通过硬杆气体中的电流涨落探测涨落流体动力学
Probing fluctuating hydrodynamics through current fluctuations in hard rod gas
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中文总结 AI 辅助
本文通过比较BMFT与CBFHD两种涨落流体动力学框架对一维硬杆气体电流全计数统计的预测，发现BMFT与微观动力学定量吻合，而CBFHD无法准确捕捉大尺度电流涨落。
中文摘要 AI 辅助
我们研究了平衡态一维硬杆气体中积分电流的全计数统计，采用了两种最近提出的涨落流体动力学框架：(i) 弹道宏观涨落理论（BMFT）和(ii) 基于硬杆准粒子相关布朗运动近似的扩散涨落流体动力学理论（CBFHD）。我们探究了这两种方法的预测彼此之间以及与底层微观动力学相比如何。我们在BMFT框架内表明，电流分布允许在弹道标度下具有大偏差形式，并推导出大偏差函数的显式表达式，该表达式对任意在点粒子坐标中分解的非均匀初始态均有效。相应的电流累积量也被获得。随后，我们在CBFHD框架内分析电流统计，该框架明确包含了随机噪声和耗散项，并证明在该方法中电流分布同样遵循大偏差原理。我们发现，虽然BMFT对前几个累积量和速率函数的预测与微观硬杆动力学的直接数值模拟结果高度一致，但CBFHD的预测则不然。我们进一步使用一组相关布朗运动独立验证了CBFHD的预测，这为硬杆准粒子的动力学提供了近似描述。我们的发现表明，CBFHD不能准确捕捉硬杆气体中的大尺度电流涨落，而BMFT产生的预测与微观动力学定量一致，至少在全计数统计的背景下如此。
英文摘要
We study the full counting statistics of the integrated current in a one-dimensional hard-rod gas in equilibrium, employing two recently proposed fluctuating hydrodynamic frameworks: (i) Ballistic Macroscopic Fluctuation Theory (BMFT) and (ii) diffusive fluctuating hydrodynamic theory based on correlated Brownian motion approximation of hard-rod quasiparticles (CBFHD). We investigate how the predictions of these two approaches compare with each other and with the underlying microscopic dynamics. We show within BMFT that the current distribution admits a large-deviation form under ballistic scaling, and we derive an explicit expression for the large-deviation function, valid for an arbitrary inhomogeneous initial state factorized in point-particle coordinates. The corresponding current cumulants are also obtained. We subsequently analyze the current statistics within the CBFHD framework, which explicitly incorporates stochastic noise and dissipative terms, and demonstrate that the current distribution likewise obeys a large-deviation principle in this approach. We find that, while BMFT predictions for the first few cumulants and the rate function are in excellent agreement with direct numerical simulations of the microscopic hard-rod dynamics, CBFHD prediction is not. We further verify the predictions of the CBFHD independently using a collection of correlated Brownian motions, which provides an approximate description of the dynamics of hard-rod quasiparticles. Our findings indicate that CBFHD does not accurately capture large-scale current fluctuations in the hard-rod gas, whereas BMFT yields predictions in quantitative agreement with the microscopic dynamics, at least in the context of full counting statistics.
发表机构
- International Centre for Theoretical Sciences, TIFR（理论科学国际中心，印度理工学院）
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