Universality in Phase Transitions for Ultracold Fermionic Atoms

We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance, BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in fermionic lithium and qualitative agreement with the condensate fraction in fermionic lithium and potassium. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms and the sound velocity.Comment: 33 pages, 13 figures, new parts added: computation of renormalization effects for the Feshbach coupling; comparison to a recent experiment on "bare molecules"; notion of enhanced universalit

Notes on the design of ailerons

Recent data have shown that certain forms or types of ailerons that are in extensive use are in reality quite inefficient and entirely unsuited for the high speeds now realized. The same data indicate that two forms (both shown here) are efficient and satisfactory in every way. The most important characteristics of ailerons are effectiveness under all flight conditions, small moments about the hinge, high efficiency (small yawing moment opposing turn), and simplicity in construction. Information required for the design of ailerons is given for chord, span, area, and plan form

Keldysh Field Theory for Driven Open Quantum Systems

Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in condensed matter. This concerns both their non-thermal flux equilibrium states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.Comment: 73 pages, 13 figure

Notes on the Construction and Testing of Model Airplanes

Here, it is shown that the construction of an airplane model can and should be simplified in order to obtain the most reliable test data. General requirements for model construction are given, keeping in mind that the general purpose of wind tunnel tests on a model airplane is to obtain the aerodynamic characteristics, the static balance, and the efficiency of controls for the particular combination of wings, tail surfaces, fuselage, and landing gear employed in the design. These parts must be exact scale reproductions. Any appreciable variation from scale reproduction must be in the remaining parts of the model, i.e., struts, wires, fittings, control horns, radiators, engines, and the various attachments found exposed to the wind in special airplanes. Interplane bracing is discussed in some detail

QCD factorizations in gamma* gamma* -> rho rho

We calculate the lowest order QCD amplitude, i.e. the quark exchange contribution, to the forward production amplitude of a pair of longitudinally polarized $\rho$ mesons in the scattering of two virtual photons $\gamma^*(Q_1) \gamma^*(Q_2) \to \rho^0_L \rho^0_L$. We show that the scattering amplitude simultaneously factorizes in two quite different ways: the part with transverse photons is described by the QCD factorization formula involving the generalized distribution amplitude of two final $\rho$ mesons, whereas the part with longitudinally polarized photons takes the QCD factorized form with the $\gamma^*_L \to \rho^0_L$ transition distribution amplitude. Perturbative expressions for these, in general, non-perturbative functions are obtained in terms of the $\rho-$meson distribution amplitude