从时间演化算符研究非扩展Airy包的动力学
Study the dynamics of the nonspreading Airy packets from the time evolution operator
摘要：
Berry和Balazs证明了初始Airy包Ai（bx）在时间演化下在自由空间和齐次时变线性势V（x，t）=-F（t）x中是不扩散的.我们发现这两个结果都可以从时间演化算子U（t）导出。我们证明了U（t）可以分解为算子的有序乘积，并且本质上是x中的移位算子;因此，Airy包的演化没有失真。将哈密顿量H记为H=H_b+H_i，其中H_b是使Ai（bx）为其本征函数的哈密顿量。H_i是一个相互作用的哈密顿量，它使Airy包作加速度为a=（-H_i/（x））/m的加速运动.非扩展的Airy包则作为一个质量为m的经典粒子，其运动可用H_i经典地描述。
英文摘要：
Berry and Balazs showed that an initial Airy packet Ai(b x) under time evolution is nonspreading in free space and also in a homogeneous time-varying linear potential V(x,t)=-F(t) x. We find both results can be derived from the time evolution operator U(t). We show that U(t) can be decomposed into ordered product of operators and is essentially a shift operator in x; hence, Airy packets evolve without distortion. By writing the Hamiltonian H as H=H_b+H_i, where H_b is the Hamiltonian such that Ai(b x) is its eigenfunction. Then, H_i is shown to be as an interacting Hamiltonian that causes the Airy packet into an accelerated motion of which the acceleration a=(-H_i/( x))/m. Nonspreading Airy packet then acts as a classical particle of mass m, and the motion of it can be described classically by H_i.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
