A fluctuation-corrected functional of convex Poisson–Boltzmann theory
A fluctuation-corrected functional of convex Poisson–Boltzmann theory
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DOI：
10.1088/1751-8121/aad352
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Ralf Blossey;A. C. Maggs
中科院分区：
文献类型：
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作者：
Ralf Blossey;A. C. Maggs
Poisson-Boltzmann理论允许研究软物质和涉及低价点状电荷的生物物理系统。包含波动校正超出平均场的方法通常需要在平均场的解决方案的静电势，或复杂的变分方法的应用程序的循环扩展。最近，泊松-玻尔兹曼理论已被重铸，通过勒让德变换，作为一个平均场理论涉及的介质位移场。在本文中，我们考虑这个对偶理论的路径积分公式。利用之间的转换，我们制定了一个双sine-Gordon场理论的位移场，并提供了一个精确的数值计算的自由能超出领先的顺序。
Poisson–Boltzmann theory allows to study soft matter and biophysical systems involving point-like charges of low valencies. The inclusion of fluctuation corrections beyond the mean-field approach typically requires the application of loop expansions around a mean-field solution for the electrostatic potential , or sophisticated variational approaches. Recently, Poisson–Boltzmann theory has been recast, via a Legendre transform, as a mean-field theory involving the dielectric displacement field . In this paper we consider the path integral formulation of this dual theory. Exploiting the transformation between ϕ and , we formulate a dual sine-Gordon field theory in terms of the displacement field and provide a strategy for precise numerical computations of free energies beyond the leading order.