critical state}) the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of an homeostatic principle imposed to neural activity