次近邻耦合一维晶格中运动离散呼吸子引起的反常慢能量弛豫
Unusual slow energy relaxation induced by mobile discrete breathers in one-dimensional lattices with next-nearest-neighbor coupling
摘要：
我们研究了一维晶格中次近邻耦合的能量弛豫过程。这种松弛是通过向晶格的边界（自由端）添加阻尼（吸收条件）来产生的。与具有在位势的一维晶格相比，作为空间局域本征模的离散呼吸子（DB）的性质在包括NNN耦合的情况下是非常不寻常的，即，这些DBs是可移动的，因此它们可以与晶格的声子和边界相互作用。对于谐波型和Fermi-Pasta-Ulam-Tsingou- $β$（FPUT- $β$）型的粒子间相互作用，我们发现了两种弛豫交叉，即，从拉伸指数松弛到规则指数松弛的第一次交叉发生在短时间尺度内，而从指数松弛到幂律松弛的另一次交叉发生在长时间尺度内。第一次和第二次弛豫是普遍的，但最终的幂律弛豫受DBs性质的强烈影响，如FPUT- $β$型系统中DBs与声子和边界的散射过程使其幂律弛豫比相同耦合下的谐波型系统中的幂律弛豫相对更快.我们的研究结果提供了新的信息和见解，了解在冷却晶格的慢能量弛豫。
英文摘要：
We study the energy relaxation process in one-dimensional (1D) lattices with next-nearest-neighbor (NNN) couplings. This relaxation is produced by adding damping (absorbing conditions) to the boundary (free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers (DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e., these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi-Pasta-Ulam-Tsingou-$β$ (FPUT-$β$) types, we find two crossovers of relaxation in general, i.e., a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-$β$ type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices.
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