Effect of Aharonov-Bohm Phase in Semiclassical Quantum Tunneling

The role of Aharonov-Bohm effect in quantum tunneling is examined when potential is defined on S1 and has N -fold symmetry. For N = 2 case the quenched tunneling splitting occurs at cos Φ/2 = 0 where Φ is magnetic flux. For N = 3 and N = 4 cases the ground state energies splitted from threeand four-fold degenerate vacua by quantum tunneling are explicitly computed. The N = 4 case is applied to the cubic spin system. Recently, Quenched tunneling splitting in biaxial spin system with an external magnetic field applied along the hard axis is theoretically predicted [1] and also experimentally examined [2]. In this letter we will show the quenching is purely due to Aharonov-Bohm(AB) effect [3] when potential defined on S has two-fold symmetry. Furthermore, the effect of AB phase when potential has N -fold symmetry is also examined for N = 3 and N = 4 cases. Finally the result of N = 4 case is applied to the cubic spin system. To discuss the effect of AB phase in semiclassical quantum tunneling it is heuristic to start with action S = ∫ dt [ 1 2 φ̇ − V0(φ) ]