
From:  Stefan Kesselheim 
Subject:  Re: [ESPResSousers] P3M epsilon 
Date:  Mon, 07 Nov 2011 09:45:39 +0100 
Useragent:  Mozilla/5.0 (X11; U; Linux x86_64; enUS; rv:1.9.2.22) Gecko/20110907 SUSE/3.1.14 Thunderbird/3.1.14 
Dear Farnoosh, On 11/07/2011 09:16 AM, Farnoosh Farahpoor wrote: This parameter is typical for coulomb interactions in 3Dperiodic systems: When taking the limit of infinitely many replicas of the box in all directions the results of the sum depends on the boundary conditions "behind" the replicas. In other words: the limit of infinitely many replicas does not remove dependence on the dielectric permittivity outside of the considered system. The dielectric properties outside of the system create a harmonic potential for the total dipole moment of the system proportional to 1/epsilon_{\infinity}. This means if epsilon_{\infinity}<\infinity the total dipole moment of the system will stay finite all the time and in thermal equilibrium be gaussian distributed, while it performs an unbounded random walk in case of metallic (infinity) boundary conditions. We spend quite some time getting a good idea of what the physical meaning of this parameter is, but we did not find a very good interpretation. It is an artifact of the fact that all real systems are large, but finite, and infinite systems create mathematical difficulties with the 1/r coulomb potential. My personal opinion is that only metallic boundary conditions correspond to "proper" physics, because then the equations of motion don't change when a particle is at the same folded position but in different replicas. I know Kai Grass used metallic boundary conditions when simulating the electrophoretic mobility of a polyelectrolyte. Maybe someone else has a better answer to that question... Cheers and good luck, Stefan

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