Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

Semiconductor devices are ubiquitous in the modern computer and telecommunications
industry. A precise knowledge of the transport equations for electron flow in semiconductors …

Shielding effects in non-degenerate and degenerate plasmas are compared. A detailed
derivation of the Wigner-Poisson system is provided for electrostatic quantum plasmas in …

The aim of this paper is to compute viscous correction terms for the isothermal quantum
Euler system of Degond, Gallego, and Méhats (SIAM Multiscale Model Simul., 6, 2007). We …

New quantum hydrodynamic equations are derived from a Wigner–Boltzmann model, using
the quantum entropy minimization method recently developed by Degond and Ringhofer …

A new approach to the construction of entropies and entropy productions for a large class of
nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of …

A quantum hydrodynamic model for charge transport in graphene is derived from a moment
expansion of the Wigner–Boltzmann equation. The needed closure relations are obtained …

Correlated many-fermion systems emerge in a broad range of phenomena in warm dense
matter, plasmonics, and ultracold atoms. Quantum hydrodynamics (QHD) complements first …

In the last two decades, the Maximum Entropy Principle (MEP) has been successfully
employed to construct macroscopic models able to describe the charge and heat transport in …

Recently, deep learning (DL) is widely used to detect physical phenomena and has
obtained encouraging results. Several works have shown that it can learn quantum …