Rescaled Perturbation Theory

A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in which information of the higher order terms is necessary, we only need a leading order perturbative formula in every step to reach the large value of $g$. The method is applied to the quantum anharmonic oscillator and quantum double well potential in one dimension. Both are known to have divergent series in the weak coupling perturbation and the latter is not Borel summable. Our method is shown to work well from the weak coupling to the strong coupling for the energy eigenvalues and the wave functions. The method is also applied successfully to the system with time-dependent external field.Comment: 8 pages, 4 figure

Chiral magnetic effect of light

We study a photonic analog of the chiral magnetic (vortical) effect. We discuss that the vector component of magnetoelectric tensors plays a role of "vector potential," and its rotation is understood as "magnetic field" of a light. Using the geometrical optics approximation, we show that "magnetic fields" cause an anomalous shift of a wave packet of a light through an interplay with the Berry curvature of photons. The mechanism is the same as that of the chiral magnetic (vortical) effect of a chiral fermion, so that we term the anomalous shift "chiral magnetic effect of a light." We further study the chiral magnetic effect of a light beyond geometric optics by directly solving the transmission problem of a wave packet at a surface of a magnetoelectric material. We show that the experimental signal of the chiral magnetic effect of a light is the nonvanishing of transverse displacements for the beam normally incident to a magnetoelectric material.Comment: 6+3 pages, 3+1 figures; (v2) supplemental material added; (v3) version accepted for publication in PR