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

In this paper we consider the global existence of weak solutions to a class of Quantum
Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These …

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 …

Navier-Stokes equations for compressible quantum fluids, including the energy equation,
are derived from a collisional Wigner equation, using the quantum entropy maximization …

We investigate the viscous model of quantum hydrodynamics in one and higher space
dimensions. Exploiting the entropy dissipation method, we prove the exponential decay to …

By using the quantum maximum entropy principle we formally derive, from a underlying
kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for …

We address the following inverse problem in quantum statistical physics: does the quantum
free energy (von Neumann entropy+ kinetic energy) admit a unique minimizer among the …

This article is devoted to the reformulation of an isothermal version of the quantum
hydrodynamic model derived by Degond and Ringhofer in [J. Statist. Phys., 112 (2003), pp …

We consider a two-dimensional electron gas with a spin-orbit interaction of Bychkov and
Rashba type. Starting from a microscopic model, represented by the von Neumann equation …