Quantum Spontaneous Magnetization in Single-Junction Superconducting π-Rings

Based upon the calculations of energy levels and quantum states, we discuss the probability of quantum spontaneous magnetization flux as a function of the screen parameter β for the superconducting ring containing one Josephson π-junction, and compare the result with that in the classical case. Our results indicate that there is significant difference in the magnetization behaviour around β=1 between the quantum and classical situations.