1 citations · 3 across the 9 of their papers we have counts for
9 papers
Cyclic Evolution on Grassmann Manifold and Berry Phase
Zakaria Giunashvili
For a given -dimensional subspace in a Hilbert space $\hilb$ and a unitary transformation $g_0:V_0\To V_0$, we find a path in the Grassmann manifold the monodromy of which…
Algebraic definition of Holonomy on Poisson Manifold
Zakaria Giunashvili
We give an algebraic construction of connection on the symplectic leaves of Poisson manifold, introduced in \cite{Ginzburg}. This construction is suitable for the definition of the…
Geometric Control Methods for Quantum Computations
Zakaria Giunashvili
The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very…
Bott Connection and Generalized Functions on Poisson Manifold
Zakaria Giunashvili
We extend the problem of finding Hamiltonian-invariant volume forms on a Poisson manifold to the problem of construction of Hamiltonian-invariant generalized functions. For this we…
Noncommutative Symplectic Geometry of the Endomorphism Algebra of a Vector Bundle
Zakaria Giunashvili
We study noncommutative generalizations of such notions of the classical symplectic geometry as degenerate Poisson structure, Poisson submanifold and quotient manifold, symplectic…
Hamiltonian Systems on Complex Grassmann Manifold. Holonomy and Schrodinger Equation
Zakaria Giunashvili
Differential geometric structures such as the principal bundle for the canonical vector bundle on a complex Grassmann manifold, the canonical connection form on this bundle, the ca…