Shaping interactions between polar molecules with far-off-resonant light

We show that dressing polar molecules with a far-off-resonant optical field leads to new types of intermolecular potentials, which undergo a crossover from the inverse-power to oscillating behavior depending on the intermolecular distance, and whose parameters can be tuned by varying the laser intensity and wavelength. We present analytic expressions for the potential energy surfaces, thereby providing direct access to the parameters of an optical field required to design intermolecular interactions experimentally.Comment: 4 pages, 3 figure

Connection between two forms of extra-dimensional metrics revisited

5D cosmological model with 3-brane with matter is considered. The brane divides bulk in two AdS half spaces. Geometry of the model can be described by two types of coordinates: in the first setting the metric is static and the brane is moving in the bulk, in the second approach the metric is time-dependent and the brane is located at a fixed position in the bulk. Coordinate transformation connecting two coordinate systems is constructed.Comment: 7 page

The Hopf algebra of odd symmetric functions

We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd symmetric functions. In the odd setting we describe counterparts of the elementary and complete symmetric functions, power sums, Schur functions, and combinatorial interpretations of associated change of basis relations.Comment: 43 pages, 12 figures. v2: some correction

Ultralong-range order in the Fermi-Hubbard model with long-range interactions

We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a $64 \times 64$ square lattice we demonstrate the existence of a novel phase, possessing an `ultralong-range' order. The fingerprint of this phase -- the density correlation function -- features a non-trivial behavior on a scale of tens of the lattice sites. We study the properties and the stability of the ultralong-range ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms