WKB method and quantum periods beyond genus one

Quantum Bubble Nucleation beyond WKB: Resummation of Vacuum Bubble Diagrams

On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rate. We study a metastable superrenormalizable field theory, D dimensional O(N) symmetric φ4 model (D < 4) with an attractive interaction. The validity of our proposal is tested in D = 1 (quantum mechanics) by using the perturbation series of ground state energy to high orde...

Quasilinearization method and WKB

Solutions obtained by the quasilinearization method (QLM) are compared with the WKB solutions. While the WKB method generates an expansion in powers of h̄, the quasilinearization method (QLM) approaches the solution of the nonlinear equation obtained by casting the Schrödinger equation into the Riccati form by approximating nonlinear terms by a sequence of linear ones. It does not rely on the ex...

Divergence-free WKB method.

A new semiclassical approach to the linear and nonlinear one-dimensional Schrödinger equation is presented. For both equations our zeroth-order solutions include nonperturbative quantum corrections to the WKB solution and the Thomas-Fermi solution, thereby allowing us to make uniformly converging perturbative expansions of the wave functions. Our method leads to a new quantization condition tha...

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Unruh Radiation via WKB Method