Porque d = 3?
Há alguns posts atrás eu conjecturei sobre a possibilidade de que a não trivialidade de grande parte dos modelos de Física Estatística em d = 3 tivesse algo a ver com o fato de vivermos em um universo complexo também com d = 3. Este artigo abaixo vai na mesma direção.
Authors: Pierre-Henri Chavanis
(Submitted on 14 Aug 2007)
Abstract: We discuss the statistical mechanics of a system of self-gravitating fermions in a space of dimension $D$. We plot the caloric curves of the self-gravitating Fermi gas giving the temperature as a function of energy and investigate the nature of phase transitions as a function of the dimension of space. We consider stable states (global entropy maxima) as well as metastable states (local entropy maxima). We show that for $D\ge 4$, there exists a critical temperature (for sufficiently large systems) and a critical energy below which the system cannot be found in statistical equilibrium. Therefore, for $D\ge 4$, quantum mechanics cannot stabilize matter against gravitational collapse. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulombian forces. This makes the dimension D=3 of our universe very particular with possible implications regarding the anthropic principle. Our study enters in a long tradition of scientific and philosophical papers who studied how the dimension of space affects the laws of physics.
Subjects:
Statistical Mechanics (cond-mat.stat-mech)
Journal reference:
Phys. Rev. E, 69, 066126 (2004)
Cite as:
arXiv:0708.1888v1 [cond-mat.stat-mech]
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