Nonperturbative Quantum Physics from Low-Order Perturbation Theory

Understand

The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes.

• Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior.
• Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy.
• The key is to use analytic continuation functions with a built in analytic structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations.