arXiv subjects

Pierre-Henri Chavanis

Publications and source records attributed to Pierre-Henri Chavanis.

At least 19 recordsLinked to original sources

arXiv2026

Thermal activation rate of dilute axion stars close to the maximum mass

We compute the thermal activation rate of metastable self-gravitating Bose-Einstein condensates with attractive self-interaction (e.g., dilute axion stars) by using the instanton theory. Explicit analytical results are given close to the maximum mass $M_{\rm max}$ [P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)] by using the normal form of the saddle-node bifurcation close to that point. We show that the lifetime of metastable states is extremely long, scaling as $t_{\rm life}\sim e^N\, t_D$, where $N$ is the number of bosons in the system and $t_D$ is the dynamical time ($N\sim 10^{57}$ and $t_D\sim 10\, {\rm hrs}$ for typical QCD axion stars; $N\sim 10^{96}$ and $t_D\sim 100\, {\rm Myrs}$ for the quantum core of a dark matter halo made of ultralight axions). Therefore, metastable equilibrium states can be considered as stable equilibrium states in practice. We compare our results with similar results obtained for Bose-Einstein condensates in laboratory, globular clusters and self-gravitating Brownian particles in astrophysics, the Brownian mean field model (BMF) in statistical mechanics, and bacterial populations in biology. Our presentation parallels the calculation of the quantum tunneling rate of dilute axion stars given in a previous paper [P.H. Chavanis, Phys. Rev. D 102, 083531 (2020)]. These calculations can find application in various domains of physics and astrophysics.

astro-ph.CO↗

arXiv2026

Energy Balance of a Boson Gas at Zero Temperature in Curved Spacetime

We develop a comprehensive thermodynamic description for a zero-temperature boson gas in curved spacetime, integrating energy conservation with information-theoretic principles. Using the hydrodynamic Madelung representation within the ADM formalism, we establish two fundamental relationships: an energy balance equation representing the first law of thermodynamics from a spacetime perspective, and an information-theoretic constraint connecting Fisher entropy to the dynamical evolution of the boson density. This dual formulation clearly separates energy transport from information conservation while revealing how quantum information is preserved in curved backgrounds. The introduction of a stochastic velocity provides a bridge between quantum potential effects and underlying spacetime fluctuations. We demonstrate the consistency of our framework through detailed analyses of quantum systems in both Minkowski and Schwarzschild spacetimes. This work provides a unified foundation for studying relativistic bosonic systems, with direct relevance to boson stars and scalar field dark matter models.

gr-qc↗

arXiv2026

Polytropes, logotropes, the universal value of the surface density of dark matter halos, and the value of the cosmological constant

We discuss the connection between logotropes and polytropes in astrophysics and cosmology. The logotropic equation of state $P=A\ln(\rho/\rho_P)$ may be seen as a degenerate form of the polytropic equation of state $P=K\rho^{\gamma}$ in the limit $\gamma\rightarrow 0$, $K\rightarrow\infty$ with $A=K\gamma$ fixed. The logotropic distribution function corresponds to the polytropic distribution function of index $\gamma=0$ for which the density is finite but the pressure diverges logarithmically. We show that the polytropic and logotropic distribution functions can be obtained in the nondegenerate limit of the Lynden-Bell theory of violent relaxation for a particular distribution of phase levels given by the $\chi$-squared distribution. This provides a justification of the Tsallis entropy from the Lynden-Bell entropy. The logotropic distribution function presents a power-law energy tail decreasing as $\epsilon^{-5/2}$. Interestingly, this ``universal'' power-law tail is predicted by recent kinetic theories of collisionless relaxation based on the coarse-grained Vlasov equation and on the secular dressed diffusion equation. When coupled to gravity, the associated density profile decreases as $r^{-1}$. This may explain the universal surface density of dark matter halos, or account for an effective NFW density cusp. This also accounts for the universal gravitational acceleration felt by a test particle and for the Tully-Fisher relation. The logotropic model can thus provide an alternative to the modification of Newtonian dynamics (MOND) theory. We recall how the logotropic model leads to a very accurate expression of the cosmological constant $\Lambda={G^2m_e^6}/{\alpha^6\hbar^4}=1.36\times 10^{-52}\, {\rm m^{-2}}$ in terms of the mass of the electron and the fundamental constants of physics.

