玻色约瑟夫森结动力学中的量子灾变和遍历性
Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions
摘要：
我们研究了玻色约瑟夫森结中的猝灭后在Fock空间中形成的彩虹（褶皱）和尖点突变。在Gross-Pitaevskii平均场论中，彩虹是奇异的焦散线，但在二次量子化理论中，波函数的Poisson重新表示表明它们是由表现良好的Airy函数描述的。这些福克空间焦散线对初始条件和哈密顿演化的变化的结构稳定性是由突变理论保证的。我们还表明，长时间的动力学是遍历的。我们的结果与Berry [M. V. Berry，Nonlinearity 21，T19（2008）]提出的问题有关：是否有必要使用二次波理论来避免奇点？
英文摘要：
We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M.V. Berry, Nonlinearity 21, T19 (2008)]: are there circumstances when it is necessary to second-quantize wave theory in order to avoid singularities?
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