We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological Bianchi type-I model with a minimally coupled massive scalar field f as the source by generalizing the calculation of Lukash and Schmidt @Astron. Nachr. 309, 25 ~1988!#. Contrary to other approaches we allow strong anisotropy. Combining analytical and numerical methods, we apply an adiabatic approximation for f , and ...

Lower hybrid (LH) waves (Ωci ω Ωce, where Ωi,e ≡ Zi,eeB/mi,ec) have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons and consequently are well-suited to driving current. Established modeling techniques use WKB expansions with self-consistent non-Maxwellian distributions. Higher order WKB expansions have shown some effects on the paralle...

We present a method of obtaining WKB type solutions for generalized .~ Schroedinger equations for which the Hamiltonian is an arbitrary matrix function of any.number of pairs of canonical operators. Our solution reduces the problem to that of finding the matrix which diagonalizes the classical Hamiltonian and determining the scalar WKB wave functions for the diagonalized Hamiltonian's entries (...

The exact steepest descent method was born in [AKT4] by combining the ordinary steepest descent method with the exact WKB analysis. (See, e.g., [AKT2] for the notion and notations of the exact WKB analysis used in this report.) It is a straightforward generalization of the ordinary steepest descent method and provides us with a new powerful tool for the description of Stokes curves as well as f...

In our earlier paper ([AKT1]), by interpreting the formal transformation to the Airy equation near a simple turning point as the symbol of a microdifferential operator, we derived the Voros connection formula or, equivalently, the discontinuity function of a Borel transformed WKB solution at its movable singularities. In this paper we extend this approach to the two turning points problem; by c...

In this paper we study the WKB-Langer asymptotic expansion of the eigenfunctions of a Schrödinger operator H = − 12 2 ∂2 ∂x2 + V (x). Then applying these asymptotic formulae we prove that the exact L eigenfunction ΨE(N, ) and its derivative ΨE(N, ) of the Schrödinger operator with a well-shaped analytic potential are approximated up to arbitrary order m by the semi-classical WKB-Langer approxim...

Recently Van Putten has suggested that superradiance of magnetosonic waves in a toroidal magnetosphere around a Kerr black hole may play a role in the central engine of gamma-ray bursts. In this context, he computed (in the WKB approximation) the superradiant amplification of scalar waves confined to a thin equatorial wedge around a Kerr hole and found that the superradiance is higher than for ...

We investigate topology changing processes in the WKB approximation of four dimensional quantum cosmology with a negative cosmological constant. As Riemannian manifolds which describe quantum tunnelings of spacetime we consider constant negative curvature solutions of the Einstein equation i.e. hyperbolic geometries. Using four dimensional polytopes, we can explicitly construct hyperbolic manif...

An accelerated algorithm for the resolution of the coupled Schrödinger/Poisson system, with open boundary conditions, is presented. This method improves the subband decomposition method (SDM) introduced in [N. Ben Abdallah, E. Polizzi, Subband decomposition approach for the simulation of quantum electron transport in nanostructures, J. Comp. Phys. 202 (2005), no. 1, 150–180]. The principal feat...

Pair-production of magnetic Reissner-Nordström black holes (of charges ±q) is studied in the next-to-leading WKB approximation. We consider generic quantum fluctuations in the corresponding instanton geometry, a detailed study of which suggests that, for sufficiently weak field B, the problem can be reduced to that of quantum fluctuations around a single truncated near-extremal Euclidean black ...