一维非线性波动流体动力学的有效场论
Effective field theories of nonlinear fluctuating hydrodynamics in one dimension
浏览论文内容
中文总结 AI 辅助
针对低维系统宏观现象描述难题，识别先前公式问题，开发通用系统方法构建一维流体动力学系统有效场论，以耦合随机朗之万型方程呈现，经数值积分方案并举例验证。
中文摘要 AI 辅助
描述低空间维度中涌现的宏观现象极具挑战性，主要因强相互作用使微扰方法不适用。低维系统有诸多非传统现象，如一维相互作用系统中的超扩散输运。本文识别并讨论了先前公式中的内部不一致性，开发了一种通用且系统的方法来构建一维流体动力学系统的有效场论，形式为与局部平衡态物理要求兼容的耦合随机朗之万型方程。实施了通用数值积分方案，并在具有非高斯平稳平衡测度的两个相互作用流体动力学模式的简单模型上举例说明了构建过程。
英文摘要
Describing emergent macroscopic phenomena in low spatial dimensions is known to be notoriously challenging, primarily due to strong interactions that render perturbative approaches inapplicable. On the other hand, low-dimensional systems host a wealth of unorthodox phenomena. A prominent example is the emergence of superdiffusive transport in one-dimensional interacting systems, traditionally studied in the framework of nonlinear fluctuating hydrodynamics. After identifying and discussing internal inconsistencies in the previous formulations, in this work we develop a general and systematic approach for constructing effective field theories of one-dimensional hydrodynamic systems in the form of coupled stochastic Langevin-type equations compatible with the physical requirements of local equilibrium states such as the thermodynamic Maxwell relation and fluctuation-dissipation symmetry. We implemented a general numerical integration scheme and exemplified our construction on a simple model of two interacting hydrodynamic modes with a non-Gaussian stationary equilibrium measure.
