开放量子系统的宽度分岔和动力学相变
Width bifurcation and dynamical phase transitions in open quantum systems
摘要：
开放量子系统的态通过散射波函数的环境耦合。系统与环境之间的复杂耦合系数$ω$由主值积分和残差产生。在共振态重叠的高水平密度下，系统的动力学由例外点决定。在这些点上，两个态的本征值相等，相应的本征函数线性相关。研究表明，在异常点附近，Im $(ω)$和Re $(ω)$对体系性质的影响是不同的。通过参数控制系统，本征值避免在Re $(ω)$的影响下在异常点附近的能量交叉，其方式与从离散状态已知的方式类似。然而，Im $(ω)$导致宽度分叉，并且最终（当系统耦合到一个通道时，即耦合到散射波函数的公共连续体时）导致系统分裂成具有不同特征时间尺度的两个部分。物理上，由于大多数（$N-1$）态的寿命比以前长，而只有一个态的寿命比以前短，因此系统通过这种分裂而稳定。在截面中，短寿命态在高分辨率实验中作为背景项出现。长寿命态的波函数在很大的参数范围内与原态的波函数混合。本征值和本征函数的数值结果示出了$N=2, ~4$和10个状态主要耦合到1个通道。
英文摘要：
The states of an open quantum system are coupled via the environment of scattering wavefunctions. The complex coupling coefficients $ω$ between system and environment arise from the principal value integral and the residuum. At high level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im$(ω)$ and Re$(ω)$ influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re$(ω)$ in a similar manner as it is well known from discrete states. Im$(ω)$ however leads to width bifurcation and finally (when the system is coupled to one channel, i.e. to a common continuum of scattering wavefunctions), to a splitting of the system into two parts with different characteristic time scales. Physically, the system is stabilized by this splitting since the lifetimes of most ($N-1$) states are longer than before while that of only one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wavefunctions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for $N=2, ~4$ and 10 states coupled mostly to 1 channel.
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