Stability of the Ground State of a Harmonic Oscillator in a Monochromatic Wave

Classical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and interacting with two lasers fields with close frequencies. Analytically and numerically a stability of the ``classical ground state'' (CGS) -- the vicinity of the point ($x=0, p=0$) -- is analyzed. In the quantum case, the method for studying a stability of the quantum ground state (QGS) is suggested, based on the quasienergy representation. The dynamics depends on four parameters: the detuning from the resonance, $\delta=\ell-\Omega/\omega$, where $\Omega$ and $\omega$ are, respectively, the wave and the oscillator's frequencies; the positive integer (resonance) number, $\ell$; the dimensionless Planck constant, $h$, and the dimensionless wave amplitude, $\epsilon$. For $\delta=0$, the CGS and the QGS are unstable for resonance numbers $\ell=1, 2$. For small $\epsilon$, the QGS becomes more stable with increasing $\delta$ and decreasing $h$. When $\epsilon$ increases, the influence of chaos on the stability of the QGS is analyzed for different parameters of the model, $\ell$, $\delta$ and $h$.Comment: RevTeX, 38 pages, 24 figure

Tax Advantages of Foundations and Exempt Organizations

Businessmen these days are playing an ever increasing role in the creation and support of non-profit philanthropic foundations. Their purpose is a dual one; to save taxes and to immortalize a family name, and they are as old as the pyramids. We know of about 20,000 foundations existing in England, but the large broad-purpose foundations were created in the United States. The greatest expansion in this area is attributable to the family and corporate foundations. The corporation tax of 52% and the individual income tax of up to 91% are so severe that high-bracket taxpayers can give to charity at a small cost

Duality Symmetric String and M-Theory

We review recent developments in duality symmetric string theory. We begin with the world sheet doubled formalism which describes strings in an extended space time with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an E_{n(n)} U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extend space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.Comment: Review article. 122 pages. V2 Published Version in Physics Report