论文标题
质量弹簧链中的无分散脉冲传输：所有可能的完美牛顿的摇篮
Dispersionless pulse transport in mass-spring chains: All possible perfect Newton's cradles
论文作者
论文摘要
分散很快就破坏了弹簧连接的$ n $块的均匀非解剖链中的脉搏。在这里表明，对质量和弹性常数的适当调制使得可以在链端之间获得周期性动力学和任何类型的脉冲的完美传输，因为初始配置在半个周期内演变为其镜像。这使连锁店成为牛顿的摇篮。通过基于正交多项式的已知算法，一个人可以在数值上求解从频谱到动态矩阵的一般反向问题，然后再解决相应的质量弹力序列，因此产生所有可能的“完美摇篮”。由于量子线性系统遵守其经典对应物的相同动力学，因此这些结果也适用于量子案例：例如，在一端定位的波函数将演变为在相反链端的镜像。
A pulse traveling on a uniform nondissipative chain of $N$ masses connected by springs is soon destructured by dispersion. Here it is shown that a proper modulation of the masses and the elastic constants makes it possible to obtain a periodic dynamics and a perfect transmission of any kind of pulse between the chain ends, since the initial configuration evolves to its mirror image in the half period. This makes the chain to behave as a Newton's cradle. By a known algorithm based on orthogonal polynomials one can numerically solve the general inverse problem leading from the spectrum to the dynamical matrix and then to the corresponding mass-spring sequence, so yielding all possible ``perfect cradles''. As quantum linear systems obey the same dynamics of their classical counterparts, these results also apply to the quantum case: for instance, a wavefunction localized at one end would evolve to its mirror image at the opposite chain end.
