Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.     

Decay amplitudes and resonances

The structure of a type of decay amplitudes, which we considered recently and its connection to scattering amplitudes (of arbitrary arrangement channel cases), to conventional decay amplitudes, and to the energy distribution is worked out in detail. The meaning of unperturbed energies in usual approaches is clarified. Our considerations include the case of overlapping resonances. Sum rules for transition amplitudes, such as are of interest for neutral kaon decays, are rigorously derived. The exact interrelations between various approaches are shown.     

Three-pion resonances

We investigate the continuum three-pion problem within a relativistic three-body model that takes into account the S andP waves. The dynamical input of the two-body subsystem is given by separable potentials, which yield a good fit to the scattering data and resonance parameters up to a two-body invariant mass of 900MeV. We introduce a parameter expressing the ambiguity in the reduction of a fully relativistic theory to a three-dimensional one. The masses and widths of the ,a ₁(1260), and (1300) mesons, which decay predominantly into three pions, are reasonably well described by our model. Theh ₁(1170) meson, however, which also decays into three pions, cannot be explained as a three-pion resonance. Some Argand diagrams are shown in those channels where resonances exist.     

Bragg-grating-enhanced polarization instabilities

Experiments demonstrate a dramatic decrease in polarization-instability threshold as an optical pulse is tuned near the short-wavelength edge of the photonic bandgap formed by a fiber Bragg grating. These enhanced nonlinear interactions and birefringent effects are modeled with coupled-mode numerical simulations. Nonlinearities are shown to increase much more rapidly than the effective birefringence as the pulse wavelength approaches the bandgap edge.     

Quantum linearization instabilities

We discuss quantizing the perturbations of a symmetrical background space-time and are led to study the quantum analogue of linearization instabilities. We outline the derivation of the second-order quantum constraints that arise whenever perturbations of symmetric space-times with compact Cauchy surfaces are quantized. These second-order constraints require invariance of all the allowed quantum states (not just the vacuum state) under the symmetry group of the background space-time. This result is discussed in light of the conclusion by Gibbons and Hawking that the thermal radiation produced by event horizons in de Sitter space is invariant under the de Sitter group and thus does not admit a semiclassical interpretation.This essay was awarded the second prize for 1978 by the Gravity Research Foundation. (Ed.)Supported in part by National Science Foundation Grant No. PHY76-82353.     

Nonequilibrium phase transitions and chemical instabilities

The effect of inhomogeneous fluctuations on instabilities in various nonlinear chemical models is studied in terms of concepts developed in the theory of equilibrium phase transitions.Chercheur qualifié au Fonds National de la Recherche Scientifique.     

Two-photon laser and optical-bistability sidemode instabilities

Two-photon laser oscillation and optical bistability have been observed and studied theoretically by various groups. The studies have not considered the buildup of sidemodes. We have extended the corresponding one-photon sidemode treatments to two-photon transitions for which no resonant intermediate levels exist. For the two-photon laser, we find a wide region of single-wavelength instability for a centrally tuned strong mode. For the corresponding two-photon absorptive optical bistability, we predict no single-wavelength instabilities. For strong-mode detuning, we find that appreciable regions of sidemode gain exist for both problems allowing multiwavelength instabilities to occur.     

The nucleon-antinucleon interaction and resonances

We present predictions for nucleon-nucleon elastic scattering phase parameters based on a unitary, relativistic, one-pion-exchange model, which takes single-pion-production inelasticity into account. The agreement of the high-L phase shifts with data is considerably improved at intermediate energies by inclusion of the NΔ inelastic channel. Our predicted inelasticities are in generally good agreement with the data, but are smaller than the predictions of Green and Sainio. The Argand plots of the ¹D₂, ³F₃, ³P₁, and ¹G₄ all show counterclockwise motion resulting from the onset of inelastic channels.     

Crackles and instabilities during lung inflation

In a variety of physico-chemical reactions, the actual process takes place in a reactive zone, called the “active surface”. We define the active surface of the lung as the set of airway segments that are closed but connected to the trachea through an open pathway, which is the interface between closed and open regions in a collapsed lung. To study the active surface and the time interval between consecutive openings, we measured the sound pressure of crackles, associated with the opening of collapsed airway segments in isolated dog lungs, inflating from the collapsed state in 120 s. We analyzed the sequence of crackle amplitudes, inter-crackle intervals, and low frequency energy from acoustic data. The series of spike amplitudes spans two orders of magnitude and the inter-crackle intervals spans over five orders of magnitude. The distribution of spike amplitudes follows a power law for nearly two decades, while the distribution of time intervals between consecutive crackles shows two regimes of power law behavior, where the first region represents crackles coming from avalanches of openings whereas the second region is due to the time intervals between separate avalanches. Using the time interval between measured crackles, we estimated the time evolution of the active surface during lung inflation. In addition, we show that recruitment and instabilities along the pressure–volume curve are associated with airway opening and recruitment. We find a good agreement between the theory of the dynamics of lung inflation and the experimental data which combined with numerical results may prove useful in the clinical diagnosis of lung diseases.     

Arnold resonances and quantum states

The dynamics of one electron interacting with a linear chain of heavy atoms bears a strong similarity with the propagation of a classical wave in a periodic non linear medium. Arnold resonances of the dynamical system play a central role. Some of the quantum states associated with these resonances are delocalized and contribute to phenomena such as Peierls dimerization while other ones are localized and are similar to the gap solitons of the classical wave theory, we call them Braggons. Complex Braggons containing several electrons inside the same localized profile are also described.     

Nucleon resonances and anomalous dimensions

It is studied whether duality analogous to that of Bloom and Gilman holds in the case in which the non-canonical scaling proves to be true. The data show that such duality holds well, independently of Q².     

Light gauginos: Masses and instabilities

Within the framework of supergravity models without grand unified steps, we analyse in detail the consequences of the hypothesis that gauginos have no bare masses due to supergravity interactions. To this purpose we have made a one-loop calculation of wino, zino, and photino masses and a renormalization group improved two-loop calculation of the gluino masses.We find that: (i) the non-observation of charged winos is compatible either with a gravitino mass m ? 300 GeV or $\text{m ?3}\text{TeV}$; (ii) with a top quark mark of about 40 GeV, gluino and photino have very similar masses ranging from O(1 GeV) to O(20 GeV). In most cases consistency with cosmology requires that the gauge singlet needed to break the SU(2) × U(1) symmetry, be the lightest stable supersymmetric particle, with a mass as low as 1 keV or less. In such cases photino (or gluino) lifetimes into one photon (gluon) and one light singlet fermion (zerino), are typically between 10^?3 and 1 sec.We discuss the problem of the experimental detection of gauginos, which, according to the various options, require rather different approaches.     

Gamow-Teller resonances and nuclear structure

By means of numerical calculations in the framework of the continuum shell model, it is shown that a resonance state with simple nuclear structure can be localized in energy despite strong fragmentation of the discrete state because of its short lifetime. Such a reduction in the degree of mixing is not taken into account in the traditional nuclear structure investigations of discrete states. The results obtained are applied to an interpretation of both the isobaric analogue and the Gamow-Teller resonances. The role of internal and external mixing is discussed.