Wentzel-Kramers-Brillouin approach and quantum corrections to classical dynamics in the Josephson problem
Wentzel-Kramers-Brillouin approach and quantum corrections to classical dynamics in the Josephson problem
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Wentzel-Kramers-Brillouin 方法和约瑟夫森问题中经典动力学的量子修正
DOI：
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发表时间：
2009
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影响因子：
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通讯作者：
Jonathan Keeling
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文献类型：
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作者：
F. Nissen;Jonathan Keeling
我们应用多体Wentzel-Kramers-Brillouin（WKB）方法来确定约瑟夫森模型的半经典动力学的主要量子修正，描述相互作用玻色子能够在两个局域态之间隧穿。已知半经典动力学分为规则振荡和自陷振荡，其中不平衡的符号保持固定。在这两种情况下，WKB波函数都与艾里函数相匹配，产生了修改后的玻尔-索末菲量子化条件。在划分正常振荡和自陷振荡的临界能量处，WKB波函数应该与抛物柱面函数相匹配，从而导致量子化公式不仅仅是玻尔-索末菲公式，并且恢复了在该能量处的已知对数量子破裂时间。因此，这项工作提供了WKB方法在某些多体问题中的有用性的另一个例证。
We apply a many-body Wentzel-Kramers-Brillouin (WKB) approach to determine the leading quantum corrections to the semiclassical dynamics of the Josephson model, describing interacting bosons able to tunnel between two localized states. The semiclassical dynamics is known to divide between regular oscillations and self-trapped oscillations where the sign of the imbalance remains fixed. In both cases, the WKB wave functions are matched to Airy functions, yielding a modified Bohr-Sommerfeld quantization condition. At the critical energy dividing normal and self-trapped oscillations, the WKB wave functions should instead be matched to parabolic cylinder functions, leading to a quantization formula that is not just the Bohr-Sommerfeld formula, and recovering the known logarithmic quantum break times at this energy. This work thus provides another illustration of the usefulness of the WKB approach in certain many-body problems.