Instanton Induced Tunneling Amplitude at Excited States with the Lsz Method

Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory and may be of importance in the study of macroscopic quantum phenomena in magnetic systems. Quantum effects on the macroscopic scale have attracted considerable attention in recent years owing mainly to the development of technology in mesoscopic physics. Legget et al. predicted that the most intriguing quantum effect which could take place on the macroscopic scale is quantum tunneling. Macroscopic magnetisation tunneling is a subject which is being investigated extensively and is of growing interest. There are two types of macroscopic quantum phenomena in magnetic systems. One appears when either a giant spin or (in bulk material) a domain wall is tunneling between degenerate states, which is the situation of macroscopic quantum coherence. Quantum tunneling in this case is dominated by the instanton configuration with nonzero topological charge, and the tunneling results in the level splitting. The second phenomenon appears in macroscopic quantum tunneling dominated by the socalled bounce configuration with zero topological charge which leads to the decay of metastable states. In the case of the quantum depinning of a domain wall, pinned by defects, the position of the wall at the pinning centre becomes metastable in the external magnetic field, and the position tunnels out of the local minimum. However, the usual instanton method only provides the amplitude for tunneling between ground states. It is therefore of interest to evaluate also the tunneling effect between excited states. Motivated by the study of baryonand lepton-number violation at high energy, recently a periodic (or nonvacuum) instanton configuration has been found and used to evaluate the quantum tunneling at high energy. In this note we present an approach with the LSZ reduction technique in field theory to calculate ∗On leave from Department of Mathematics, Dublin City University, Dublin, Ireland