gr-qc↗

arXiv2025

Kinetic theory of two-dimensional point vortices at order $1/N$ and $1/N^{2}$

We investigate the long-term relaxation of a distribution of $N$ point vortices in two-dimensional hydrodynamics. To focus on the regime of weak collective amplification, we embed these point vortices within a static background potential and soften their pairwise interaction on small scales. Placing ourselves within the limit of an average axisymmetric distribution, we stress the connections with generic long-range interacting systems, whose relaxation is described within angle-action coordinates. In particular, we emphasise the existence of two regimes of relaxation, depending on whether the system's profile of mean angular velocity (frequency) is a non-monotonic [resp. monotonic] function of radius, which we refer to as profile (1) [resp. profile (2)]. For profile (1), relaxation occurs through two-body non-local resonant couplings, i.e. $1/N$ effects, as described by the inhomogeneous Landau equation. For profile (2), the impossibility of such two-body resonances submits the system to a ``kinetic blocking''. Relaxation is then driven by three-body couplings, i.e. ${1/N^{2}}$ effects, whose associated kinetic equation has only recently been derived. For both regimes, we compare extensively the kinetic predictions with large ensemble of direct $N$-body simulations. In particular, for profile (1), we explore numerically an effect akin to ``resonance broadening'' close to the extremum of the angular velocity profile. Quantitative description of such subtle nonlinear effects will be the topic of future investigations.

cond-mat.stat-mech↗

arXiv2025

On the long-term evolution of razor-thin galactic discs: Balescu-Lenard prediction and perspectives

In the last five decades, numerical simulations have provided invaluable insights into the evolution of galactic discs over cosmic times. As a complementary approach, developments in kinetic theory now also offer a theoretical framework to understand statistically their long-term evolution. The current state-of-the-art kinetic theory of isolated stellar systems is the inhomogeneous Balescu-Lenard equation. It can describe the long-term evolution of a self-gravitating razor-thin disc under the effect of resonant interactions between collectively amplified noise-driven fluctuations. In this work, confronting theoretical predictions to numerical simulations, we quantitatively show that kinetic theory indeed captures the average long-term evolution of cold stellar discs. Leveraging the versatility of kinetic methods, we then offer some new perspectives on this problem, namely (i) the crucial impact of collective effects in accelerating the relaxation; (ii) the role of (weakly) damped modes in shaping the disc's orbital heating; (iii) the bias introduced by gravitational softening on long timescales; (iv) the resurgence of strong stochasticity near marginal stability. These elements call for an appropriate choice of softening kernel when simulating the long-term evolution of razor thin discs and for an extension of kinetic theory beyond the average evolution. Notwithstanding, kinetic theory captures quantitatively the ensemble-averaged long-term response of such discs.

astro-ph.GA↗

arXiv2024

Galactic Rotation Curves of LSB Galaxies using core-halo FDM configurations

In this work, we construct galactic halos in order to fit the rotation curves (RCs) of a sample of low surface brightness (LSB) galaxies. These halos are made of Fuzzy Dark Matter (FDM) with a multimode expansion of non-spherical modes that in average contribute to the appropriate density profile consisting of a core and an envelope needed to fit the rotation curves. The coefficients of the expansion are calculated using a genetic algorithm, that minimizes the difference between the spatial average density of the multimode order parameter describing the FDM and the target dark matter density that fits the RCs. The FDM halos are constructed assuming a solitonic core at the center and two types of envelopes, Navarro-Frenk-White and Pseudo-Isothermal density profiles. The resulting FDM configurations are then evolved in order to show how the average density changes in time due to the secular dynamical evolution, along with a condensation process that lead to the growth of the solitonic core.

astro-ph.GA↗

arXiv2024

Kinetic theory of stellar systems and two-dimensional vortices

We discuss the kinetic theory of stellar systems and two-dimensional vortices and stress their analogies. We recall the derivation of the Landau and Lenard-Balescu equations from the Klimontovich formalism. These equations take into account two-body correlations and are valid at the order $1/N$, where $N$ is the number of particles in the system. They have the structure of a Fokker-Planck equation involving a diffusion term and a drift term. The systematic drift of a vortex is the counterpart of the dynamical friction experienced by a star. At equilibrium, the diffusion and the drift terms balance each other establishing the Boltzmann distribution of statistical mechanics. We discuss the problem of kinetic blocking in certain cases and how it can be solved at the order $1/N^2$ by the consideration of three-body correlations. We also consider the behavior of the system close to the critical point following a recent suggestion by Hamilton and Heinemann (2023). We present a simple calculation, valid for spatially homogeneous systems with long-range interactions described by the Cauchy distribution, showing how the consideration of the Landau modes regularizes the divergence of the friction by polarization at the critical point.

cond-mat.stat-mech↗

arXiv2024

A simple model of magnetic universe without singularity associated with a quadratic equation of state

A 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 $t=0$, 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 $t=0$, 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.

gr-qc↗

arXiv2024

The Boltzmann-Poisson equation with a central body: analytical solutions in one and two dimensions

