Related papers: Cyclic Evolution on Grassmann Manifold and Berry P…

We point out that unitary representations of the Virasoro algebra contain Berry phases obtained by acting on a primary state with conformal transformations that trace a closed path on a Virasoro coadjoint orbit. These phases can be computed…

We give lowed bounds on the number of periodic trajectories in strictly convex smooth billiards in $\R^{m+1}$ for $m\ge 3$. For plane billiards (when m=1) such bounds were obtained by G. Birkhoff in the 1920's. Our proof is based on…

Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…

A particle which lives in a d-dimensional ordinary and a d-dimensional Grassmann space manifests itself in an ordinary four-dimensional subspace as a spinor, a scalar or a vector with charges. Operators of the Lorentz transformations and…

We propose a novel evolutionary algorithm for optimizing real-valued objective functions defined on the Grassmann manifold Gr}(k,n), the space of all k-dimensional linear subspaces of R^n. While existing optimization techniques on Gr}(k,n)…

The influence of the geometric phase, in particular the Berry phase, on an entangled spin-1/2 system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to…

We consider the KdV equation on a circle and its Lie-Poisson reconstruction, which is reminiscent of an equation of motion for fluid particles. For periodic waves, the stroboscopic reconstructed motion is governed by an iterated map whose…

In this work we consider Randall-Sundrum brane-world type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic…

In the vector-field guided path-following problem, a sufficiently smooth vector field is designed such that its integral curves converge to and move along a one-dimensional geometric desired path. The existence of singular points where the…

Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where they extend the ubiquitous role of toric geometry. The Gibbs…

In this paper we are investigated the monodromy group for linearly polymorphic functions on compact Riemann surface of genus $g \geq 2,$ in connection with standard uniformization of these surfaces by Kleinian groups, and are found a…

We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the…

In some previous work, we defined an invariant of genus zero nonabelian Hodge spaces taking the form of a diagram. Here, enriching the diagram by fission data to obtain a refined invariant, the enriched tree, including a partition of the…

The canonical evolution and symmetry generators are exhibited for a Klein-Gordon (K-G) system which has been partitioned by an accelerated coordinate frame into a pair of subsystems. This partitioning of the K-G system is conveyed to the…

In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel…

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, "states" with negative probability can be identified on…

We investigate cosmological evolution in models where the effective potential V(\phi) may become negative for some values of the field \phi. Phase portraits of such theories in space of variables (\phi,\dot\phi,H) have several qualitatively…

We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact K\"ahler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation…

Let X be a complex submanifold of projective space. Schnell showed that the middle-dimensional primitive cohomology of X is generated by tube classes, which arise from the monodromy of the vanishing homology on hyperplane sections. Clemens…

Let S be a K3 surface. In part I of this paper, we constructed a representation of the group Aut D(S), of auto-equivalences of the derived category of S. We interpreted this infinite dimensional representation, as the natural action of Aut…