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...

We apply exact WKB methods to the study of the partition function of pure N = 2 i-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in 2/ 1 (i.e. at large central charge) and in an expansion in 1. We find corrections of the form ∼ exp[− periods 1 ] to this expansion. We attribute these to the exchange of the ord...

In this paper, based on lectures by the authors at the May 2015 workshop Resurgence, Physics and Numbers, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB. Exact quantization conditions naturally arise, and their expa...

We study the non-linear Schödinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.

We calculate both the exponential and pre-factor contributions in a WKB approximation of the master equation for a stochastic SIR model with highly oscillatory dynamics. Fixing the basic parameters of the model we investigate how the outbreak distribution changes with the population size. We show that this distribution rapidly becomes highly non-Gaussian, acquiring large tails indicating the pr...

For a higher order linear ordinary differential operator P , its Stokes curve bifurcates in general when it hits another turning point of P . This phenomenon is most neatly understandable by taking into account Stokes curves emanating from virtual turning points, together with those from ordinary turning points. This understanding of the bifurcation of a Stokes curve plays an important role in ...

M. Akhalkatsi Physics Department, Tbilisi State University, Tbilisi 0179, Georgia (Dated: October 2004) Abstract The linear dynamics of acoustic waves and vortices in uniform shear flow is studied. For flows with very low shear rates, the dynamics of perturbations is adiabatic and can be described by the WKB approximation. However, for flows with moderate and high shear rates the WKB approximat...

We compute the exact spectral density of random matrices in the ground state of the quantum hamiltonian corresponding to the matrix model whose double scaling limit describes pure gravity in 2D. We show that the non-perturbative effects are very large and in certain cases dominate the semi-classical WKB contribution studied in the earlier literature. The physical observables in this model are t...

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 ...