We consider an isothermal self-gravitating system surrounding a central body. This model can represent a galaxy or a globular cluster harboring a central black hole. It can also represent a gaseous atmosphere surrounding a protoplanet. In three dimensions, the Boltzmann-Poisson equation must be solved numerically in order to obtain the density profile of the gas [Chavanis {\it et al.}, Phys. Rev. E {\bf 109}, 014118 (2024)]. In one and two dimensions, we show that the Boltzmann-Poisson equation can be solved analytically. We obtain explicit analytical expressions of the density profile around a central body which generalize the analytical solutions found by Camm (1950) and Ostriker (1964) in the absence of a central body. Our results also have applications for self-gravitating Brownian particles (Smoluchowski-Poisson system), for the chemotaxis of bacterial populations (Keller-Segel model), and for two-dimensional point vortices (Onsager's model). In the case of bacterial populations, the central body could represent a supply of ``food'' that attracts the bacteria (chemoattractant). In the case of two-dimensional vortices, the central body could be a central vortex

cond-mat.stat-mech↗

arXiv2023

Kinetic theory of inhomogeneous systems with long-range interactions and fluctuation-dissipation theorem

We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic perturbation and determine the response of the system to the perturbation. We derive the diffusion tensor and the friction by polarization of a test particle. We introduce a general Fokker-Planck equation involving a diffusion term and a friction term. When the friction by polarization can be neglected, we obtain a secular dressed diffusion (SDD) equation sourced by the external noise. When the external perturbation is created by a discrete collection of $N$ field particles, we obtain the inhomogeneous Lenard-Balescu kinetic equation reducing to the inhomogeneous Landau kinetic equation when collective effects are neglected. We consider a multi-species system of particles. When the field particles are at statistical equilibrium (thermal bath), we establish the proper expression of the fluctuation-dissipation theorem for systems with long-range interactions relating the power spectrum of the fluctuations to the response function of the system. In that case, the friction and diffusion coefficients satisfy the Einstein relation and the Fokker-Planck equation reduces to the inhomogeneous Kramers equation. We also consider a gas of Brownian particles with long-range interactions described by $N$ coupled stochastic Langevin equations and determine its mean and mesoscopic evolution. We discuss the notion of stochastic kinetic equations and the role of fluctuations possibly triggering random transitions from one equilibrium state to the other. Our presentation parallels the one given for two-dimensional point vortices in a previous paper [P.H. Chavanis, Eur. Phys. J. Plus 138, 136 (2023)].

cond-mat.stat-mech↗

arXiv2023

Cosmological Structure Formation and Soliton Phase Transition in Fuzzy Dark Matter with Axion Self-Interactions

We investigate cosmological structure formation in Fuzzy Dark Matter (FDM) with an attractive self-interaction (SI) with numerical simulations. Such a SI would arise if the FDM boson were an ultra-light axion, which has a strong CP symmetry-breaking scale (decay constant). Although weak, the attractive SI may be strong enough to counteract the quantum 'pressure' and alter structure formation. We find in our simulations that the SI can enhance small-scale structure formation, and soliton cores above a critical mass undergo a phase transition, transforming from dilute to dense solitons.

astro-ph.CO↗

arXiv2022

Kinetic theory of two-dimensional point vortices and fluctuation-dissipation theorem

We complete the kinetic theory of two-dimensional (2D) point vortices initiated in previous works. We use a simpler and more physical formalism. We consider a system of 2D point vortices submitted to a small external stochastic perturbation and determine the response of the system to the perturbation. We derive the diffusion coefficient and the drift by polarization of a test vortex. We introduce a general Fokker-Planck equation involving a diffusion term and a drift term. When the drift by polarization can be neglected, we obtain a secular dressed diffusion (SDD) equation sourced by the external noise. When the external perturbation is created by a discrete collection of $N$ point vortices, we obtain a Lenard-Balescu-like kinetic equation reducing to a Landau-like kinetic equation when collective effects are neglected. We consider a multi-species system of point vortices. We discuss the process of kinetic blocking in the single and multi-species cases. When the field vortices are at statistical equilibrium (thermal bath), we establish the proper expression of the fluctuation-dissipation theorem for 2D point vortices relating the power spectrum of the fluctuations to the response function of the system. In that case, the drift coefficient and the diffusion coefficient satisfy an Einstein-like relation and the Fokker Planck equation reduces to a Smoluchowski-like equation. We mention the analogy between 2D point vortices and stellar systems. In particular, the drift of a point vortex in 2D hydrodynamics is the counterpart of the Chandrasekhar dynamical friction in astrophysics. We also consider a gas of 2D Brownian point vortices described by $N$ coupled stochastic Langevin equations and determine its mean and mesoscopic evolution. In the present paper, we treat the case of unidirectional flows but our results can be straightforwardly generalized to axisymmetric flows.

