Related papers: On linear hypersingular Boltzmann transport equati…
The half-Heusler (hH) compounds are currently considered promising thermoelectric (TE) materials due to their favorable thermopower and electrical conductivity. Accurate estimates of these properties are therefore highly desirable and…
Carrier mobility in bulk semiconductors is typically governed by electron-phonon (e-ph) scattering. In nanostructures, spatial confinement can lead to significant surface scattering, lowering mobility and breaking the spatial homogeneity…
We prove an existence and uniqueness result for Neumann boundary problem of a parabolic partial differential equation (PDE for short) with a singular nonlinear divergence term which can only be understood in a weak sense. A probabilistic…
In this work we exploit the integrability of the two-lead Anderson model to compute transport properties of a quantum dot, in and out of equilibrium. Our method combines the properties of integrable scattering together with a…
It is a fundamental problem in mathematical physics to derive macroscopic transport equations from microscopic models. In this paper we derive the linear Boltzmann equation in the low-density limit of a damped quantum Lorentz gas for a…
The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum-statistical mechanics provide consistent but computational costly approaches;…
We introduce the \emph{transport energy} functional $\mathcal E$ (a variant of the Bouchitt\'e-Buttazzo-Seppecher shape optimization functional) and we prove that its unique minimizer is the optimal transport density $\mu^*$, i.e., the…
We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…
We present a generalization of Bloch's theorem to finite-range lattice systems of independent fermions, in which translation symmetry is broken only by arbitrary boundary conditions, by providing exact, analytic expressions for all energy…
We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by…
In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then the…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
A spatially-periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearised limit of the macroscopic conservation equations within…
A new form of the model collision operator for a Boltzmann gas of hard spheres and Coulomb plasma is derived. One-component and many-component systems are considered. The collision operator proposed takes properly into account the…
The calculations of electronic transport coefficients and optical properties require a very dense interpolation of the electronic band structure in reciprocal space that is computationally expensive and may have issues with band crossing…
Electron transport through a single-level quantum dot weakly coupled to Luttinger liquid leads is considered in the master equation approach. It is shown that for a weak or moderately strong interaction the differential conductance…
Starting from the Boltzmann-Enskog kinetic equations, the charge transport equation for bidisperse granular flows with contact electrification is derived with separate mean velocities, total kinetic energies, charges and charge variances…
We present BTE-Barna (Boltzmann Transport Equation - Beyond the Rta for NAnosystems), a software package that extends the Monte Carlo (MC) module of the almaBTE solver of the Peierls-Boltzmann transport equation for phonons (PBTE) to work…
This work develops a rigorous mathematical formulation of proton transport by integrating both deterministic and stochastic perspectives. The deterministic framework is based on the Boltzmann-Fokker-Planck equation, formulated as an…
This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view,…