102 research outputs found
Lettres d'Afrahat le sage de la Perse: Étudiées au point de vue de l’histoire et de la doctrine
No full textThis volume, the author’s doctoral thesis, contains a detailed but concise study of Aphrahat’s Letters (i.e. Demonstrations). After an introduction dealing with Aphrahat’s life and writings, Chavanis moves into the main part of the book, which is divided into two parts. In the first, he looks at the historical situation against which Aphrahat’s works must be read, namely matters dealing with the Church in Persia, such as its ecclesiastical structure, the persecutions under Shapur II, and controversies with the Jews. In the second part, Chavanis examines the Demonstrations for the doctrines they present. He considers themes such as Scripture and tradition as sources for Aphrahat’s theology, God, Trinity, Angels, the World, Man, Original Sin, the Sacraments, the Church, and others. This volume, which is also suitable for non-specialists in Syriac, takes its place among others dealing specifically with this early Syriac author and stands out for its clarity and conciseness
Out-of-equilibrium phase re-entrance(s) in long-range interacting systems
No full textSystems with long-range interactions display a short-time relaxation toward quasistationary states (QSSs) whose lifetime increases with system size. The application of Lynden-Bell’s theory of “violent relaxation” to the Hamiltonian Mean Field model leads to the prediction of out-of-equilibrium first- and second-order phase transitions between homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSSs, as well as an interesting phenomenon of phase re-entrances. We compare these theoretical predictions with direct N-body numerical simulations. We confirm the existence of phase re-entrance in the typical parameter range predicted from Lynden-Bell’s theory, but also show that the picture is more complicated than initially thought. In particular, we exhibit the existence of secondary re-entrant phases: we find unmagnetized states in the theoretically magnetized region as well as persisting magnetized states in the theoretically unmagnetized region. We also report the existence of a region with negative specific heats for QSSs both in the numerical and analytical caloric curves
Dynamical and thermodynamical stability of two-dimensional flows: variational principles and relaxation equations
No full textWe review and connect different variational principles that have been proposed to settle the dynamical and thermodynamical stability of two-dimensional incompressible and inviscid flows governed by the 2D Euler equation. These variational principles involve functionals of a very wide class that go beyond the usual Boltzmann functional. We provide relaxation equations that can be used as numerical algorithms to solve these optimization problems. These relaxation equations have the form of nonlinear mean field Fokker-Planck equations associated with generalized “entropic”
functionals [P.H. Chavanis, Eur. Phys. J. B 62, 179 (2008)]
Negative Specific Heat in the Canonical Statistical Ensemble
No full textAccording to thermodynamics, the specific heat of Boltzmannian short-range interacting systems is a positive quantity. Less intuitive properties are instead displayed by systems characterized by long-range interactions. In that case, the sign of specific heat depends on the considered statistical ensemble: Negative specific heat can be found in isolated systems, which are studied in the framework of the microcanonical ensemble; on the other hand, it is generally recognized that a positive specific heat should always be measured in systems in contact with a thermal bath, for which the canonical ensemble is the appropriate one. We demonstrate that the latter assumption is not generally true: One can, in principle, measure negative specific heat also in the canonical ensemble if the system under scrutiny is non-Boltzmannian and/or out-of-equilibrium
A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
No full textInternational audienceThe Gross–Pitaevskii–Poisson equations that govern the evolution of self-gravitating Bose–Einstein condensates, possibly representing dark matter halos, experience a process of gravitational cooling and violent relaxation. We propose a heuristic parametrization of this complicated process in the spirit of Lynden-Bell’s theory of violent relaxation for collisionless stellar systems. We derive a generalized wave equation that was introduced phenomenologically in Chavanis (Eur Phys J Plus 132:248, 2017) involving a logarithmic nonlinearity associated with an effective temperature and a damping term associated with a friction . These terms can be obtained from a maximum entropy production principle and are linked by a form of Einstein relation expressing the fluctuation-dissipation theorem. The wave equation satisfies an H-theorem for the Lynden-Bell entropy and relaxes towards a stable equilibrium state which is a maximum of entropy at fixed mass and energy. This equilibrium state represents the most probable state of a Bose–Einstein condensate dark matter halo. It generically has a core-halo structure. The quantum core prevents gravitational collapse and may solve the core-cusp problem. The isothermal halo leads to flat rotation curves in agreement with the observations. These results are consistent with the phenomenology of dark matter halos. Furthermore, as shown in a previous paper (Chavanis in Phys Rev D 100:123506, 2019), the maximization of entropy with respect to the core mass at fixed total mass and total energy determines a core mass–halo mass relation which agrees with the relation obtained in direct numerical simulations. We stress the importance of using a microcanonical description instead of a canonical one. We also explain how our formalism can be applied to the case of fermionic dark matter halos.[graphic not available: see fulltext][graphic not available: see fulltext
