A realization of the Lie algebra associated to a Kantor triple system

We present a nonlinear realization of the 5-graded Lie algebra associated to a Kantor triple system. Any simple Lie algebra can be realized in this way, starting from an arbitrary 5-grading. In particular, we get a unified realization of the exceptional Lie algebras f_4, e_6, e_7, e_8, in which they are respectively related to the division algebras R, C, H, O.Comment: 11 page

On structure of effective action in four-dimensional quantum dilaton supergravity

A general structure of effective action in new chiral superfield model associated with $N=1$, $D=4$ supergravity is investigated. This model corresponds to finite quantum field theory and does not demand the regularization and renormalization at effective action calculation. It is shown that in local approximation the effective action is defined by two objects called general superfield effective lagrangian and chiral superfield effective lagrangian. A proper-time method is generalized for calculation of these two effective lagrangians in superfield manner. Power expansion of the effective action in supercovariant derivatives is formulated and the lower terms of such an expansion are calculated in explicit superfield form

Effect of the Spatial Dispersion on the Shape of a Light Pulse in a Quantum Well

Reflectance, transmittance and absorbance of a symmetric light pulse, the carrying frequency of which is close to the frequency of interband transitions in a quantum well, are calculated. Energy levels of the quantum well are assumed discrete, and two closely located excited levels are taken into account. A wide quantum well (the width of which is comparable to the length of the light wave, corresponding to the pulse carrying frequency) is considered, and the dependance of the interband matrix element of the momentum operator on the light wave vector is taken into account. Refractive indices of barriers and quantum well are assumed equal each other. The problem is solved for an arbitrary ratio of radiative and nonradiative lifetimes of electronic excitations. It is shown that the spatial dispersion essentially affects the shapes of reflected and transmitted pulses. The largest changes occur when the radiative broadening is close to the difference of frequencies of interband transitions taken into account.Comment: 7 pages, 5 figure

Back reaction of vacuum and the renormalization group flow from the conformal fixed point

We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. In this case the dominating quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to the renormalization group flow from the conformal point. In the supersymmetric conformal invariant model such an effect produces a very weak violation of sypersymmetry at lower energies.Comment: 15 pages, LaTex, ten figures, uuencoded fil

Instability of coherent states of a real scalar field

We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic nonlinearity. The linear analysis of time-dependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the Lindemann-Stieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stability-instability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be long-lived. Further, we use the obtaned stability-instability chart to examine the Affleck-Dine type condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review

Elastic Light Scattering by Semiconductor Quantum Dots

Elastic light scattering by low-dimensional semiconductor objects is investigated theoretically. The differential cross section of resonant light scattering on excitons in quantum dots is calculated. The polarization and angular distribution of scattered light do not depend on the quantum-dot form, sizes and potential configuration if light wave lengths exceed considerably the quantum-dot size. In this case the magnitude of the total light scattering cross section does not depend on quantum-dot sizes. The resonant total light scattering cross section is about a square of light wave length if the exciton radiative broadening exceeds the nonradiative broadening. Radiative broadenings are calculated

Coulomb Blockade Peak Spacings: Interplay of Spin and Dot-Lead Coupling

For Coulomb blockade peaks in the linear conductance of a quantum dot, we study the correction to the spacing between the peaks due to dot-lead coupling. This coupling can affect measurements in which Coulomb blockade phenomena are used as a tool to probe the energy level structure of quantum dots. The electron-electron interactions in the quantum dot are described by the constant exchange and interaction (CEI) model while the single-particle properties are described by random matrix theory. We find analytic expressions for both the average and rms mesoscopic fluctuation of the correction. For a realistic value of the exchange interaction constant J_s, the ensemble average correction to the peak spacing is two to three times smaller than that at J_s = 0. As a function of J_s, the average correction to the peak spacing for an even valley decreases monotonically, nonetheless staying positive. The rms fluctuation is of the same order as the average and weakly depends on J_s. For a small fraction of quantum dots in the ensemble, therefore, the correction to the peak spacing for the even valley is negative. The correction to the spacing in the odd valleys is opposite in sign to that in the even valleys and equal in magnitude. These results are robust with respect to the choice of the random matrix ensemble or change in parameters such as charging energy, mean level spacing, or temperature.Comment: RevTex, 11 pages, 9 figures. v2: Conclusions section expanded. Accepted for publication in PR