Novel p-wave superfluids of fermionic polar molecules.

Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry.

Localization at the edge of a 2D topological insulator by Kondo impurities with random anisotropies.

We consider chiral electrons moving along the one-dimensional helical edge of a two-dimensional topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.

Field theory for the global density of states distribution function of disordered conductors.

A field-theoretical representation is suggested for the electron global density of states distribution function P(nu) in extended disordered conductors. This opens a way to study the complete statistics of fluctuations. The approach is based on a functional integration over bilocal functions Psir(1)(r(2)) instead of the integration over local functions in the usual functional representation for moments of physical quantities. The formalism allows one to perform the disorder averaging and to derive an analog of the usual nonlinear sigma model-a slow functional of a supermatrix field Qr(1)(r(2))(r) approximately Psi(rr(1)) composite functionPsi (r(2)r). As an application of the formalism, the long-tail asymptotics of P(nu) is derived.

Classical diffusion in channels with a spatially varying cross-section.

We study the diffusion of classical particles in channels with varying boundaries. The problem is characterized by the Neumann boundary condition (zero normal current) in contrast to the Dirichlet boundary condition (zero function) for "quantum confinement" problems. Eliminating transverse modes, we derive an effective diffusion equation that describes particle propagation in the space of reduced dimension in the presence of a frozen drift field. The latter stems from boundary variations of the original boundary problem. Boundary variations may thus result in an appreciable change of the particle transport and, in particular, in a nonlinear response to an external field. We show also that there is a difference between the nonlinear responses of open and closed channels.