Topology-controlled spectra of imaginary cubic oscillators in the large-L approach

TL;DR

This paper demonstrates a method to approximate bound-state energies of quantum particles on complex Riemann surfaces, revealing how the spectrum varies with the winding number in a cubic-oscillator model.

Contribution

It introduces a large-L approach to evaluate topology-controlled spectra of imaginary cubic oscillators on complex toboggan-shaped curves.

Findings

Spectrum decreases with increasing winding number N

Feasible approximation of bound-state energies on complex Riemann sheets

Method applicable to complex quantum systems with topological features

Abstract

For quantum (quasi)particles living on complex toboggan-shaped curves which spread over N Riemann sheets the approximate evaluation of topology-controlled bound-state energies is shown feasible. In a cubic-oscillator model the low-lying spectrum is shown decreasing with winding number N.