论文标题
量子伪积聚的汉密尔顿冲击系统
Quantum pseudo-integrable Hamiltonian impact systems
论文作者
论文摘要
引入了假汉密尔顿影响系统的玩具模型的量化，包括EBK量化条件，对Weyl定律的验证，其波函数的研究以及对其能级特性的研究。证明能量水平的统计数据与可构成台球的统计数据相似。然而，在这里，集中在经典水平集合到配置空间的投影上的波形密度不会在大能量下消失，这表明在较大能量限制中，配置空间中没有等分分布。对于某些极限对称情况，可以在分析上显示这一点，并在某些非对称情况下在数值上证明了这一点。
Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties. It is demonstrated that the energy levels statistics are similar to those of pseudointegrable billiards. Yet, here, the density of wavefunctions which concentrate on projections of classical level sets to the configuration space does not disappear at large energies, suggesting that there is no equidistribution in the configuration space in the large energy limit; this is shown analytically for some limit symmetric cases and is demonstrated numerically for some nonsymmetric cases.
