Search results for "82C70"
showing 3 items of 3 documents
A 1D coupled Schrödinger drift-diffusion model including collisions
2005
We consider a one-dimensional coupled stationary Schroedinger drift-diffusion model for quantum semiconductor device simulations. The device domain is decomposed into a part with large quantum effects (quantum zone) and a part where quantum effects are negligible (classical zone). We give boundary conditions at the classic-quantum interface which are current preserving. Collisions within the quantum zone are introduced via a Pauli master equation. To illustrate the validity we apply the model to three resonant tunneling diodes.
Macroscopic conductivity of free fermions in disordered media
2014
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint. We show, in particular, the existence and finiteness of the conductivity measure $\mu _{\mathbf{\Sigma }}$ for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, $\mu _{\mathbf{\Sigma }}$ converges in the weak$^{\ast } $-topology to the trivial measure in the case of perfect insulators (strong disorder, compl…
Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
2019
We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, we give a first answer to an old open problem in mathematical physics - first addressed by Ginibre in 1968 within a different context - about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show tha…