WKB p-forms are constructed as approximate solutions to boundary value problems associated with semi-classical Witten Laplacians. Naturally distorted Neumann or Dirichlet boundary conditions are considered. MSC 2000: 58J37 (58J10 58J32 81Q20)

The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.

We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found from the analysis of the Hamilton trajectories of the particle in complex phase space and time. In a magnetic field, the tunneling particle comes from beneath...

We investigate the system of a particle moving on a half line x ≥ 0 under the general walls at x = 0 that are permitted quantum mechanically. These quantum walls, characterized by a parameter L, are shown to be realized as a limit of regularized potentials. We then study the classical aspects of the quantum walls, by seeking a classical counterpart which admits the same time delay in scattering...

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We cir...

We re-examine the semiclassical approximation to quantum gravity in the canonical formulation. It is shown that the usual interpretation of a WKB state does not give an adequate semiclassical description of both matter and gravity degrees of freedom. A state for the gravitational eld is proposed which has the necessary properties to describe quantum eld theory on a background spacetime with sma...

We consider the Cauchy problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of the high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first di...

We consider a quantum cosmology with a massless background scalar field φB and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field φB. In this model it is shown that to trace the formalism of the WKB time is seriously difficult without introducing a complex value for a time. We de...