1,721,144 research outputs found
Long-range interacting systems and dynamical phase transitions
No full textWe briefly review the derivation of the Vlasov equation, which is a convenient approximation for the description of the transport properties of long-range interacting systems. We then point out that the presence of an external source of noise, like for instance a heat bath, induces dynamical phase transitions from ordered non-equilibrium Vlasov-stable states to disordered ones
Mécanique statistique des sytèmes autogravitants en relativité générale
No full textLa mécanique statistique des systèmes auto-gravitants constitue un des plus fascinants et mystérieux champs de recherche. À cause de la nature à longue-portée de la force gravitationnelle, la notion usuelle d'équilibre statistique est modifiée, faisant de cette étude un problème hors-équilibre. Par conséquent, ces systèmes exhibent certaines propriétés particulières comme, par exemple, l'existence de transitions de phase associées à un effondrement gravitationnel. Le travail présenté dans cette thèse a comme but une description détaillée des transitions de phase dans un cadre général relativiste en considérant, en particulier, le cas des fermions auto-gravitants. La thèse est conceptuellement divisée en trois parties, selon le niveau de dégénérescence du système. D'abord, nous focalisons notre attention sur le cas des fermions dégénérés (T = 0), en étudiant en détail l'équilibre gravitationnel. Ensuite, en considérant la limite de haute température (T >> 1), nous montrons l'existence de deux types d'effondrement gravitationnel dans les séries d'équilibre. Enfin, nous explorons le cas général, en illustrant la présence des transitions de phase gravitationnelles, soit dans l'ensemble micro-canonique soit dans l'ensemble canonique.The statistical mechanics of self-gravitating systems constitutes one of the most fascinating and puzzling fields of research. Due to the long-range nature of the gravitational force, the usual notion of statistical equilibrium is modified, making of this study an out-of-equilibrium problem. As a consequence, these systems exhibit some peculiar features such as the occurrence of phase transitions associated with a gravitational collapse. The work presented in this thesis aims at providing a detailed description of the phase transitions in a general relativistic framework by considering, in particular, the case of self-gravitating fermions. The thesis is conceptually divided in three parts, according to the degeneracy level of the system. We firstly focus our attention on the case of degenerate fermions (T = 0), by studying in detail the gravitational equilibrium. Successively, considering the high temperature limit (T >> 1), we show the existence of two kinds of gravitational collapse in the series of equilibria. Finally, we explore the general case, by illustrating the occurrence of the gravitational phase transitions, in both microcanonical and canonical ensembles
Derivation of a generalized Schrödinger equation for dark matter halos from the theory of scale relativity
No full textInternational audienceUsing Nottale’s theory of scale relativity, we derive a generalized Schrödinger equation applying to dark matter halos. This equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Fundamentally, this wave equation arises from the nondifferentiability of the trajectories of the dark matter particles whose origin may be due to ordinary quantum mechanics, classical ergodic (or almost ergodic) chaos, or to the fractal nature of spacetime at the cosmic scale. The generalized Schrödinger equation involves a coefficient D , possibly different from ħ∕2m (where ħ is the Planck constant and m the mass of the particles), whose value for dark matter halos is D=1.02×1023 m 2 /s. This model is similar to the Bose–Einstein condensate dark matter model except that it does not require the dark matter particle to be ultralight. It can accommodate any type of particles provided that they have nondifferentiable trajectories. We suggest that the cold dark matter crisis may be solved by the fractal (nondifferentiable) structure of spacetime at the cosmic scale, or by the chaotic motion of the particles on a very long timescale, instead of ordinary quantum mechanics. The equilibrium states of the generalized Schrödinger equation correspond to configurations with a core-halo structure. The quantumlike potential generates a solitonic core that solves the cusp problem of the classical cold dark matter model. The logarithmic nonlinearity accounts for the presence of an isothermal halo that leads to flat rotation curves (it also accounts for the isothermal core of large dark matter halos). The damping term ensures that the system relaxes towards an equilibrium state. This property is guaranteed by an H -theorem satisfied by a Boltzmann-like free energy functional. In our approach, the temperature and the friction arise from a single formalism. They correspond to the real and imaginary parts of the complex friction coefficient present in the scale covariant equation of dynamics that is at the basis of Nottale’s theory of scale relativity. They may be the manifestation of a cosmic aether or the consequence of a process of violent relaxation and gravitational cooling on a coarse-grained scale
