Abstract
It is a huge challenge in both classical and quantum physics to solve analytically the equation of motion in a strongly anharmonic confinement. For an isolated nanoring, we propose a continuous and bounded potential model, which patches up the disadvantages of the usual square-well and parabolic potentials. A fully nonlinear and nonperturbative approach is developed to solve analytically the equation of motion, from which various frequency shifts and dynamic displacements are exactly derived by an order-by-order self-consistent method. A series of new energy levels and new energy states are found, indicating an alternative magnetic response mechanism. In nominally identical rings, especially, we observe a diamagnetic-paramagnetic transition in the period-halving Φ(0)/2-current with Φ(0) the flux quantum and a large increase in the Φ(0)-current at least one order of magnitude, which explain well the experimental observations. This work opens a new way to solve the strong or weak nonlinear problems.