We present a Floquet treatment of multiphoton quantum interference in a strongly driven superconducting flux qubit. The periodically time-dependent Schrödinger equation can be reduced to an equivalent timeindependent infinite-dimensional Floquet matrix eigenvalue problem. For resonant or nearly resonant multiphoton transitions, we extend the generalized Van Vleck GVV nearly degenerate high-orde...

The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection operators are found which extract solutions of the wave equation corresponding to pure spin states of particles. The density of the electromagnetic current is...

The generalized Dirac equation of the second order, describing particles with spin 1/2 and two mass states, is analyzed. The projection operators extracting states with definite energy and spin projections are obtained. The first order generalized Dirac equation in the 20-dimensional matrix form and the relativistically invariant bilinear form are derived. We obtain the canonical energy-momentu...

We construct the string eld Hamiltonian for c = 1 6 m(m+1) string theory in the temporal gauge. In order to do so, we rst examine the Schwinger-Dyson equations of the matrix chain models and propose the continuum version of them. Results of boundary conformal eld theory are useful in making a connection between the discrete and continuum pictures. The W constraints are derived from the continuu...

There are hamiltonians that solve a search problem of finding one of N items in O( √ N) steps. They are hamiltonians to describe an oscillation between two states. In this paper we propose a generalized search hamiltonian, Hg. Then the known search hamiltonians become special cases of Hg. From the generalized search hamiltonian, we present remarkable results that searching with 100% is subject ...

We consider a linear Hamiltonian Difference System for the so-called singular case so that discrete Sturm]Liouville Equations of higher order are included in our theory. We introduce the concepts of focal points for matrix-valued and generalized zeros for vector-valued solutions of the system and define disconjugacy for linear Hamiltonian Difference Systems. We prove a Reid Roundabout Theorem w...