• Corpus ID: 211132470

Non-Archimedean Electrostatics

@article{Sinclair2020NonArchimedeanE,
  title={Non-Archimedean Electrostatics},
  author={Christopher D. Sinclair},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
  • C. Sinclair
  • Published 17 February 2020
  • Mathematics
  • arXiv: Mathematical Physics
We introduce ensembles of repelling charged particles restricted to a ball in a non-archimedean field (such as the $p$-adic numbers) with interaction energy between pairs of particles proportional to the logarithm of the ($p$-adic) distance between them. In the {\em canonical ensemble}, a system of $N$ particles is put in contact with a heat bath at fixed inverse temperature $\beta$ and energy is allowed to flow between the system and the heat bath. Using standard axioms of statistical physics… 

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References

SHOWING 1-10 OF 18 REFERENCES
log-Coulomb Gas with Norm-Density in $$p$$-Fields
The main result of this paper is a formula for the integral $$\int_{K^N}\rho(x)\big(\max_{i 0$ represent the charges of an $N$-particle log-Coulomb gas in $K$ with background density $\rho$ and
Statistical Theory of the Energy Levels of Complex Systems. I
New kinds of statistical ensemble are defined, representing a mathematical idealization of the notion of ``all physical systems with equal probability.'' Three such ensembles are studied in detail,
The importance of the Selberg integral
It has been remarked that a fair measure of the impact of Atle Selberg’s work is the number of mathematical terms that bear his name. One of these is the Selberg integral, an n-dimensional
p-Adic mathematical physics: the first 30 years
TLDR
A brief review of main achievements in some selected topics of p-adic mathematical physics and its applications, especially in the last decade, mainly paid to developments with promising future prospects.
An introduction to Berkovich analytic spaces and non-archimedean potential theory on curves
TLDR
This is an expository set of lecture notes meant to accompany the author’s lectures at the 2007 Arizona Winter School on p-adic geometry, purposely chosen to emphasize examples, pictures, discussion, and the intuition behind various constructions rather than emphasizing formal proofs and rigorous arguments.
Equidistribution and the heights of totally real and totally p-adic numbers
C.J. Smyth was among the first to study the spectrum of the Weil height in the field of all totally real numbers, establishing both lower and upper bounds for the limit infimum of the height of all
The Probability That a Random Monic p-adic Polynomial Splits
TLDR
It is shown that rn satisfies an interesting recursion, a conjecture on the asymptotic behavior of rn as n goes to infinity is made, and the conjecture in the case that the residue field has two elements is proved.
Energy integrals and small points for the Arakelov height
We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we
Igusa’s local zeta functions of semiquasihomogeneous polynomials
In this paper, we prove the rationality of Igusa's local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field K. The proof of this result is based on
An Introduction to the Theory of Local Zeta Functions
...
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