Related papers: Predicting Steady States of One-dimensional Collis…
The current paradigm for understanding galaxy formation in the universe depends on the existence of self-gravitating collisionless dark matter. Modeling such dark matter systems has been a major focus of astrophysicists, with much of that…
In an effort to better understand collisionless relaxation processes in gravitational systems, we investigate one-dimensional models. Taking advantage of a Hermite-Legendre expansion of relevant distribution functions, we present analytical…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial…
We present stability conditions for the category of coherent systems on an integral curve. We define a three-parameter family of pre-stability conditions in its derived category using tilting, and we then investigate when these conditions…
We study, using both theory and simulations, a system of self-gravitating sheets. A new statistical mechanics theory - free of any adjustable parameters - is derived to quantitatively predict the final stationary state achieved by this…
We consider a family of isolated inhomogeneous steady states to the gravitational Vlasov-Poisson system with a point mass at the centre. They are parametrised by the polytropic index $k>1/2$, so that the phase space density of the steady…
We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
We present a systematic study of statistical mechanics for non-Hermitian quantum systems. Our work reveals that the stability of a non-Hermitian system necessitates the existence of a single path-dependent conserved quantity, which, in…
We address the problem of stability of one-dimensional non-periodic ground-state configurations with respect to finite-range perturbations of interactions in classical lattice-gas models. We show that a relevant property of non-periodic…
Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…
This talk provides a critical assessment of collisionless galactic dynamics, focusing on the interpretation and limitations of the collisionless Boltzmann equation and the physical mechanisms associated with collisionless relaxation.…
Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal…
We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every…
We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…
Non-equilibrium steady states (NESS) describe particularly simple and stationary non-equilibrium situations. A possibility to obtain such states is to consider the asymptotic evolution of two infinite heat baths brought into thermal…