Related papers: ON THE LARGE ORDER ASYMPTOTICS OF THE WAVE FUNCTIO…
The problem of large order behaviour of perturbation theory for quantum mechanical systems is considered. A new approach to it is developed. An explicit mechanism showing the connection between large order recursive relations and classical…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
We solve the higher order equations of the theory of the strong perturbations in quantum mechanics given in M. Frasca, Phys. Rev. A 45, 43 (1992), by assuming that, at the leading order, the wave function goes adiabatically. This is…
High orders of perturbation theory can be calculated by the Lipatov method, whereby they are determined by saddle-point configurations (instantons) of the corresponding functional integrals. For most field theories, the Lipatov asymptotics…
The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the…
We discuss a few, apparently different (but actually, tightly related) problems: 1. The relation between QCD and valence quark model, 2. The evaluation of the nonlocal condensate $ \la \bar{q}(x)q(0)\ra $, its relation to heavy-light…
The spectral problem for O(D) symmetric polynomial potentials allows for a partial algebraic solution after analytical continuation to negative even dimensions D. This fact is closely related to the disappearance of the factorial growth of…
In these lectures, we provide an introduction to the complex WKB method, using as a guiding example a class of anharmonic oscillators that appears in the ODE/IM correspondence. In the first three lectures, we introduce the main objects of…
Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
We prove that, for a quantum system that undergoes a strong perturbation, the solution of the leading order equation of the strong field approximation (M.Frasca, Phys. Rev. A, {\bf 45}, 43 (1992)) can be derived by the adiabatic…
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…
We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…
In a large variety of quantum mechanical systems, we show that the full non-perturbative expression for energy eigenvalues, containing all orders of perturbative, non-perturbative and quasi-zero-mode terms, may be generated directly from…
We discuss recent developments in the study of quantum wavefunctions and transport in classically ergodic systems. Surprisingly, short-time classical dynamics leaves permanent imprints on long-time and stationary quantum behavior, which are…
Thesis includes review on the large order behaviour of perturbation theory in quantum mechanical and field theory models; generalization of the Borel summability and strong asymptotic conditions to various (including horn-shaped) regions;…
Sphalerons -- unstable static solutions of classical field equations in (d+1)-dimensional space-time -- may be viewed as euclidean solutions in d dimensions. We discuss their role in the large order asymptotics of the perturbation theory.…
We consider a three-dimensional Fourier integral in which the exponent in the exponential factor is the product of some phase function and a large parameter. The asymptotics of this integral is sought when the large parameter tends to…
After revealing difficulties of the standard time-dependent perturbation theory in quantum mechanics mainly from the viewpoint of practical calculation, we propose a new quasi-canonical perturbation theory. In the new theory, the dynamics…