谐振子中玻色-爱因斯坦凝聚的复相互作用泛函重整化分析Bendixson判据能推广到复时间吗？
Functional Renormalization analysis of Bose-Einstien Condensation through complex interaction in Harmonic Oscillator; Can Bendixson criteria be extended to complex time?
摘要：
在开放量子系统中，振子中任意形式的复势微扰是一个令人兴奋的问题。当量子系统与外部环境相互作用时，这些通常在现实场景中提供有价值的见解。作用量重整化将捕获波函数的相位，因此我们用Bethe方法和Frobenius方法构造波函数。统一和非统一的制度进行了讨论，连接功能的计算。本文给出了非厄米振子的泛函重整化计算。在泛函玻色变量中建立了一个对偶空间的左-右公式，导出了尺度相关作用的流动方程。证明了顶点算子与置换算子的等价性。计算结果与WKB（WentzelKramersBrillouin）计算结果进行了比较。我们在对偶空间中构造了玻色相干态，对称性破缺将导致任意玻色相干态。在重整化轨迹的极限环复杂的流动参数，特别是在延长，复杂的时间限制表明，需要重新考虑的Bendixson定理。
英文摘要：
An arbitrary form of complex potential perturbation in an oscillator consists of many exciting questions in open quantum systems. These often provide valuable insights in a realistic scenario when a quantum system interacts with external environments. Action renormalization will capture the phase of the wave functions; hence we construct wave function from Bethe ansatz and Frobenius methods. The unitary and non-unitary regimes are discussed to connect with functional calculations. We present a functional renormalization calculation for a non-hermitian oscillator. A dual space Left-Right formulation is worked out in functional bosonic variables to derive the flow equation for scale dependent action. We show equivalence between vertex operator and permutation operators. The results can be compared with Wentzel Kramers Brillouin(WKB) calculation. We formally construct the Bosonic coherent states in the dual space;breaking symmetry will lead to anyonic coherent states. The limit cycle in renormalization trajectories for complex flow parameters, especially in extended, complex time limits indicates the need for revisiting the Bendixson theorem.
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