Macroscopic Quantum Nucleation in cis-Polyacetylene

Abstract

331The metastable phase (trans-cisoid) of cis-polyacetylene is expected to decay into the ground state (cis-transoid) through the formation of a polaron. In the present paper, the quantum nucleation rate of the polaron is analyzed within the framework of the WKB approximation. The electronic degrees of freedom are integrated exactly, by which the field theoretical equation of motion is reduced to that for the polaron size alone. Then the quantum nucleation rate for this coordinate is evaluated. It is shown that the nucleation rate thus obtained is much larger than that previously speculated. § 1. IntroductionIn 1972, Lifshitz and Kagan 1 > have studied the quantum nucleation of droplets of a stable state in a metastable phase. They calculated the relevant probabilities in the semiclassical approximation. Their theory has been subsequently applied to the quantum nucleation of the pure 3 He droplets in the supercooled mixture of 3 He-4 He at very low temperatures. 2 > There has not been much progress since then, however, until Satoh et al. 3 > made an observation in which they have shown that the nucleation rate of the 3 He bubbles saturates at 10 mK below which the nucleation is supposed to be purely quantum mechanical. Nakamura and Takagi 4 > have pointed out that if one naively applies Lifshitz and Kagan's theory, which they call WKBO, to the observed data one would find that the discrepancy.between theory and experiment is astronomical! To solve this problem, they have proposed that one should apply the WKB approximation properly. In particular, one cannot simply put the virtual bound state energy to be zero, which Lifshitz and Kagan have assumed in their 1972 paper.Lifshitz and Kagan's analysis and those of their successors' are based on a phenomenological Lagrangian, which has no quantum-field-theoretical justification. It is, therefore, desirable to have a concrete field theoretical model from which one can derive an analogue of the phenomenological Lagrangian to justify the abovementioned analyses. Recently, Boyanovsky et al. 5 > have studied the metastable phase (trans-cisoid) of cis-polyacetylene and proposed that the decay of this metastable phase proceeds by a formation of a polaron, which is an island of the stable phase (cis-transoid) embedded in a trans-cisoid chain. Once a polaron of a critical size nucleates in a trans-cisoid chain it expands to flip the metastable trans-cisoid to cis-transoid until all the cis-polyacetylene turns into the stable phase. Boyanovsky et al.'s theory, however, is based on the WKBO analysis, according to Nakamura and Takagi's nomenclature, and neglected the subtlety associated with the coordinatedependent mass. Inthe present paper, we will be concerned with the nucleation of a polaron in a trans-cisoid chain and compute the nucleation rate by employing the WKB approximation with the position-dependence of the effective mass taken into