Kinetic theory of spatially homogeneous systems with long-range interactions: I. General results
No full textarXiv admin note: text overlap with arXiv:1107.1475 and arXiv:1107.1447International audienceWe review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the Lenard-Balescu equation which is valid in a weak coupling approximation. When collective effects are neglected it reduces to the Landau equation and when collisions (correlations) are neglected it reduces to the Vlasov equation. The relaxation of a test particle in a bath is described by a Fokker-Planck equation involving a diffusion term and a friction term. For a thermal bath, the diffusion and friction coefficients are connected by an Einstein relation. General expressions of the diffusion and friction coefficients are given, depending on the potential of interaction and on the dimension of space. We also discuss the scaling with (number of particles) or with (plasma parameter) of the relaxation time towards statistical equilibrium. Finally, we consider the effect of an external stochastic forcing on the evolution of the system and compute the corresponding term in the kinetic equation
Mass-radius relation of self-gravitating Bose-Einstein condensates with a central black hole
No full textInternational audienceWe determine the mass-radius relation of self-gravitating Bose-Einstein condensates with an attractive -1/r external potential created by a central mass. Following our previous work (P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)), we use an analytical approach based on a Gaussian ansatz. We consider the case of noninteracting bosons as well as the case of self-interacting bosons with a repulsive or an attractive self-interaction. These results may find application in the context of dark matter halos made of self-gravitating Bose-Einstein condensates. In that case, the central mass may mimic a supermassive black hole. We apply our results to ultralight axions with an attractive self-interaction. We determine how the central black hole affects the mass-radius relation and the maximum mass of axionic halos found in our previous papers. Our approximate analytical results based on the Gaussian ansatz are compared with exact analytical results obtained in particular limits
A simple model of magnetic universe without singularity associated with a quadratic equation of state
No full textInternational audienceA model of magnetic universe based on nonlinear electrodynamics has been introduced by Kruglov. This model describes an early inflation era followed by a radiation era. We show that this model is related to our model of universe based on a quadratic equation of state. We discuss two quantitatively different models of early universe. In Model I, the primordial density of the universe is identified with the Planck density. At , the universe had the characteristics of a Planck black hole. During the inflation, which takes place on a Planck timescale, the size of the universe evolves from the Planck length to a size comparable to the Compton wavelength of the neutrino. If we interpret the radius of the universe at the end of the inflation (neutrino's Compton wavelength) as a minimum length related to quantum gravity and use Zeldovich's first formula of the vacuum energy, we obtain the correct value of the cosmological constant. In Model II, the primordial density of the universe is identified with the electron density as a consequence of nonlinear electrodynamics. At , the universe had the characteristics of an electron. During the inflation, which takes place on a gravitoelectronic timescale, the size of the universe evolves from the electron's classical radius to a size comparable to the size of a dark energy star of the stellar mass. If we interpret the radius of the universe at the begining of the inflation (electron's classical radius) as a minimum length related to quantum gravity and use Zeldovich's second formula of the vacuum energy, we obtain the correct value of the cosmological constant. This provides an accurate form of Eddington relation between the cosmological constant and the mass of the electron. We also introduce a nonlinear electromagnetic Lagrangian that describes simultaneously the early inflation, the radiation era, and the dark energy era
