一维经典分形子的统计力学
Statistical mechanics of classical fractons on a line
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中文总结 AI 辅助
本文研究一维经典分形子的平衡统计力学，分析非紧支撑相互作用核的遍历性，发现指数衰减核具有广延自由能，并通过ECMC算法揭示平衡液体的短程团簇和非高斯动量尾部。
中文摘要 AI 辅助
我们研究一维经典Machian分形子的平衡统计力学：这些粒子的动力学守恒全局偶极矩，其哈密顿量通过依赖于位置的成对惯性核耦合动量差。紧支撑相互作用核在吉布斯配分函数中存在发散，并已被证明通过形成具有粒子团簇的非平衡稳态来破坏遍历性和对称性，从而规避了Hohenberg-Mermin-Wagner-Coleman定理。在本文中，我们考虑非紧支撑的核并研究其遍历性质。对于指数衰减核，图拉普拉斯和矩阵树界提供了广延自由能，表明一个假定的统计力学描述是有效的。类似地，均匀非局域核具有超广延自由能，需要Kac重标度。一个广义的Hohenberg-Mermin-Wagner-Coleman论证，辅以有限尺寸标度，意味着对称性破缺的密度序参量在所有波矢下消失，从而融化了紧支撑核的长程平移破缺密度序。为了研究所得到的平衡系综，我们构造了一个不可逆事件链蒙特卡洛（ECMC）算法，该算法在保持偶极矩和总动量的同时采样耦合的位置-动量相空间。ECMC采样被证明与哈密顿动力学中的长时间平均量定量匹配。平衡液体表现出优选的短程团簇化以及强非高斯的单粒子动量尾部，这与位置和动量的关联性质相关。本文对非紧支撑区域的平衡液体性质进行了详细研究，而配套论文则研究了使液体松弛的机制。
英文摘要
We study the equilibrium statistical mechanics of one-dimensional classical Machian fractons: particles whose dynamics conserves a global dipole moment and whose Hamiltonian couples momentum differences through a position-dependent pair-inertia kernel. Compactly supported interaction kernels have a divergence in the Gibbs partition function, and have been shown to break ergodicity and symmetry by forming non-equilibrium steady states with particle clusters, evading the Hohenberg-Mermin-Wagner-Coleman theorem. In this paper, we consider kernels with non-compact support and study their ergodic properties. For exponentially decaying kernels, graph-Laplacian and matrix-tree bounds provide an extensive free energy suggesting that a putative statistical mechanical description is valid. Similarly, uniform non-local kernels have a super-extensive free energy and require a Kac rescaling. A generalized Hohenberg--Mermin--Wagner--Coleman argument, supported by finite-size scaling, implies symmetry-breaking density order parameter vanishes at all wave vectors melting the long-range translation-breaking density order of compact kernels. To study the resulting equilibrium ensemble, we construct a nonreversible event-chain Monte Carlo (ECMC) algorithm that samples the coupled position-momentum phase space while preserving the dipole moment and total momentum. The ECMC sampling is shown to quantitatively match long time-averaged quantites in Hamiltonian dynamics. The equilibrium liquid exhibits preferred short-range clustering and strongly non-Gaussian single-particle momentum tails associated with the correlated nature of positions and momenta. This paper provides a detailed investigation into the equilibrium liquid properties of the non-compact regime, whilst the companion paper investigates the mechanisms that relax the liquid.
发表机构
- University of Oxford（牛津大学）
- Harish-Chandra Research Institute (HRI)（哈里什-钱德拉研究所）
- Homi Bhabha National Institute (HBNI)（霍米·巴巴国立研究所）
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