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

Synchronization Landscapes in Small-World-Connected Computer Networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.Comment: 20 pages, 22 figure

Extreme fluctuations in noisy task-completion landscapes on scale-free networks

We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally-constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short-tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.Comment: 16 pages, 6 figures, revte

The lepton pair production in heavy ion collisions in perturbation theory

We derive the first terms in the amplitude of lepton pair production in the Coulomb fields of two relativistic heavy ions. Using the Sudakov technique, which very simplify the calculations in momentum space for the processes at high energies, we get the compact analytical expressions for differential cross section of the process under consideration in the lowest order in fine structure constant (Born approximation) valid for any momentum transfer and in a wide kinematics region for produced particles. Exploiting the same technique we consider the next terms of perturbation series (up to fourth order in fine structure constant) and investigate their energy dependence and limiting cases. It has been shown that taking in account all relevant terms in corresponding order one obtains the expressions which are gauge invariant and finite. We estimate the contribution of the Coulomb corrections to the total cross section and discuss the cancellations of the different terms which holds in the total cross section.Comment: LaTeX2e, 18 pages, 4 eps figure

Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.Comment: 10 pages, 12 figures, additional references adde

A light-fronts approach to electron-positron pair production in ultrarelativistic heavy-ion collisions

We perform a gauge-transformation on the time-dependent Dirac equation describing the evolution of an electron in a heavy-ion collision to remove the explicit dependence on the long-range part of the interaction. We solve, in an ultra-relativistic limit, the gauged-transformed Dirac equation using light-front variables and a light-fronts representation, obtaining non-perturbative results for the free pair-creation amplitudes in the collider frame. Our result reproduces the result of second-order perturbation theory in the small charge limit while non-perturbative effects arise for realistic charges of the ions.Comment: 39 pages, Revtex, 7 figures, submitted to PR

Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function. This result is valid for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the Edwards-Wilkinson interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [ S.N. Majumdar and A. Comtet, Phys. Rev. Lett., 92, 225501 (2004)].Comment: 27 pages, 10 .eps figures included. Two figures improved, new discussion and references adde

Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.Comment: The original publication is available at www.springerlink.com/content/8528v8563r7u2742