Mithun Thudiyangal, Maluckov Aleksandra, Manda Bertin Many, Skokos Charalampos, Bishop Alan, Saxena Avadh, Khare Avinash, Kevrekidis Panayotis G
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Vinca Institute of Nuclear Sciences, University of Belgrade, National Institute of the Republic of Serbia, P.O.B. 522, 11001 Belgrade, Serbia.
Phys Rev E. 2021 Mar;103(3-1):032211. doi: 10.1103/PhysRevE.103.032211.
The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (nonintegrable) discrete nonlinear Schrödinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS toward AL) is varied, the region in the space of initial energy and norm densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.
萨勒诺模型构成了可积的阿布洛维茨 - 拉迪克（AL）模型与更标准的（不可积的）离散非线性薛定谔（DNLS）模型之间一种有趣的内插。局域在位非线性和非线性色散之间的竞争支配着该模型的热化过程。在此，我们研究非可积情形下萨勒诺一维晶格模型的统计力学，并说明吉布斯区域中的热化现象。当在两个极限之间（从DNLS向AL）进行插值的参数变化时，导致热化的初始能量和范数密度空间中的区域会扩大。非吉布斯区域中的热化过程严重依赖于有限系统尺寸；我们通过针对不同参数区域的直接数值计算来探究这一特性。
