A measure of tripartite entanglement in bosonic and fermionic systems

We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or -fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible amount of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (both for bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: the bosonic bunching results into a low amount of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.Comment: 19 pages, 3 figure

Quantum theory of transient transport in semiconductors: A Monte Carlo approach

A new Monte Carlo method is presented for the evaluation of the density matrix from the solution of the Liouville–von Neumann equation for an ensemble of noninteracting electrons in a semiconductor crystal. The method is applied to the study of the electron transient response to a high external electric field in Si and to the relaxation of photoexcited electrons in GaAs in absence of external electric fields. The phonon population is always assumed at equilibrium, but no assumptions are made about the strength of the electron-phonon interaction. Results show that typical quantum features such as energy-nonconserving transitions, intracollisional field effect, and multiple collisions change the very first transient of the system with respect to a semiclassical description

Quantum theory of impact ionization in coherent high-field semiconductor transport

Generation of carriers in semiconductors by impact ionization is studied under the influence of a constant, arbibrarily high electric field. Using the density-matrix approach a system of equations for the coherent dynamics of electrons and holes in the presence of impact ionization and Auger recombination is derived, which extends the semiconductor Bloch equations by the inclusion of impact-ionization density-correlation functions as additional dynamic variables. From these equations we recover the pure (Zener) and the photon-induced (Franz-Keldysh) carrier tunneling rate and derive an expression for the field-assisted impact-ionization scattering rate. Different levels of approximation of the kinetic equations are discussed. It is shown that in contrast to the semiclassical treatment in the presence of an electric field, a fixed impact-ionization threshold does no longer exist, and the impact-ionization scattering rate is drastically enhanced around the semiclassical threshold by the intracollisional field effect. The close connection of field-assisted impact ionization to the Franz-Keldysh effect is emphasized

Quantum theory of transient transport in semiconductors: A Monte Carlo approach

A new Monte Carlo method is presented for the evaluation of the density matrix from the solution of the Liouville-von Neumann equation for an ensemble of noninteracting electrons in a semiconductor crystal. The method is applied to the study of the electron transient response to a high external electric field in Si and to the relaxation of photoexcited electrons in GaAs in absence of external electric fields. The phonon population is always assumed at equilibrium, but no assumptions are made about the strength of the electron-phonon interaction. Results show that typical quantum features such as energy-nonconserving transitions, intracollisional field effect, and multiple collisions change the very first transient of the system with respect to a semiclassical description

Quantum theory of impact ionization in coherent high-field semiconductor transport

Generation of carriers in semiconductors by impact ionization is studied under the influence of a constant, arbibrarily high electric field. Using the density-matrix approach a system of equations for the coherent dynamics of electrons and holes in the presence of impact ionization and Auger recombination is derived, which extends the semiconductor Bloch equations by the inclusion of impact-ionization density-correlation functions as additional dynamic variables. From these equations we recover the pure (Zener) and the photon-induced (Franz-Keldysh) carrier tunneling rate and derive an expression for the field-assisted impact-ionization scattering rate. Different levels of approximation of the kinetic equations are discussed. It is shown that in contrast to the semiclassical treatment in the presence of an electric field, a fixed impact-ionization threshold does no longer exist, and the impact-ionization scattering rate is drastically enhanced around the semiclassical threshold by the intracollisional field effect. The close connection of field-assisted impact ionization to the Franz-Keldysh effect is emphasized

Time-Domain Analysis of Chalcogenide Threshold Switching: From ns to ps Scale

A space- and time-dependent theoretical model based on a trap-assisted, charge-transport framework for the amorphous phase of a chalcogenide material is used here to interpret available experimental results for the electric current of nanoscale devices in the ns–ps time domain. A numerical solution of the constitutive equations of the model for a time-dependent bias has been carried out for GST-225 devices. The “intrinsic” rise time of the device current after the application of a suitable external bias is controlled by the microscopic relaxation of the mobile-carrier population to the steady-state value. Furthermore, the analysis is extended to include the effect of the external circuit on the electrical switching. A quantitative estimate of the current delay time due to unavoidable parasitic effects is made for the optimised electrical set up configurations recently used by experimental groups

Nonequilibrium electron heating in inter-subband terahertz lasers

Inter-subband laser performance can be critically dependent on the nature of the electron distributions in each subband. In these first Monte Carlo device simulations of optically pumped inter-subband THz lasers, we can see that there are two main causes of electron heating: intersubband decay processes, and inter-subband energy transfer from the "hot" nonequilibrium tails of lower subbands. These processes mean that devices relying on low electron temperatures are disrupted by electron heating, to the extent that slightly populated subbands can have average energies far in excess of the that of either the lattice or other subbands. However, although these heating effects invalidate designs relying on low temperature electron distributions, we see that population inversion is still possible in the high-THz range at 77 K in both stepped and triple-well structures, and that our 11.7 THz triple-well structure even promises inversion at 300 K. © 2002 American Institute of Physics

Modeling of open quantum devices within the closed-system paradigm

We present an alternative simulation strategy for the study of nonequilibrium carrier dynamics in quantum devices with open boundaries. We propose to replace the usual modeling of open quantum systems based on phenomenological injection/loss rates with a kinetic description of the system-reservoir thermalization process. In this simulation scheme the partial carrier thermalization induced by the device spatial boundaries is treated within the standard Boltzmann-transport approach via an effective scattering mechanism between the highly nonthermal device electrons and the thermal carrier distribution of the reservoir. Applications to state-of-the-art semiconductor nanostructures are discussed. Finally, the proposed approach is extended to the quantum-transport regime; to this end, we introduce an effective Liouville superoperator, able to describe the effect of the device spatial boundaries on the time evolution of the single-particle density matrix

First Principles Analysis of Electron-Phonon Interaction in Graphene

The electron-phonon interaction in monolayer graphene is investigated by using density functional perturbation theory. The results indicate that the electron-phonon interaction strength is of comparable magnitude for all four in-plane phonon branches and must be considered simultaneously. Moreover, the calculated scattering rates suggest an acoustic phonon contribution that is much weaker than previously thought, revealing the role of optical phonons even at low energies. Accordingly it is predicted, in good agreement with a recent measurement, that the intrinsic mobility of graphene may be more than an order of magnitude larger than the high values reported in suspended samples.Comment: 12 pages, 4 figure

Collision number statistics for transport processes

Many physical observables can be represented as a particle spending some random time within a given domain. For a broad class of transport-dominated processes, we detail how it is possible to express the moments of the number of particle collisions in an arbitrary volume in terms of repeated convolutions of the ensemble equilibrium distribution. This approach is shown to generalize the celebrated Kac formula for the moments of residence times, which is recovered in the diffusion limit. Some practical applications are illustrated for bounded, unbounded and absorbing domains.Comment: 4 pages, 4 figure