arXiv subjects
Publications and source records attributed to C. A. A. de Carvalho.
We present a study of the role of fermions in the decay of metastable states of a scalar field via bubble nucleation. We analyze both one and three-dimensional systems by using a gradient expansion for the calculation of the fermionic determinant. The results of the one-dimensional case are compared to the exact results of previous work.
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths appear, including tunneling paths. The transition from single to multiple-path regime corresponds to well-defined catastrophes. Tunneling sets in whenever they occur. (Our formula fully accounts for this feature.)
We present a study of the nucleation mechanism that allows the decay of the metastable phase (trans-cisoid) to the stable phase (cis-transoid) in quasi one-dimensional non-degenerate polymers within the continuum electron-phonon model. The electron-phonon configurations that lead to the decay, i.e. the critical droplets (or transition state), are identified as polarons of the metastable phase. We obtain an estimate for the decay rate via thermal activation within a range of parameters consistent with experimental values for the gap of the cis-configuration. It is pointed out that, upon doping, the activation barriers of the excited states are quite smaller and the decay rate is greatly enhanced. Typical activation energies for electron or hole polarons are $\approx 0.1$ eV and the typical size for a critical droplet (polaron) is about $20 Å$. Decay via quantum nucleation is also studied and it is found that the crossover temperature between quantum nucleation and thermal activation is of order $T_c \leq 40 ^oK$. Metastable configurations of non-degenerate polymers may provide examples for mesoscopic quantum tunneling.