Application of Instantons: Quenching of Macroscopic Quantum Coherence and Macroscopic Fermi-Particle Configurations

Abstract

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels $E = ε_0 - 2\triangleεcos (s+ξ)π$ of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of $cos (s+ξ)π$ in disagreement with the suppression of tunneling (i.e. $\triangleε= 0$) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunneling rate ($(2\triangleε)/(π)$) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.