Nonlinear Grassmann Sigma Models in Any Dimension and An Infinite Number of Conserved Currents

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions and, therfore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen). Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, $G/H$ sigma models in any dimension.Comment: 11 pages, AMSLaTe

Flow Representation of the Bose-Hubbard Hamiltonian : General Case

In this paper the explicit flow representation to the Bose-Hubbard Hamiltonian is given in the general case. This representation may be useful in creating cat states for the system of atoms trapped in the optical ring.Comment: Latex ; 8 pages ; 1 figure ; minor change

More on the Isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4)

In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes entanglements in the case of $n=2$ is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3

General Solution of the Quantum Damped Harmonic Oscillator

In this paper the general solution of the quantum damped harmonic oscillator is given.Comment: Latex ; 10 pages ; no figure ; typos corrected. The quantum damped harmonic oscillator is solved completel

An Approximate Solution of the Jaynes-Cummings Model with Dissipation

In this paper we treat the Jaynes-Cummings model with dissipation and give an approximate solution to the master equation for the density operator {\bf under the general setting} by making use of the Zassenhaus expansion.Comment: Latex ; 18 pages ; no figure. This is a paper based on hard calculatio

Submodels of Nonlinear Grassmann Sigma Models in Any Dimension and Conserved Currents, Exact Solutions

In the preceding paper(hep-th/9806084), we constructed submodels of nonlinear Grassmann sigma models in any dimension and, moreover, an infinite number of conserved currents and a wide class of exact solutions. In this paper, we first construct almost all conserved currents for the submodels and all ones for the one of ${\bf C}P^1$-model. We next review the Smirnov and Sobolev construction for the equations of ${\bf C}P^1$-submodel and extend the equations, the S-S construction and conserved currents to the higher order ones.Comment: 13 pages, AMSLaTex; an new section and an appendix adde