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.     

Virtual states and resonances

The distinction between an s-wave virtual state and a resonance is explained by exhibiting the characteristic phase shifts and scattering cross-section shapes attributable to each. They are described in both R-matrix and S-matrix terms, and the relation between these two parametrizations is explained. As an application, in the two succeding papers we investigate the energy dependence of the s-wave neutron strength function and show how it is affected by the presence of a virtual state in the complex optical potential. Such a state is expected to occur for A ≈ 50 and A ≈ 150, where the 3s and 4s optical states are slightly unbound.     

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.     

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.     

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.     

Sasakian and Parabolic Higgs Bundles

Let M be a quasi-regular compact connected Sasakian manifold, and let N = M/S ¹ be the base projective variety. We establish an equivalence between the class of Sasakian G–Higgs bundles over M and the class of parabolic (or equivalently, ramified) G–Higgs bundles over the base N.     

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.     

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.     

Scaling and instabilities in bubble pinch-off

We have used a 100 000 frame-per-second video to analyze the pinch-off of nitrogen gas bubbles in fluids with a wide range of viscosity. If the external fluid is highly viscous (eta(ext)>100 cP), the bubble neck radius is proportional to the time before break, tau, and decreases smoothly to zero. If the external fluid has low viscosity (eta(ext)<10 cP), the radius scales as tau(1/2) until an instability develops in the gas bubble, which causes the neck to rupture and tear apart. Finally, if the viscosity of the external fluid is in an intermediate range, an elongated thread is formed, which breaks apart into micron-sized bubbles.     

Motor-driven bacterial flagella and buckling instabilities

Many types of bacteria swim by rotating a bundle of helical filaments also called flagella. Each filament is driven by a rotary motor and a very flexible hook transmits the motor torque to the filament. We model it by discretizing Kirchhoff’s elastic-rod theory and develop a coarse-grained approach for driving the helical filament by a motor torque. A rotating flagellum generates a thrust force, which pushes the cell body forward and which increases with the motor torque. We fix the rotating flagellum in space and show that it buckles under the thrust force at a critical motor torque. Buckling becomes visible as a supercritical Hopf bifurcation in the thrust force. A second buckling transition occurs at an even higher motor torque. We attach the flagellum to a spherical cell body and also observe the first buckling transition during locomotion. By changing the size of the cell body, we vary the necessary thrust force and thereby obtain a characteristic relation between the critical thrust force and motor torque. We present a elaborate analytical model for the buckling transition based on a helical rod which quantitatively reproduces the critical force-torque relation. Real values for motor torque, cell body size, and the geometry of the helical filament suggest that buckling should occur in single bacterial flagella. We also find that the orientation of pulling flagella along the driving torque is not stable and comment on the biological relevance for marine bacteria.     

Expanding color flux tubes and instabilities

We present an analytic study of the physics of the glasma which is a strong classical gluon field created at early stage of high-energy heavy-ion collisions. Our analysis is based on the picture that the glasma just after the collision is made of color electric and magnetic flux tubes extending in the longitudinal direction with their diameters of the order of 1/Q_s (Q_s is the saturation scale of the colliding nuclei). We find that both the electric and magnetic flux tubes expand outwards and the field strength inside the flux tube decays rapidly in time. Next we investigate whether there exist instabilities against small rapidity-dependent perturbations for a fixed color configuration. We find that the magnetic background field exhibits an instability induced by the fluctuations in the lowest Landau level, and it grows exponentially in the time scale of 1/Q_s. For the electric background field we find no apparent instability while the possible relation to the Schwinger mechanism for particle pair creations is suggested.     

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.