Elliptic operators in even subspaces

In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces defined by even projections on odd-dimensional manifolds and for boundary value problems, generalizing the classical result of Atiyah-Bott. Besides a topological contribution of Atiyah-Singer type, the index formulas contain an invariant of subspaces defined by even projections. This homotopy invariant can be expressed in terms of the eta-invariant. The results also shed new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure

Elliptic operators in odd subspaces

An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with boundary, or as spectral subspaces for self-adjoint elliptic differential operators of odd order. Index formulas are obtained for operators in odd subspaces on closed manifolds and for general boundary value problems. We prove that the eta-invariant of operators of odd order on even-dimesional manifolds is a dyadic rational number.Comment: 27 page

Curvature-induced symmetry breaking in nonlinear Schrodinger models

We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states decreases with increasing curvature, i.e. bending is a trap for nonlinear excitations. A violation of the Vakhitov-Kolokolov stability criterium is found in the case where the instability is due to the softening of the Peierls internal mode.Comment: 4 pages (LaTex) with 6 figures (EPS

Mueller-Navelet jets in high-energy hadron collisions

We consider within QCD collinear factorization the process $p+p\to {\rm jet} +{\rm jet} +X$, where two forward high-$p_T$ jets are produced with a large separation in rapidity $\Delta y$ (Mueller-Navelet jets [1]). The hard part of the reaction receives large higher-order corrections $\sim \alpha^n_s (\Delta y)^n$, which can be accounted for in the BFKL approach. We calculate cross section and azimuthal decorrelation, using the next-to-leading order jet vertices, in the small-cone approximation [2].Comment: 4 pages, 3 figures; presented at the International Workshop "Diffraction 2012", Puerto del Carmen (Spain), September 10-15, 201