On the analyticity of the pressure for a non-ideal gas with high density boundary conditions

IF 0.5 4区 数学 Q3 MATHEMATICS Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI:10.1063/5.0136724
P. M. S. Fialho, B. D. de Lima, A. Procacci, B. Scoppola
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Abstract

We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.
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高密度边界条件下非理想气体压力的解析性
我们考虑一个连续系统的经典粒子限制在一个立方体盒子Λ通过一个稳定的和有限范围的对势与一个吸引尾巴相互作用。我们研究了系统pΛω(β,λ)在逆温度β和逸度λ下的Mayer级数,该系统属于一类非常大的局部有限粒子构型。这类允许的边界条件是在满足Ruelle估计的局部有限粒子组态空间上的任何概率测度的基础。我们证明pΛω(β,λ)可以写成两项的和。第一项是解析的和有界的,它随逸度λ在Λ-independent和ω无关的圆盘上的变化而变化,与热力学极限下的自由边界条件压力一致。第二项,在ω相关的收敛半径中是解析的,在热力学极限下趋于零。据我们所知,这是在低密度/高温条件下,当粒子通过非纯排斥对势相互作用时,非理想气体在非自由和非周期边界条件下的Mayer系列行为的第一次严格分析。
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来源期刊
CiteScore
0.70
自引率
20.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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