标题： 真空衰变过程中 sphalerons 的长期行为在$φ^4$模型中的表现 显示英文标题

标题： Long-time behaviour of sphalerons in $φ^4$ models with a false vacuum

摘要： 非线性克莱因-戈登模型中的磁单极子是不稳定的块状解，它们来源于能量泛函中真真空和假真空之间的鞍点。 给出了数值模拟，显示磁单极子演变为一个加速的孤子-反孤子对，其分离距离在长时间后逐渐接近光速。 利用非线性集体坐标方法，推导出这种演化的近似解析解。 这些结果表明，精确解在长时间内预计将表现出梯度爆破，这是由于能量集中在孤子-反孤子对的边缘所致。 显示英文摘要

摘要： Sphalerons in nonlinear Klein-Gordon models are unstable lump-like solutions that arise from a saddle point between true and false vacua in the energy functional. Numerical simulations are presented which show the sphaleron evolving into an accelerating kink-antikink pair whose separation approaches the speed of light asymptotically at large times. Utilizing a nonlinear collective coordinate method, an approximate analytical solution is derived for this evolution. These results indicate that an exact solution is expected to exhibit a gradient blow-up for large times,caused by energy concentrating at the flanks of the kink-antikink pair.