Universal scaling in a trapped Fermi super-fluid in the BCS-unitarity crossover

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear Schrodinger equation for a superfluid Fermi gas in the BCS-BEC crossover

We introduce a quasianalytic nonlinear Schrodinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where k(F)parallel to a parallel to << 1 with a the s-wave scattering length and k(F) the Fermi momentum, through the unitarity limit k(F)a ->+/-infinity to the Bose-Einstein condensation (BEC) regime where k(F)a > 0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.

BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Self-trapping of a Fermi superfluid in a double-well potential in the Bose-Einstein-condensate-unitarity crossover

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The BCS-Bose crossover theory

We contrast four distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons and holes in a single-band model that is easily converted into a two-band model. The GBEC theory is essentially an extension of the Friedberg-Lee 1989 BEC theory of superconductors that excludes 2h-CPs. It can thus recover, when the numbers of 2h- and 2e-CPs in both BE-condensed and non-condensed states are separately equal, the BCS gap equation for all temperatures and couplings as well as the zero-temperature BCS (rigorous-upper-bound) condensation energy for all couplings. But ignoring either 2h- or 2e-CPs it can do neither. In particular, only half the BCS condensation energy is obtained in the two crossover versions ignoring either kind of CPs. We show how critical temperatures T-c from the original BCS-Bose crossover theory in 2D require unphysically large couplings for the Cooper/BCS model interaction to differ significantly from the T(c)s of ordinary BCS theory (where the number equation is substituted by the assumption that the chemical potential equals the Fermi energy). (c) 2007 Published by Elsevier B.V.

BCS-BEC crossover in an asymmetric two-component Fermi gas

We discuss the superfluid phase transition of a strongly interacting Fermi gas with unequal ( asymmetric) chemical potentials in two pairing hyperfine states, and map out its phase diagram near the BCS-BEC crossover. Our approach includes the fluctuation contributions of preformed Cooper pairs to the thermodynamic potential at finite temperature. We show that, below a critical difference in chemical potentials between species, a normal gas is unstable towards the formation of either a finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov superconducting phase or a uniform superfluid, depending on the asymmetry and interaction strengths. We determine the value of critical chemical potential mismatch, and find that it is consistent with a recent measurement by Zwierlein et al. ( Science, 311 ( 2006) 492).

Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozieres and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available.

Many-body approach to the BCS-BEC crossover for an imbalanced ultra-cold Fermi gas

The aim of this thesis is the study of the normal phase of a mass imbalanced and polarized ultra-cold Fermi gas in the context of the BCS-BEC crossover, using a diagrammatic approach known as t-matrix approximation. More specifically, the calculations are implemented using the fully self-consistent t-matrix (or Luttinger- Ward) approach, which is already experimentally and numerically validated for the balanced case. An imbalance (polarization) between the two spin populations works against pairing and superfluidity. For sufficiently large polarization (and not too strong attraction) the system remains in the normal phase even at zero temperature. This phase is expected to be well described by the Landau’s Fermi liquid theory. By reducing the spin polarization, a critical imbalance is reached where a quantum phase transition towards a superfluid phase occurs and the Fermi liquid description breaks down. Depending on the strength of the interaction, the exotic superfluid phase at the quantum critical point (QCP) can be either a FFLO phase (Fulde-Ferrell-Larkin-Ovchinnikov) or a Sarma phase. In this regard, the presence of mass imbalance can strongly influence the nature of the QCP, by favouring one of these two exotic types of pairing over the other, depending on whether the majority of the two species is heavier or lighter than the minority. The analysis of the system is made by focusing on the temperature-coupling-polarization phase diagram for different mass ratios of the two components and on the study of different thermodynamic quantities at finite temperature. The evolution towards a non-Fermi liquid behavior at the QCP is investigated by calculating the fermionic quasi-particle residues, the effective masses and the self-energies at zero temperature.

One dimensional extended Hubbard model: two-particle bound states and resonances.

