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arXiv 0811.3391quant-phhep-thnlin.CD
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隧穿中不稳定半经典轨道的特征

Signatures of unstable semiclassical trajectories in tunneling

D. G. Levkov, A. G. Panin, S. M. Sibiryakov

备注：
Journal version; 48 pages, 16 figures
发表信息：
J. Phys. A: Math. Theor. 42 (2009) 205102
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摘要：

最近发现，多维隧穿过程一般在高能下由不稳定的半经典轨道描述。我们研究了两个观测签名相关的轨迹的不稳定性。首先，我们发现一个额外的幂律依赖的半经典参数的隧穿概率相比，潜在的隧穿的标准情况。第二个特征是在终态量子数上概率分布的显著加宽。这些影响进行了研究，采用修改后的半经典技术，其中包括稳定的隧道轨迹。该技术源自第一原理。我们得到的包容性和排他性的隧道概率的情况下，不稳定的半经典轨道的表达式。我们还调查了“相变“的情况下，稳定和不稳定的轨迹之间的某些“临界”的能量值。最后，我们导出了从低激发态和高激发态隧穿的半经典几率之间的关系。这就为先前在场论中碰撞诱导隧穿的半经典描述中提出的一个猜想奠定了坚实的基础。

英文摘要：

It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we find an additional power-law dependence of the tunneling probability on the semiclassical parameter as compared to the standard case of potential tunneling. The second signature is substantial widening of the probability distribution over final-state quantum numbers. These effects are studied using modified semiclassical technique which incorporates stabilization of the tunneling trajectories. The technique is derived from first principles. We obtain expressions for the inclusive and exclusive tunneling probabilities in the case of unstable semiclassical trajectories. We also investigate the "phase transition" between the cases of stable and unstable trajectories across certain "critical" value of energy. Finally, we derive the relation between the semiclassical probabilities of tunneling from the low-lying and highly excited initial states. This puts on firm ground a conjecture made previously in the semiclassical description of collision-induced tunneling in field theory.

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