Conditions for the existence of a gyroscope in spaces with affine connections and metrics are found. They appear as special types of Fermi-Walker transports for vector fields, lying in a subspace, orthogonal to the velocity vector field (a non-null contravariant vector field) of an observer.

The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin components are automatically satisfied. In general the spin is not Fermi-Walker transported nor does the position follow a geodesic, although the deviations...

We develop a new formalism for the description of the condensates of cold Fermi atoms whose speed of sound can be tuned with the aid of a narrow Feshbach resonance. We use this to look for spontaneous phonon creation that mimics spontaneous particle creation in curved space-time in Friedmann-Robertson-Walker and other model universes.

This thesis has three parts. In the first, we study the Das-Jevicki collective field description of arbitrary classical solutions in the c = 1 matrix model, which are believed to describe nontrivial spacetime backgrounds in 2D string theory. Our analysis naturally includes the case of a Fermi droplet cosmology. We cast the droplet collective field theory in standard coordinates and comment on t...

Here Ω is a bounded domain in RN with smooth boundary, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, and ∂/∂ν is the outer normal derivative. In the linear case, that is for p = 2, this eigenvalue problem is known as the Steklov problem (see [3]). Problems of the form (1.1) appear in a natural way when one considers the Sobolev trace inequality. In fact, the immersionW1,p(Ω) ↪→ Lp(∂Ω) is compact, he...

The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss interesting dynamics of the energy transfer process starting from a large-scale excitation. This failure is traced to an enforcement of the exact resonance conditi...