Burin Alexander L, Maksymov Andrii O, Schmidt Ma'ayan, Polishchuk Il'ya Ya
Department of Chemistry, Tulane University, New Orleans, LA 70118, USA.
National Research Center "Kurchatov Institute", 123182 Moscow, Russia.
Entropy (Basel). 2019 Jan 10;21(1):51. doi: 10.3390/e21010051.
We investigate the emergence of chaotic dynamics in a quantum Fermi-Pasta-Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed.
我们运用共振相互作用的半定量分析，并辅以精确对角化数值研究，来研究原子链中非谐振动的量子费米-帕斯塔-乌拉姆问题中混沌动力学的出现。估算了区分混沌高能相和局域化（可积）低能相的交叉能量。它与原子数成反比减小，直至接近量子 regime，此时这种依赖关系达到饱和。与周期系统相比，在具有自由或固定端边界条件的系统中，混沌行为出现在更低的能量处。讨论了该理论在实际分子中的应用。
