Analytic approach to semiclassical logarithmic potential theory

Semiclassical treatment of the logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon ¯ h-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same ...

Logarithmic Potential Theory with Applications to Approximation Theory

We provide an introduction to logarithmic potential theory in the complex plane that particularly emphasizes its usefulness in the theory of polynomial and rational approximation. The reader is invited to explore the notions of Fekete points, logarithmic capacity, and Chebyshev constant through a variety of examples and exercises. Many of the fundamental theorems of potential theory, such as Fr...

Large deviation principle in logarithmic potential theory

Semiclassical Approach to Relativistic Nuclear Mean Field Theory

Approach to equilibrium of diffusion in a logarithmic potential.

The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x∼t(1/2)) and a subdiffusive (x∼t(γ) with a given γ<1/2) length scale, respectively, (ii) the...