Linear response of a superfluid Fermi gas inside its pair-breaking continuum.

We study the signatures of the collective modes of a superfluid Fermi gas in its linear response functions for the order-parameter and density fluctuations in the Random Phase Approximation (RPA). We show that a resonance associated to the Popov-Andrianov (or sometimes "Higgs") mode is visible inside the pair-breaking continuum at all values of the wavevector q, not only in the (order-parameter) modulus-modulus response function but also in the modulus-density and density-density responses. At nonzero temperature, the resonance survives in the presence of thermally broken pairs even until the vicinity of the critical temperature Tc, and coexists with both the Anderson-Bogoliubov modes at temperatures comparable to the gap Δ and with the low-velocity phononic mode predicted by RPA near Tc. The existence of a Popov-Andrianov-"Higgs" resonance is thus a robust, generic feature of the high-energy phenomenology of pair-condensed Fermi gases, and should be accessible to state-of-the-art cold atom experiments.

Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases.

We demonstrate the existence of a collective excitation branch in the pair-breaking continuum of superfluid Fermi gases and BCS superconductors. At zero temperature, we analytically continue the equation on the collective mode energy in Anderson's Random Phase Approximation or Gaussian fluctuations through its branch cut associated with the continuum, and obtain the full complex dispersion relation, including in the strong coupling regime. The branch exists as long as the chemical potential µ is positive and the wave number below sqrt[2mµ]/ℏ (with m the fermion mass). In the long wavelength limit, the branch varies quadratically with the wave number, with a complex effective mass that we compute analytically for an arbitrary interaction strength.

Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation.

In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer options under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential.

Novel methods to create multielectron bubbles in superfluid helium.

An equilibrium multielectron bubble (MEB) in liquid helium is a fascinating object with a spherical two-dimensional electron gas on its surface. We discuss two ways in which they have been created. For MEBs that have been observed in the dome of a cylindrical cell with an unexpectedly short lifetime, we show analytically why these MEBs can discharge by tunneling. Using a novel method, MEBs have been extracted from a vapor sheath around a hot filament in superfluid helium by applying electric fields up to 15 kV∕cm, and photographed with high-speed video. Charges as high as 1.6×10(-9) C (∼10(10) electrons) have been measured. The latter method provides a means of capture in an electromagnetic trap to allow the study of the extensive exciting properties of these elusive objects.

Vortex core deformation and stepper-motor ratchet behavior in a superconducting aluminum film containing an array of holes.

We investigated experimentally the frequency dependence of a superconducting vortex ratchet effect by means of electrical transport measurements and modeled it theoretically using the time-dependent Ginzburg-Landau formalism. We demonstrate that the high frequency vortex behavior can be described as a discrete motion of a particle in a periodic potential, i.e., the so-called stepper-motor behavior. Strikingly, in the more conventional low frequency response a transition takes place from an Abrikosov vortex rectifier to a phase slip line rectifier. This transition is characterized by a strong increase in the rectified voltage and the appearance of a pronounced hysteretic behavior.

Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models.

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

Effect of pressure on statics, dynamics, and stability of multielectron bubbles.

The effect of positive and negative pressure on the modes of oscillation of a multielectron bubble in liquid helium is calculated. Already at low pressures of the order of 10-100 mbar, these effects are found to significantly modify the frequencies of oscillation of the bubble. Stabilization of the bubble is shown to occur in the presence of a small negative pressure, which expands the bubble radius. Above a threshold negative pressure, the bubble is unstable.