AI 中文总结
研究具有非均匀对称性的多体系统，开发统一框架，通过附加场理解其效应，导致运动学约束重塑红外动力学，在对称破缺系统和有限温度下有新表现，产生新物理现象。
AI 中文摘要
多体系统的低能动力学由无隙模式主导，其性质由对称性决定。在均匀对称性下这些原理已被熟知，但非均匀对称性（其生成元与时空平移不对易）的情况不同。本文为具有非均匀对称性的多体系统开发了统一框架，表明其效应可通过低能时非独立且可消除的附加场来理解，从而导致重塑红外动力学的运动学约束。在自发对称破缺系统中修改有效理论，在有限温度下表现为对宏观电流的约束，产生新物理现象。
英文摘要
The low-energy dynamics of many-body systems is governed by gapless modes whose properties are dictated by symmetry. Their existence follows from Goldstone's theorem, while their effective description at zero temperature is determined by the pattern of symmetry breaking. At finite temperature, an analogous role is played by hydrodynamics, which describes the universal behavior of many-body systems over long times and large distances. These principles are well understood for uniform symmetries, which act homogeneously in spacetime and lead to a correspondence between massless Goldstone modes and broken generators, as well as gapless hydrodynamic modes and conserved charges. However, this simple picture changes in the presence of nonuniform symmetries, whose generators do not commute with spacetime translations. The low-energy implications of these symmetries remain less understood, as they do not introduce additional gapless modes but instead constrain the dynamics of the existing degrees of freedom. In this thesis, we develop a unified framework for many-body systems with nonuniform symmetries and show that their effects can be understood in terms of additional fields that are not independent at low energies and can be eliminated, leading to kinematic constraints that reshape the infrared dynamics. In systems with spontaneous symmetry breaking, this mechanism modifies the effective theory and often softens the dispersion relations of the remaining modes. At finite temperature, it manifests in hydrodynamics as constraints on macroscopic currents. As a result, nonuniform symmetries give rise to qualitatively new physical phenomena, including modified spectra of collective excitations, exemplified by transverse Tkachenko oscillations in quantum vortex crystals, and unconventional transport phenomena, such as anomalously slow diffusion and softened sound modes in dipole-conserving systems.
CommentsPhD thesis
