具有连续非阿贝尔对称的格子模型中的流体力学
Hydrodynamics in lattice models with continuous non-Abelian symmetries
摘要：
本文发展了一个系统的非阿贝尔对称格点上多体系统流体力学的有效场论。具有连续非阿贝尔对称性的模型在物理学中无处不在，从热的核物质到冷的原子气体和量子自旋链的各种环境中都有出现。在每一个维度上，对于每一个味对称群，低能理论都是一组耦合的噪声扩散方程。在我们的流体动力学展开中，物理学对正则系综或微正则系综的选择是独立的，即使系综的选择会导致准正态模谱的明显位移。我们用我们的形式主义来解释为什么味对称性是定性不同的流体力学与其他非阿贝尔守恒定律，包括角动量和电荷多极。作为我们的框架的一个重要应用，我们研究了经典一维SU（2）不变自旋链中的自旋和能量扩散，包括海森堡模型以及多个推广。我们认为，数值模拟和我们的有效场论框架的基础上，不可积的自旋链上的晶格表现出传统的自旋扩散，在最近的一些预测，扩散常数的增长在晚些时候。我们表明，扩散的明显增强是由于（非阿贝尔）流体动力学波动造成的缓慢平衡。
英文摘要：
We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
