11,560 research outputs found
On Weyl-Titchmarsh Theory for Singular Finite Difference Hamiltonian Systems
We develop the basic theory of matrix-valued Weyl-Titchmarsh M-functions and
the associated Green's matrices for whole-line and half-line self-adjoint
Hamiltonian finite difference systems with separated boundary conditions.Comment: 30 pages, to appear in J. Comput. Appl. Mat
Alternating Quotients of Fuchsian Groups
It is shown that any finitely generated non-elementary Fuchsian group has
among its homomorphic images all but finitely many of the alternating groups.
This settles in the affirmative a conjecture of Graham Higman.Comment: 20 pages, 7 figure
Graphs, free groups and the Hanna Neumann conjecture
A new bound for the rank of the intersection of finitely generated subgroups
of a free group is given, formulated in topological terms, and very much in the
spirit of Stallings. The bound is a contribution to (although unfortunately not
a solution of) the strengthened Hanna Neumann conjecture.Comment: J. Group Theory (to appear
Multiphoton resonances for all-optical quantum logic with multiple cavities
We develop a theory for the interaction of multilevel atoms with multimode cavities yielding cavity-enhanced multiphoton resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realized when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the Fredkin gate and iSWAP operation; the system seems promising for scalability
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