On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation

A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field and running mass models. It is demonstrated that the perturbative approach is more reliable than could be naively suspected and, in general, only breaks down at the very end of inflation.Comment: 7 pages, 3 figure

Closed form representation for a projection onto infinitely dimensional subspace spanned by Coulomb bound states

The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the $n^2$ dimensional subspace corresponding to the $n$-th eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of $n$-th and $(n-1)$-th order. The latter allows us to derive an analog of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two body subsystems is one of the most difficult technical problems.Comment: 7 page

Collective excitations of degenerate Fermi gases in anisotropic parabolic traps

The hydrodynamic low-frequency oscillations of highly degenerate Fermi gases trapped in anisotropic harmonic potentials are investigated. Despite the lack of an obvious spatial symmetry the wave-equation turns out to be separable in elliptical coordinates, similar to a corresponding result established earlier for Bose-condensates. This result is used to give the analytical solution of the anisotropic wave equation for the hydrodynamic modes.Comment: 11 pages, Revte

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us

QED on Curved Background and on Manifolds with Boundaries: Unitarity versus Covariance

Some recent results show that the covariant path integral and the integral over physical degrees of freedom give contradicting results on curved background and on manifolds with boundaries. This looks like a conflict between unitarity and covariance. We argue that this effect is due to the use of non-covariant measure on the space of physical degrees of freedom. Starting with the reduced phase space path integral and using covariant measure throughout computations we recover standard path integral in the Lorentz gauge and the Moss and Poletti BRST-invariant boundary conditions. We also demonstrate by direct calculations that in the approach based on Gaussian path integral on the space of physical degrees of freedom some basic symmetries are broken.Comment: 29 pages, LaTEX, no figure

Crossover from strong to weak confinement for excitons in shallow or narrow quantum wells

We present a theoretical study of the crossover from the two-dimensional (2D, separate confinement of the carriers) to the three-dimensional (3D, center-of-mass confinement) behavior of excitons in shallow or narrow quantum wells (QW's). Exciton binding energies and oscillator strengths are calculated by diagonalizing the Hamiltonian on a large nonorthogonal basis set. We prove that the oscillator strength per unit area has a minimum at the crossover, in analogy with the similar phenomenon occurring for the QW to thin-film crossover on increasing the well thickness, and in agreement with the analytic results of a simplified δ-potential model. Numerical results are obtained for GaAs/Alx Ga1-xAs and InxGa1-xAs/GaAs systems. Our approach can also be applied to obtain an accurate description of excitons in QW's with arbitrary values of the offsets (positive or negative) and also for very narrow wells. In particular, the crossover from 2D to 3D behavior in narrow GaAs/AlxGa1-xAs QW's is investigated: the maximum binding energy of the direct exciton in GaAs/AlAs QW's is found to be ∼26 meV and to occur between one and two monolayers