Dynamics and thermodynamics of systems with long-range interactions: interpretation of the different functionals
No full textChapter of the volume "Dynamics and Thermodynamics of systems with long range interactions: theory and experiments", A. Campa, A. Giansanti, G. Morigi, F. Sylos Labini Eds., American Institute of Physics Conference proceedings, 970 (2008)International audienceWe discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary state (QSS), followed by a slow collisional relaxation leading to the Boltzmann statistical equilibrium state. These two regimes can be explained by a kinetic theory, using an expansion of the BBGKY hierarchy in powers of 1/N, where N is the number of particles. We discuss the physical meaning of the different functionals appearing in the analysis: the Boltzmann entropy, the Lynden-Bell entropy, the "generalized" entropies arising in the reduced space of coarse-grained distribution functions, the Tsallis entropy, the generalized H-functions increasing during violent relaxation (not necessarily monotonically) and the convex Casimir functionals used to settle the formal nonlinear dynamical stability of steady states of the Vlasov equation. We show the connection between the different variational problems associated with these functionals. We also introduce a general class of nonlinear mean field Fokker-Planck (NFP) equations that can be used as numerical algorithms to solve these constrained optimization problems
Phase transitions between dilute and dense axion stars
No full textInternational audienceWe study the nature of phase transitions between dilute and dense axion stars interpreted as self-gravitating Bose-Einstein condensates. We develop a Newtonian model based on the Gross-Pitaevskii-Poisson equations for a complex scalar field with a self-interaction potential V(|ψ|2) involving an attractive |ψ|4 term and a repulsive |ψ|6 term. Using a Gaussian Ansatz for the wave function, we analytically obtain the mass-radius relation of dilute and dense axion stars for arbitrary values of the self-interaction parameter λ≤0. We show the existence of a critical point |λ|c∼(m/MP)2, where m is the axion mass and MP is the Planck mass, above which a first-order phase transition takes place. We qualitatively estimate general relativistic corrections on the mass-radius relation of axion stars. For weak self-interactions |λ||λ|c, a system of self-gravitating axions forms a stable dilute axion star below a Newtonian maximum mass Mmax,Ndilute=5.073MP/|λ| [Phys. Rev. D 84, 043531 (2011)PRVDAQ1550-799810.1103/PhysRevD.84.043531], collapses into a dense axion star above that mass, and collapses into a black hole above a general relativistic maximum mass Mmax,GRdense∼|λ|MP3/m2. Dense axion stars explode below a Newtonian minimum mass Mmin,Ndense=98.9m/|λ| and form dilute axion stars of large size or disperse away. We determine the phase diagram of self-gravitating axions and show the existence of a triple point (|λ|*,M*/(MP2/m)) separating dilute axion stars, dense axion stars, and black holes. We make numerical applications for QCD axions and ultralight axions. Our approximate analytical results are in good agreement with the exact numerical results of Braaten et al. [Phys. Rev. Lett. 117, 121801 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.121801] for Newtonian dense axion stars. They are also qualitatively similar to those obtained by Helfer et al. [J. Cosmol. Astropart. Phys. 03 (2017) 055JCAPBP1475-751610.1088/1475-7516/2017/03/055] for general relativistic axion stars, but they differ quantitatively for weak self-interactions presumably due to the use of a different self-interaction potential V(|ψ|2). We point out analogies between the evolution of self-gravitating axions (bosons) at zero temperature evolving from dilute axion stars to dense axion stars and black holes and the evolution of compact degenerate (fermion) stars at zero temperature evolving from white dwarfs to neutron stars and black holes. We also discuss some analogies between the phase transitions of Newtonian axion stars at zero temperature and the phase transitions of Newtonian self-gravitating fermions at nonzero temperature. Finally, we suggest that a dense axionic nucleus may form at the center of dark matter halos through the collapse of a dilute axionic core (soliton) passing above the maximum mass Mmax,Ndilute. It would have a mass 1.11×109(f/m)M⊙, a radius 0.949/(mf1/3) pc, a density 2.10×10-8(m2f2) g/m3, a pulsation period 8.24/(mf1/3) yr, and an energy -5.59×1062(f/m) erg, where the axion mass m is measured in units of 10-22 eV/c2 and the axion decay constant f is measured in units of 1015 GeV. This dense axionic nucleus could be the remnant of a bosenova associated with the emission of a characteristic radiation [Phys. Rev. Lett. 118, 011301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.011301]
- …
