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

How natural is a small but nonzero cosmological constant?

Based on our previous attempt, we propose a better way to understand a small but nonzero cosmological constant, as indicated by a number of recent observational studies. We re-examine the assumptions of our model of two scalar fields, trying to explain the basic mechanism resulting in a series of mini-inflations occuring nearly periodically with respect to $\ln t$ with $t$ the cosmic time. We also discuss how likely the solution of this type would be, depending on the choice of the parameters.Comment: 12 pages, latex, 5 figures as epsf files included, compressed uuencode

Possible time-variability of the fine-structure constant expected from the accelerating universe

We present a theoretical calculation on the time-variability of the fine-structure constant to fit the result of the recent precise analysis of the measurement of the QSO absorption lines. We find the parameters and initial values of the scalar-tensor theory to be determined much more accurately than fitting the accelerating universe itself, but leading not to easy detections of the effect on the equation of state of the dark energy in the earlier epochs.Comment: 9 pages, 9 figures. Revised interpretation of the theoretical fit; more recent reference

Mathematical Structure of Rabi Oscillations in the Strong Coupling Regime

In this paper we generalize the Jaynes--Cummings Hamiltonian by making use of some operators based on Lie algebras su(1,1) and su(2), and study a mathematical structure of Rabi floppings of these models in the strong coupling regime. We show that Rabi frequencies are given by matrix elements of generalized coherent operators (quant--ph/0202081) under the rotating--wave approximation. In the first half we make a general review of coherent operators and generalized coherent ones based on Lie algebras su(1,1) and su(2). In the latter half we carry out a detailed examination of Frasca (quant--ph/0111134) and generalize his method, and moreover present some related problems. We also apply our results to the construction of controlled unitary gates in Quantum Computation. Lastly we make a brief comment on application to Holonomic Quantum Computation.Comment: Latex file, 24 pages. I added a new section (Quantum Computation), so this paper became self-contained in a certain sens

Note on Coherent States and Adiabatic Connections, Curvatures

We give a possible generalization to the example in the paper of Zanardi and Rasetti (quant-ph/9904011). For this generalized one explicit forms of adiabatic connection, curvature and etc. are given.Comment: Latex file, 12 page

Induced Violation of Weak Equivalence Principle in the Brans-Dicke Theory

A quantum correction to the Brans-Dicke theory due to interactions among matter fields is calculated, resulting in violation of WEP, hence giving a constraint on the parameter $\omega$ far more stringent than accepted so far. The tentative estimate gives the lower bounds \gsim 10^{6} and \gsim 10^{8} for the assumed force-range \gsim 1m and \gsim 1AU, respectively.Comment: 7 pages, LaTe