Numerical simulations of time resolved quantum electronics

This paper discusses the technical aspects - mathematical and numerical - associated with the numerical simulations of a mesoscopic system in the time domain (i.e. beyond the single frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time resolved observables in a general multiterminal system subject to an arbitrary time dependent perturbation (oscillating electrostatic gates, voltage pulses, time-vaying magnetic fields) The approach is mathematically equivalent to (i) the time dependent scattering formalism, (ii) the time resolved Non Equilibrium Green Function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrodinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time resolved observables (current, density. . .) and the (inelastic) scattering matrix are simply expressed in term of this wave function. We use our approach to develop a numerical technique for simulating time resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation capabilities of available approaches.Comment: Typographic mistakes in appendix C were correcte

Magnetic noise spectrum measurement by an atom laser in gravity

Bose-Einstein condensates of ultracold atoms can be used to sense fluctuations of the magnetic field by means of transitions into untrapped hyperfine states. It has been shown recently that counting the outcoupled atoms can yield the power spectrum of the magnetic noise. We calculate the spectral resolution function which characterizes the condensate as a noise measurement device in this scheme. We use the description of the radio-frequency outcoupling scheme of an atom laser which takes into account the gravitational acceleration. Employing both an intuitive and the exact three-dimensional and fully quantum mechanical approach we derive the position-dependent spectral resolution function for condensates of different size and shape

A fast direct solver for a class of two-dimensional separable elliptic equations on the sphere

An efficient, direct, second-order solver for the discrete solution of two-dimensional separable elliptic equations on the sphere is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wavenumber and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK