Newtonian gravity in <i>d</i> dimensions

Pierre-Henri Chavanis

doi:10.1016/j.crhy.2006.01.005

Newtonian gravity in d dimensions
[Quelques aspects de la gravité newtonienne en dimension d]

Pierre-Henri Chavanis ¹

¹ Laboratoire de physique théorique, université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse, France

Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 331-342.

Résumé
Abstract

J'étudie l'influence de la dimension de l'espace sur la thermodynamique du gaz auto-gravitant classique et quantique. Je considère des systèmes hamiltoniens de particules auto-gravitantes décrits par l'ensemble microcanonique et des systèmes de particules browniennes auto-gravitantes décrits par l'ensemble canonique. Je présente une galerie de courbes caloriques pour différentes dimensions de l'espace et discute la nature des transitions de phase en fonction de la dimension d. Je fournis aussi la forme générale du théorème du Viriel en d dimensions et discute la particularité de la dimension $d = 4$ pour les systèmes hamiltoniens et de la dimension $d = 2$ pour les systèmes browniens.

We study the influence of the dimension of space on the thermodynamics of the classical and quantum self-gravitating gas. We consider Hamiltonian systems of self-gravitating particles described by the microcanonical ensemble and self-gravitating Brownian particles described by the canonical ensemble. We present a gallery of caloric curves in different dimensions of space and discuss the nature of phase transitions as a function of the dimension d. We also provide the general form of the Virial theorem in d dimensions and discuss the particularity of the dimension $d = 4$ for Hamiltonian systems and the dimension $d = 2$ for Brownian systems.

Publié le : 2006-04-01

DOI : 10.1016/j.crhy.2006.01.005

Keywords: Newtonian gravity, Self-gravitating gas, Brownian systems
Mots-clés : Gravité newtonienne, Gaz auto-gravitant, Systèmes browniens

Affiliations des auteurs :

Pierre-Henri Chavanis ¹

¹ Laboratoire de physique théorique, université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse, France

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Pierre-Henri Chavanis. Newtonian gravity in d dimensions. Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 331-342. doi : 10.1016/j.crhy.2006.01.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.01.005/

Bibliographie
Cité par

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Pierre-Henri Chavanis; Julien Sopik; Clément Sire Phase transitions in self-gravitating systems and bacterial populations surrounding a central body, Physical Review E, Volume 109 (2024) no. 1 | DOI:10.1103/physreve.109.014118
Pierre-Henri Chavanis Boltzmann-Poisson equation with a central body: Analytical solutions in one and two dimensions, Physical Review E, Volume 110 (2024) no. 6 | DOI:10.1103/physreve.110.064117
Michael Kirejczyk; Gerhard Müller; Pierre-Henri Chavanis Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: Gaseous density profiles and onset of condensation, Physical Review E, Volume 105 (2022) no. 3 | DOI:10.1103/physreve.105.034145
Michael Kirejczyk; Gerhard Müller; Pierre-Henri Chavanis Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: Evolution of density profiles with temperature, Physical Review E, Volume 106 (2022) no. 2 | DOI:10.1103/physreve.106.024132
Pierfrancesco Di Cintio; Shamik Gupta; Lapo Casetti Dynamical origin of non-thermal states in galactic filaments, Monthly Notices of the Royal Astronomical Society, Volume 475 (2018) no. 1, p. 1137 | DOI:10.1093/mnras/stx3244
Pierre-Henri Chavanis Dissipative self-gravitating Bose-Einstein condensates with arbitrary nonlinearity as a model of dark matter halos, The European Physical Journal Plus, Volume 132 (2017) no. 6 | DOI:10.1140/epjp/i2017-11544-3
Pierre-Henri Chavanis Gravitational phase transitions with an exclusion constraint in position space, The European Physical Journal B, Volume 87 (2014) no. 1 | DOI:10.1140/epjb/e2013-40833-4
Bruno Marcos Collisional relaxation of two-dimensional self-gravitating systems, Physical Review E, Volume 88 (2013) no. 3 | DOI:10.1103/physreve.88.032112
Pierre-Henri Chavanis Kinetic theory of spatially homogeneous systems with long-range interactions: III. Application to power law potentials, plasmas, stellar systems, and to the HMF model, The European Physical Journal Plus, Volume 128 (2013) no. 10 | DOI:10.1140/epjp/i2013-13128-7
PIERRE-HENRI CHAVANIS VIRIAL THEOREM FOR ROTATING SELF-GRAVITATING BROWNIAN PARTICLES AND TWO-DIMENSIONAL POINT VORTICES, International Journal of Modern Physics B, Volume 26 (2012) no. 12, p. 1241002 | DOI:10.1142/s0217979212410020
Pierre-Henri Chavanis Virial theorem for Onsager vortices in two-dimensional hydrodynamics, The European Physical Journal Plus, Volume 127 (2012) no. 12 | DOI:10.1140/epjp/i2012-12159-x
P. H. Chavanis; R. Mannella Self-gravitating Brownian particles in two dimensions: the case of N = 2 particles, The European Physical Journal B, Volume 78 (2010) no. 2, p. 139 | DOI:10.1140/epjb/e2010-90839-3
P. H. Chavanis Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes, Astronomy Astrophysics, Volume 483 (2008) no. 3, p. 673 | DOI:10.1051/0004-6361:20078287
P.-H. Chavanis White dwarf stars inDdimensions, Physical Review D, Volume 76 (2007) no. 2 | DOI:10.1103/physrevd.76.023004
P. H. Chavanis Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions, The European Physical Journal B, Volume 57 (2007) no. 4, p. 391 | DOI:10.1140/epjb/e2007-00187-2
P. H. CHAVANIS PHASE TRANSITIONS IN SELF-GRAVITATING SYSTEMS, International Journal of Modern Physics B, Volume 20 (2006) no. 22, p. 3113 | DOI:10.1142/s0217979206035400

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