On the lifetime of metastable states in self-gravitating systems
No full textWe discuss the physical basis of the statistical
mechanics of self-gravitating systems. We show the correspondance
between statistical mechanics methods based on the evaluation of
the density of states and partition function and thermodynamical
methods based on the optimization of a thermodynamical potential
(entropy or free energy). We address the question of the
thermodynamic limit of self-gravitating systems, the justification
of the mean-field approximation, the validity of the saddle point
approximation near the transition point, the lifetime of metastable
states and the fluctuations in isothermal spheres. In particular,
we emphasize the tremendously long lifetime of metastable states of
self-gravitating systems which increases exponentially with the
number of particles N except in the vicinity of the critical
point. More specifically, using an adaptation of the Kramers
formula justified by a kinetic theory, we show that the lifetime of
a metastable state scales as in microcanonical
ensemble and in canonical ensemble, where and are the barriers of entropy and free energy
per particle respectively. The physical
caloric curve must take these metastable states (local entropy
maxima) into account. As a result, it becomes multi-valued and
leads to microcanonical phase transitions and “dinosaur's necks”
(Chavanis [CITE], [arXiv:astroph/0205426
Classification of robust isolated vortices in two-dimensional hydrodynamics
No full textWe determine solutions of the Euler equation
representing isolated vortices (monopoles,
dipoles) in an infinite domain, for arbitrary values of
energy, circulation, angular momentum and impulse. A linear
relationship between vorticity and stream function is
assumed inside the vortex (while the flow is irrotational
outside). The emergence of
these solutions in a turbulent flow is justified by the
statistical mechanics of continuous
vorticity fields. The additional restriction of mixing to a
‘maximum-entropy bubble’,
due to kinetic constraints, is assumed. The linear
relationship between vorticity and
stream function is obtained from the statistical theory in
the limit of strong mixing
(when constraints are weak). In this limit, maximizing
entropy becomes equivalent to
a kind of enstrophy minimization. New stability criteria
are investigated and imply
in particular that, in most cases, the vorticity must be
continuous (or slightly discontinuous) at the vortex boundary.
Then, the vortex radius is automatically determined
by the integral constraints and we can obtain a classification
of isolated vortices
such as monopoles and dipoles (rotating or translating) in
terms of a single control
parameter. This article generalizes the classification
obtained in a bounded domain
by Chavanis & Sommeria (1996).</jats:p
Landau equation for self-gravitating classical and quantum particles: Application to dark matter
No full textWe develop the kinetic theory of classical and quantum particles (fermions
and bosons) in gravitational interaction. The kinetic theory of quantum
particles may have applications in the context of dark matter. For simplicity,
we consider an infinite and spatially homogeneous system (or make a local
approximation) and neglect collective effects. This leads to the quantum Landau
equation derived heuristically in [Chavanis, Physica A 332, 89 (2004)]. We
establish its main properties: conservation laws, -theorem, equilibrium
state, relaxation time, quantum diffusion and friction coefficients, quantum
Rosenbluth potentials, self-consistent evolution, (thermal) bath approximation,
quantum Fokker-Planck equation, quantum King model... For bosonic particles,
the Landau equation can describe the process of Bose-Einstein condensation. We
discuss the relation of our study with the works of [Levkov et al., Phys. Rev.
Lett. 121, 151301 (2018); Bar-Or et al., Astrophys. J. 871, 28 (2019)] on fuzzy
dark matter halos and the formation of Bose stars and solitons
Statistical mechanics of Fofonoff flows in an oceanic basin
No full textWe study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the β-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function ψ. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or β-effect). Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011
Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive self-interaction
No full textWe derive an approximate analytical expression of the maximum mass of
relativistic self-gravitating Bose-Einstein condensates with repulsive or
attractive self-interaction. This expression interpolates between
the general relativistic maximum mass of noninteracting bosons stars, the
general relativistic maximum mass of bosons stars with a repulsive
self-interaction in the Thomas-Fermi limit, and the Newtonian maximum mass of
dilute axion stars with an attractive self-interaction [P.H. Chavanis, Phys.
Rev. D {\bf 84}, 043531 (2011)]. We obtain the general structure of our formula
from simple considerations and determine the numerical coefficients in order to
recover the exact asymptotic expressions of the maximum mass in particular
limits. As a result, our formula should provide a relevant approximation of the
maximum mass of relativistic boson stars for any value (positive and negative)
of the self-interaction parameter. We discuss the evolution of the system above
the maximum mass and consider application of our results to dark matter halos
and inflaton clusters. We also make a short review of boson stars and
Bose-Einstein condensate dark matter halos, and point out analogies with models
of extended elementary particles.Comment: arXiv admin note: text overlap with arXiv:gr-qc/9801063 by other
author
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