Vittorio Romano

TL;DR: In this paper, the maximum entropy principle of semiconductors is applied to the high field approximation of the collision term in a relaxation form, and a limit on energy-transport and drift-diffusion models is derived.

TL;DR: In this article, a group analysis of drift-diffusion systems is performed and Lie symmetries starting from weak equivalence transformations are obtained for applications to the transport of charges in semiconductors.

TL;DR: A hydrodynamic subband model for semiconductors is formulated by closing the moment system derived from the Schrodinger–Poisson–Boltzmann equations on the basis of the maximum entropy principle, by taking into account non parabolic energy bands of Kane’s type.

TL;DR: The tracial analog of Hilbert's classical result on positive binary quartics is presented in this article, where a trace-positive bivariate noncommutative polynomial of degree at most four is a sum of hermitian squares and commutators.

TL;DR: In the last two decades, the Maximum Entropy Principle has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices by taking—as macroscopy variables—suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments.