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Benjamin Anwasia

Publications and source records attributed to Benjamin Anwasia.

5 recordsLinked to original sources
arXiv2025

Hydrodynamics of degenerate Fermi gases on spherical Fermi surfaces

We consider the description of a Fermi gas of free electrons given by the Boltzmann--Fermi--Dirac equation, and aim at providing a precise mathematical understanding of the Fermi ground state and its first-order approximation of excited states on the Fermi sphere. In order to achieve that, using the framework of hydrodynamic limits in collisional kinetic theory, we identify the low-temperature regimes in which charge-density fluctuations concentrate on the Fermi sphere. In three spatial dimensions or higher, we also characterize the thermodynamic equilibra and energy spectra of fluctuations. This allows us to derive the macroscopic hydrodynamic equations describing how charge densities flow and propagate in metals, thereby providing a precise description of plasma oscillations in conductors. The two-dimensional case is fundamentally different and is handled in a companion article. Remarkably, our results establish that excited electrons and their energy can be distributed on the Fermi sphere anisotropically, which deviates from the common intuitive assumption that electrons and their energy should be distributed uniformly in all directions. The hydrodynamic regimes featured in this work are akin to the acoustic limit of the classical Boltzmann equation. However, we emphasize that our derivation holds for arbitrarily fast rates of convergence of the Knudsen number, which significantly extends the applicability of the known proofs of the classical acoustic limit. This suggest that low-temperature limits of Fermi gases provide a promising avenue of research toward a complete understanding of the compressible Euler limit.

math.AP↗
arXiv2023

Quantized collision invariants on the sphere

We show that a measurable function $g:\mathbb{S}^{d-1}\to\mathbb{R}$, with $d\geq 3$, satisfies the functional relation \begin{equation*} g(\omega)+g(\omega_*)=g(\omega')+g(\omega_*'), \end{equation*} for all admissible $\omega,\omega_*,\omega',\omega_*'\in\mathbb{S}^{d-1}$ in the sense that \begin{equation*} \omega+\omega_*=\omega'+\omega_*', \end{equation*} if and only if it can be written as \begin{equation*} g(\omega)=A+B\cdot\omega, \end{equation*} for some constants $A\in \mathbb{R}$ and $B\in\mathbb{R}^d$. Such functions form a family of quantized collision invariants which play a fundamental role in the study of hydrodynamic regimes of the Boltzmann--Fermi--Dirac equation near Fermionic condensates, i.e., at low temperatures. In particular, they characterize the elastic collisional dynamics of Fermions near a statistical equilibrium where quantum effects are predominant.

math.CA↗
arXiv2020

The Maxwell-Stefan Diffusion Limit of a Hard-Sphere Kinetic Model for Mixtures

We study a kinetic model for non-reactive mixtures of monatomic gases with hard-sphere cross-sections under isothermal condition. By considering a diffusive scaling of the kinetic model and using the method of moments, we formally obtain from the continuity and momentum balance equations of the species, in the limit as the scaling parameter goes to zero, the Maxwell-Stefan diffusion equations, with an explicit expression for the diffusion coefficients.

physics.comp-ph↗
arXiv2017

From the simple reacting sphere kinetic model to the reaction-diffusion system of Maxwell-Stefan type

In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting spheres for a quaternary mixture of monatomic ideal gases that undergoes a reversible chemical reaction of bimolecular type. Then, we consider a scaling describing a physical situation in which mechanical collisions play a dominant role in the evolution process, while chemical reactions are slow, and compute explicitly the production terms associated to the concentration and momentum balance equations for each species in the reactive mixture. Finally, we prove that, under isothermal assumptions, the limit equations for the scaled kinetic model is the reaction diffusion system of Maxwell-Stefan type.

physics.flu-dyn↗