Frobenius Manifolds And Virasoro Constraints

For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus $\leq 1$ Virasoro conjecture of T.Eguchi, K.Hori, M.Jinzenji, and C.-S.Xiong and of S.Katz is proved for smooth projective varieties having semisimple quantum cohomology.Comment: Latex, 40 page

Extended affine Weyl groups and Frobenius manifolds

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions $F(t_1, ..., t_n)$ of WDVV equations of associativity polynomial in $t_1, ..., t_{n-1}, \exp t_n$.Comment: 69 pages, amslatex, some references added, position of Table 1 is corrected. Revised version for Compositio Mathematic

Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation

We compute the genus one correction to the integrable hierarchy describing coupling to gravity of a 2D topological field theory. The bihamiltonian structure of the hierarchy is given by a classical W-algebra; we compute the central charge of this algebra. We also express the generating function of elliptic Gromov - Witten invariants via tau-function of the isomonodromy deformation problem arising in the theory of WDVV equations of associativity.Comment: 53 pages, Latex, two references added, some typos corrected, version to appear in Commun. Math. Phy

Two-dimensional gap solitons in elliptic-lattice potentials

We study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed eccentricity of the lattice, soliton families are found in both the repulsive and attractive models. In the former case, the analysis reveals two kinds of gap solitons trapped in the first oval trough (the ring-shaped potential minimum closest to the center): elliptic annular solitons (EASs), and double solitons (DSs), which are formed by two tightly localized density peaks located at diametrically opposite points of the trough, with zero phase difference between them. With the decrease of the norm, the density distribution in the EAS along the azimuthal direction changes from nearly-uniform to double-peaked and, eventually, to the DS. In the attractive model, there exist only DSs in the oval trough, while EASs are not found. All such solitons without the angular momentum (l = 0) are fully stable. For l is not equal to 0, vortical solitons - both EASs with a sufficiently large norm (in the repulsive model) and DSs (in models with both signs of the nonlinearity) - are quasi-stable, exhibiting rocking motion in the elliptic trough (we consider the cases of l=1 and l=2). At smaller values of the norm, the vortical annular solitons (in the repulsive model) are unstable. Stable fundamental solitons trapped in the central potential well are investigated too, in both the attractive and repulsive models, by means of the variational approximation and numerical methods.Comment: Phys. Rev. A, in pres

Fast Compact Laser Shutter Using a Direct Current Motor and 3D Printing

We present a mechanical laser shutter design that utilizes a DC electric motor to rotate a blade which blocks and unblocks a light beam. The blade and the main body of the shutter are modeled with computer aided design (CAD) and are produced by 3D printing. Rubber flaps are used to limit the blade's range of motion, reducing vibrations and preventing undesirable blade oscillations. At its nominal operating voltage, the shutter achieves a switching speed of (1.22 $\pm$ 0.02) m/s with 1 ms activation delay and 10 $\mu$s jitter in its timing performance. The shutter design is simple, easy to replicate, and highly reliable, showing no failure or degradation in performance over more than $10^8$ cycles.Comment: 4 pages, 6 figures; supplementary materials for shutter replication added under "Ancillary files