Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures

In this article we propose a rapid method to compute the steady states, including bifurcation diagrams, of resonant tunneling heterostructures in the far from equilibrium regime. Those calculations are made on a simplified model which takes into account the characteristic quantities which arise from an accurate asymptotic analysis of the nonlinear Schrödinger-Poisson system. After a summary of the former theoretical results, the asymptotical model is explicitly adapted to physically realistic situations and numerical results are shown in various cases. UNE VERSION MODIFIEE DE CE TEXTE EST PARUE DANS J. COMPUT. PHYS

Spin characterization and control over the regime of radiation-induced zero-resistance states

Over the regime of the radiation-induced zero-resistance states and associated oscillatory magnetoresistance, we propose a low magnetic field analog of quantum-Hall-limit techniques for the electrical detection of electron spin- and nuclear magnetic- resonance, dynamical nuclear polarization via electron spin resonance, and electrical characterization of the nuclear spin polarization via the Overhauser shift. In addition, beats observed in the radiation-induced oscillatory-magnetoresistance are developed into a method to measure and control the zero-field spin splitting due to the Bychkov-Rashba and bulk inversion asymmetry terms in the high mobility GaAs/AlGaAs system.Comment: IEEE Transactions in Nanotechnology (to be published); 10 pages, 10 color figure

An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances

This paper is concerned with a linearized version of the transport problem where the Schr\"{o}dinger-Poisson operator is replaced by a non-autonomous Hamiltonian, slowly varying in time. We consider an explicitly solvable model where a semiclassical island is described by a flat potential barrier, while a time dependent 'delta' interaction is used as a model for a single quantum well. Introducing, in addition to the complex deformation, a further modification formed by artificial interface conditions, we give a reduced equation for the adiabatic evolution of the sheet density of charges accumulating around the interaction point.Comment: latex; 26 page

Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells I

We describe the asymptotic of the steady states of the out-of equilibrium Schrödinger-Poisson system, in the regime of quantum wells in a semiclassical island. After establishing uniform estimates on the nonlinearity, we show that the nonlinear steady states lie asymptotically in a finite-dimensional subspace of functions and that the involved spectral quantities are reduced to a finite number of so-called asymptotic resonant energies. The asymptotic finite dimensional nonlinear system is written in a general setting with only a partial information on its coefficients. After this first part, a complete derivation of the asymptotic nonlinear system will be done for some specific cases in a forthcoming article. UNE VERSION MODIFIEE DE CE TEXTE EST PARUE DANS LES ANNALES DE L'INSTITUT H. POINCARE, ANALYSE NON LINEAIRE

Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach

Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr\"odinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape resonances, the Hamiltonian becomes dissipative. This makes possible an adiabatic theory for the time evolution of resonant states for arbitrarily large time scales. The effect of the artificial interface conditions on the important stationary quantities involved in quantum transport models is also checked to be as small as wanted, in the polynomial scale $(h^N)_{N\in \N}$ as $h\to 0$, according to $\theta_{0}$.Comment: 60 pages, 13 figure