Beyond the Child-Langmuir limit

Beyond the Child-Langmuir limit.

This article presents a new formulation of the solution for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables (i.e., variables that follow particle paths) the solution is expressed through an exact analytic, but implicit, formula for any choice of incoming velocity v(0), electric field E(0), and current J(0). For steady solutions, this appro...

The Child–langmuir Limit for Semiconductors: a Numerical Validation

Abstract. The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the currentvoltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger...

Quantum extension of Child-Langmuir law.

Computation beyond the turing limit.

Extensive efforts have been made to prove the Church-Turing thesis, which suggests that all realizable dynamical and physical systems cannot be more powerful than classical models of computation. A simply described but highly chaotic dynamical system called the analog shift map is presented here, which has computational power beyond the Turing limit (super-Turing); it computes exactly like neur...

Holography beyond the Penrose limit

The flat pp-wave background geometry has been realized as a particular Penrose limit of AdS5 × S. It describes a string that has been infinitely boosted along an equatorial null geodesic in the S subspace. The string worldsheet Hamiltonian in this background is free. Finite boosts lead to curvature corrections that induce interacting perturbations of the string worldsheet Hamiltonian. We develo...