Time-Dependent Matrix Product Ansatz for Interacting Reversible Dynamics
Time-Dependent Matrix Product Ansatz for Interacting Reversible Dynamics
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DOI：
10.1007/s00220-019-03494-5
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发表时间：
2019-10-01
影响因子：
2.4
通讯作者：
Vanicat, Matthieu
中科院分区：
文献类型：
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作者：
Klobas, Katja;Medenjak, Marko;Vanicat, Matthieu
我们提出了一个显式的时间相关矩阵乘积 ansatz (tMPA)，它描述了相互作用和确定性晶格气体中任何局部可观测值的时间演化，特别是针对 Bobenko 等人的规则 54 可逆元胞自动机。 （《公共数学物理》158（1）：127，1993。10.1007/BF02097234）。我们的构造基于真实空间实时逆散射问题的显式解决方案。我们考虑该 tMPA 的两个应用。首先，我们在相互作用的确定性模型中首次提供了动态结构因子的精确和显式计算，其次，我们解决了非均匀淬灭问题的极端情况，其中最大熵状态的半无限晶格与空的半无限晶格连接。这两个精确结果都严格证明了模型中弹道和扩散传输行为的共存，正如正常流体所预期的那样。
We present an explicit time-dependent matrix product ansatz (tMPA), which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of Bobenko et al. (Commun Math Phys 158(1):127, 1993. 10.1007/BF02097234). Our construction is based on an explicit solution of real-space real-time inverse scattering problem. We consider two applications of this tMPA. Firstly, we provide the first exact and explicit computation of the dynamic structure factor in an interacting deterministic model, and secondly, we solve the extremal case of the inhomogeneous quench problem, where a semi-infinite lattice in the maximum entropy state is joined with an empty semi-infinite lattice. Both of these exact results rigorously demonstrate a coexistence of ballistic and diffusive transport behaviour in the model, as expected for normal fluids.