In questo lavoro di tesi è stato svolto uno studio analitico sul modello di Hubbard esteso unidimensionale al fine di osservare la presenza di eventuali risonanze che possano dare origine alla formazione di stati legati di due particelle. L'esistenza di uno stato legato stabile ha suscitato grande interesse negli ultimi anni, sia in ambito teorico che sperimentale, poichè è alla base di molti fenomeni che vengono osservati nei sistemi a molti corpi a basse temperature, come il BCS-BEC crossover. Pertanto si è ritenuto utile studiare il problema a due corpi nel modello di Hubbard esteso, che in generale non è integrabile. Il modello considerato contiene interazioni a primi e secondi vicini, in aggiunta all'interazione di contatto presente nel modello di Hubbard. Il problema è stato indagato analiticamente attraverso il Bethe ansatz, che consente di trovare tutti gli autovalori e le autofunzioni dell'Hamiltoniana. L'ansatz di Bethe sulla funzione d'onda è stato generalizzato per poter tener conto dei termini di interazione a più lungo raggio rispetto all'interazione di contatto. Si trova che, in questo modello, nel limite termodinamico, possono avvenire delle risonanze (o quasi-risonanze) in cui la lunghezza di scattering diverge, contrariamente a quanto avviene nel modello di Hubbard. Tale fenomeno si verifica quando il livello energetico discreto degli stati legati “tocca” la banda di scattering. Inoltre, con l'aggiunta di nuovi termini di interazione emergono nuovi stati legati. Nel caso in esame, si osservano due famiglie di stati legati, se lo spin totale delle due particelle è 1, e tre famiglie di stati legati, se lo spin totale è 0.

Scaling in the BCS to Bose crossover problem in different partial waves

The BCS superconductivity to Bose condensation crossover problem is studied in two dimensions in S, P, and D waves, for a simple anisotropic pairing, with a finite-range separable potential at zero temperature. The gap parameter and the chemical potential as a function of Cooper-pair binding B c exhibit universal scaling. In the BCS limit the results for coherence length ξ and the critical temperature T c are appropriate for highT c cuprate superconductors and also exhibit universal scaling as a function of B c.

Nonlinear Schrodinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schrodinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where an(1/3)<<1 with a the interatomic s-wave scattering length and n the bosonic density, to the unitarity limit, where a ->+infinity. We call this equation the unitarity Schrodinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

Metronidazole Immediate Release Formulations: A Fasting Randomized Open-Label Crossover Bioequivalence Study in Healthy Volunteers

Metronidazole is a BCS (Biopharmaceutics Classification System) class 1 drug, traditionally considered the choice drug in the infections treatment caused by protozoa and anaerobic microorganisms. This study aimed to evaluate bioequivalence between 2 different marketed 250 mg metronidazole immediate release tablets. A randomized, open-label, 2 x 2 crossover study was performed in healthy Brazilian volunteers under fasting conditions with a 7-day washout period. The formulations were administered as single oral dose and blood was sampled over 48 h. Metronidazole plasma concentrations were determined by a liquid chromatography mass spectrometry (LC-MS/MS) method. The plasma concentration vs. time profile was generated for each volunteer and the pharmacokinetic parameters C-max, T-max, AUC(0-t), AUC(0-infinity), k(e), and t(1/2) were calculated using a noncompartmental model. Bioequivalence between pharmaceutical formulations was determined by calculating 90% CIs (Confidence Intervall) for the ratios of C-max, AUC(0-t), and AUC(0-infinity) values for test and reference using log-transformed data. 22 healthy volunteers (11 men, 11 women; mean (SD) age, 28 (6.5) years [range, 21-45 years]; mean (SD) weight, 66 (9.3) kg [range, 51-81 kg]; mean (SD) height, 169 (6.5) cm [range, 156-186 cm]) were enrolled in and completed the study. The 90% CIs for C-max (0.92-1.06), AUC(0-t) (0.97-1.02), and AUC(0-infinity) (0.97-1.03) values for the test and reference products fitted in the interval of 0.80-1.25 proposed by most regulatory agencies, including the Brazilian agency ANVISA. No clinically significant adverse effects were reported. After pharmacokinetics analysis, it concluded that test 250 mg metronidazole formulation is bioequivalent to the reference product according to the Brazilian agency requirements.

Double-blind, crossover, placebo-controlled clinical trial with clobetasol propionate in desquamative gingivitis

The aim of this study was to evaluate the efficacy of a 0.05% clobetasol propionate ointment administered in trays to 22 patients with desquamative gingivitis in a double-blind, crossover, placebo-controlled trial. Patients received container number 1 and were instructed to apply the ointment 3 times a day for 2 weeks, and to reduce the application to once a day in the third week. Next, the patients were then instructed to discontinue the treatment for 2 weeks, and were then given container 2, used in the same way and for the same length of time as container 1. Regarding signs, 17 patients presented some improvement, while 5 experienced worsening with clobetasol propionate. With the placebo, 14 patients presented some improvement, and 8 patients presented worsening. For symptoms, there was complete improvement in 2 patients, partial improvement in 12, no response in 7, and worsening in 1 with clobetasol propionate. With the placebo, there was partial improvement in 8 patients, no response in 12 and worsening in 2. No statistically significant difference was found between clobetasol and placebo (p>0.05). Within the period designed to treat the gingival lesions of the patients, clobetasol propionate did not significantly outperform the placebo.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.