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...

Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes immigration, binary reproduction, and death. The unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution (MPD) of t...

We consider the problem of high-frequency asymptotics for the time-dependent onedimensional Schrödinger equation with rapidly oscillating initial data. This problem is commonly studied via the WKB method. An alternative method is based on the limit Wigner measure. This approach recovers geometrical optics, but, like the WKB method, it fails at caustics. To remedy this deficiency we employ the s...

Rigorous asymptotic approximations of the WKB (or LiouvilleGreen) type are obtained for a basis of solutions to y+[ +g(t)]y = 0 in C -algebras. The WKB asymptotics being important in wave propagation, this contribution represents a rst step toward a theory applicable to PDE's, which should be developed within the framework of operator algebras. The nature of this approximation is such that it i...

Using semiclassical expressions for eigenphase shifts and bound state energies arising from WKB approximations to the solutions of coupled equations. we show that quantum mechanical formulas for the third virial coefficient (restricted to positive potentials) and for the second virial cofficient (with anisotropic interactions) lead to the known classical results when Ii goes to zero. The proced...