cond-mat.stat-mech↗

arXiv2022

Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|φ|^4$ self-interaction

We derive an approximate analytical expression of the maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|φ|^4$ 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.

gr-qc↗

arXiv2022

Hydrodynamic representation and Energy Balance for Dirac and Weyl fermions in curved space-times

Using a generalized Madelung transformation, we derive the hydrodynamic representation of the Dirac equation in arbitrary curved space-times coupled to an electromagnetic field. We obtain Dirac-Euler equations for fermions involving a continuity equation and a first integral of the Bernoulli equation. Comparing between the Dirac and Klein-Gordon equations we obtain the balance equation for fermion particles. We also use the correspondence between fermions and bosons to derive the hydrodynamic representation of the Weyl equation which is a chiral form of the Dirac equation.

gr-qc↗

arXiv2022

Orbital alignment and mass segregation in galactic nuclei via vector resonant relaxation

Supermassive black holes dominate the gravitational potential in galactic nuclei. In these dense environments, stars follow nearly Keplerian orbits and see their orbital planes relax through the potential fluctuations generated by the stellar cluster itself. For typical astrophysical galactic nuclei, the most likely outcome of this vector resonant relaxation (VRR) is that the orbital planes of the most massive stars spontaneously self-align within a narrow disc. We present a maximum entropy method to systematically determine this long-term distribution of orientations and use it for a wide range of stellar orbital parameters and initial conditions. The heaviest stellar objects are found to live within a thin equatorial disk. The thickness of this disk depends on the stars' initial mass function, and on the geometry of the initial cluster. This work highlights a possible (indirect) novel method to constrain the distribution of intermediate mass black holes in galactic nuclei.

astro-ph.GA↗

arXiv2022

Self-gravitating clusters of Bose-Einstein gas with planar, cylindrical, or spherical symmetry: gaseous density profiles and onset of condensation

We calculate density profiles for self-gravitating clusters of an ideal Bose-Einstein gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium. Our study includes clusters with planar symmetry in dimensions $\mathcal{D}=1,2,3$, clusters with cylindrical symmetry in $\mathcal{D}=2,3$, and clusters with spherical symmetry in $\mathcal{D}=3$. Wall confinement is imposed where needed to prevent escape. The length scale and energy scale in use for the gaseous phase render density profiles for gaseous macrostates independent of total mass. Density profiles for mixed-phase macrostates have a condensed core surrounded by a gaseous halo. The spatial extension of the core is negligibly small on the length scale tailored for the halo. The mechanical stability conditions as evident in caloric curves permit multiple macrostates to coexist. Their status regarding thermal equilibrium is examined by a comparison of free energies. The onset of condensation takes place at a nonzero temperature in all cases. The critical singularities and the nature of the phase transition vary with the symmetry of the cluster and the dimensionality of the space.

cond-mat.stat-mech↗

arXiv2022

Long-term relaxation of ${1D}$ self-gravitating systems

We investigate the long-term relaxation of one-dimensional (${1D}$) self-gravitating systems, using both kinetic theory and $N$-body simulations. We consider thermal and Plummer equilibria, with and without collective effects. All combinations are found to be in clear agreement with respect to the Balescu-Lenard and Landau predictions for the diffusion coefficients. Interestingly, collective effects reduce the diffusion by a factor ${\sim 10}$. The predicted flux for Plummer equilibrium matches the measured one, which is a remarkable validation of kinetic theory. We also report on a situation of quasi kinetic blocking for the same equilibrium.

cond-mat.stat-mech↗

arXiv2022

Generalized Logotropic Models and their Cosmological Constraints

We propose a new class of cosmological unified dark sector models called "{\em Generalized Logotropic Models}". They depend on a free parameter $n$. The original logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130 (2015)] is a special case of our generalized model corresponding to $n=1$. In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure $P$ includes higher order logarithmic terms of the rest-mass density $ρ_m$. The total energy density $ε$ is the sum of the rest-mass energy density $ρ_m c^2$ and the internal energy density $u$ which play the role of dark matter energy density $ε_m$ and dark energy density $ε_{de}$, respectively. We investigate the cosmological behavior of the generalized logotropic models by focusing on the evolution of the energy density, scale factor, equation of state parameter, decceleration parameter and squared speed of sound. Low values of $n\le 3$ are favored. We also study the asymptotic behavior of the generalized logotropic models. In particular, we show that the model presents a phantom behavior and has three distinct ways of evolution depending on the value of $n$. For $n\le 2$, it leads to a little rip and for $n>2$ to a big rip. We predict the value of the big rip time as a function of $n$ without any free (undetermined) parameter.

gr-qc↗