李-杨零点与粒子涨落
Lee-Yang Zeros And Particle Fluctuations
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中文总结 AI 辅助
该研究证明了巨正则系综中经典粒子系统的李-杨零点性质，得出热力学极限与求导可交换的结论，且结果可扩展到两类边界条件。
中文摘要 AI 辅助
我们研究巨正则系综中连续介质内的经典粒子，其具有稳定、缓变且下正则的对势，以及密度一致有界的边界条件。我们证明，若巨正则配分函数在复逸度平面$z = e^{\beta\mu}$上的李-杨零点对所有足够大的体积都与实点$z_0 > 0$保持有界距离，则沿立方体序列，热力学极限与求导在$z_0$处可交换：有限体积压强对化学势的各阶导数，在$z_0$的邻域内一致收敛到极限压强的对应导数。所有导数的极限值与边界条件无关；特别地，单位体积的密度和粒子数方差分别收敛到$\beta^{-1}\partial_\mu p$和$\beta^{-2}\partial^{2}_{\mu} p$。该结果除适用于Ruelle的缓变边界条件外，还扩展到Procacci和Yuhjtman提出的超稳定势的无界边界条件。
英文摘要
We consider classical particles in the continuum in the grand canonical ensemble, with a stable, tempered and lower-regular pair potential and boundary conditions of uniformly bounded density. We prove that if the Lee--Yang zeros of the grand canonical partition function in the complex fugacity plane $z = e^{βμ}$ remain bounded away from a real point $z_0 > 0$ for all sufficiently large volumes, then along cubes the thermodynamic limit and differentiation commute at $z_0$: every derivative of the finite-volume pressure in the chemical potential converges, uniformly in a neighborhood of $z_0$, to the corresponding derivative of the limiting pressure. The limiting values of all derivatives are independent of the boundary condition; in particular, the density and the particle-number variance per unit volume converge to $β^{-1}\partial_μp$ and $β^{-2}\partial^{2}_μ p$, respectively. The result extends to the unbounded boundary conditions of Procacci and Yuhjtman for super-stable potentials in addition to Ruelle's tempered boundary conditions.
