AI 中文总结
研究单文件扩散，通过正则变换求解扩展BHR气体及有限体积排斥晶格气体的宏观涨落理论，计算示踪剂位置和积分电流的大偏差统计量，并用罕见事件模拟验证结果。
AI 中文摘要
单文件扩散是低维系统中普遍存在的现象，出现在狭窄通道内的输运中。其自然连续模型是扩展布朗硬棒（BHR）的一维气体。由于该问题难处理，传统文献多聚焦晶格排斥模型，虽有显著但有限的精确结果。近期重大进展是排斥过程的宏观涨落理论（MFT）的形式解，但明确的性质仍少。本文表明扩展BHR气体的相应MFT可通过正则变换精确求解，通过计算示踪剂位置和积分电流在退火和淬火系综中的大偏差统计量证明了这一点。还表明类似正则变换适用于有限体积排斥晶格气体的MFT，给出相应统计量。用连续和晶格模型的罕见事件模拟验证了结果。
英文摘要
Single-file diffusion is a ubiquitous phenomenon in low-dimensional systems, arising in transport inside narrow channels. Its natural continuum model is a one-dimensional gas of extended Brownian hard rods (BHR). Perhaps owing to the perceived intractability of this problem, much of the literature has traditionally focused on lattice exclusion models, where integrability methods have yielded remarkable, albeit limited, exact results. A major recent advance comes from a formal solution of macroscopic fluctuation theory (MFT) for the exclusion process. Yet, despite the formal solution, only a handful of properties have been made explicit. We show that the corresponding MFT of the extended BHR gas is in fact exactly solvable through a canonical transformation. We demonstrate this by explicit computation of the large-deviation statistics of the tracer-position and integrated-current in both annealed and quenched ensembles. We further show that an analogous canonical transformation applies to the MFT of lattice gases with finite-volume exclusion, yielding corresponding tracer and current statistics. We validate our results using rare-event simulations for both the continuum and the lattice models.
Comments8 pages, 3 figures + 8 pages of supplement
