Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low- or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of (low-field) dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features (maxima, minima, plateaus, etc.) and several critical currents (which depend on the values of the contact parameters). Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation.

Reply to "Comment on 'Solutions of the telegrapher's equation in the presence of traps'"

This reply adds a number of details to remarks by Foong and Kanno [preceding Comment, Phys. Rev. A 46, 5296 (1992)] on our paper [Phys. Rev. A 45, 2222 (1992)] regarding the discontinuities observed in the curves generated in that paper.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.

Damage spreading transition in glasses: A probe for the ruggedness of the configurational landscape

We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of metastable states. For systems evolving under identical but arbitrarily correlated noises, we demonstrate that there exists a critical temperature T0 which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high temperatures, being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations, we show that the asymptotic damage has the good properties of a dynamical order parameter, such as (i) independence of the initial damage; (ii) independence of the class of initial condition; and (iii) stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as metastable states) in the thermodynamic limit consequence of the ruggedness of the free-energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading an interesting tool to probe the ruggedness of the configurational landscape.

Adsorption kinetics in the presence of external fields

In this article we present a detailed analysis of the kinetics of a class of sequential adsorption models that take into account the effect of externally applied fields (as an electric field, or a shear rate) on the adsorption. The excluded volume interactions related to the finite size of the adsorbing particles are modified by the external fields. As a result, new adsorption mechanisms appear with respect to the ones used to describe the kinetics in a quiescent fluid. In particular, if the adsorbing particles are allowed to roll over preadsorbed ones, adsorption becomes non local even in the simplest geometry. An exact analytic theory cannot be developed, but we introduce a self-consistent theory that turns out to agree with the simulation results over all the range of the parameters.

Application of the microcanonical multifractal formalism to monofractal systems

The design of appropriate multifractal analysis algorithms, able to correctly characterize the scaling properties of multifractal systems from experimental, discretized data, is a major challenge in the study of such scale invariant systems. In the recent years, a growing interest for the application of the microcanonical formalism has taken place, as it allows a precise localization of the fractal components as well as a statistical characterization of the system. In this paper, we deal with the specific problems arising when systems that are strictly monofractal are analyzed using some standard microcanonical multifractal methods. We discuss the adaptations of these methods needed to give an appropriate treatment of monofractal systems.

Topology of the world trade web

Economy, and consequently trade, is a fundamental part of human social organization which, until now, has not been studied within the network modeling framework. Here we present the first, to the best of our knowledge, empirical characterization of the world trade web, that is, the network built upon the trade relationships between different countries in the world. This network displays the typical properties of complex networks, namely, scale-free degree distribution, the small-world property, a high clustering coefficient, and, in addition, degree-degree correlation between different vertices. All these properties make the world trade web a complex network, which is far from being well described through a classical random network description.

Dynamical properties of the Zhang model of self-organized criticality

Critical exponents of the infinitely slowly driven Zhang model of self-organized criticality are computed for d=2 and 3, with particular emphasis devoted to the various roughening exponents. Besides confirming recent estimates of some exponents, new quantities are monitored, and their critical exponents computed. Among other results, it is shown that the three-dimensional exponents do not coincide with the Bak-Tang-Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] (Abelian) model, and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide, as is usually implicitly assumed. An explanation for this is provided. The possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed.

Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Effect of the output of the system in signal detection

We analyze the consequences that the choice of the output of the system has in the efficiency of signal detection. It is shown that the output signal and the signal-to-noise ratio (SNR), used to characterize the phenomenon of stochastic resonance, strongly depend on the form of the output. In particular, the SNR may be enhanced for an adequate output.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Dimerization of polyacetylene treated as a spin-Peierls distortion of the Heisenberg Hamiltonian

Extracting a bond-length-dependent Heisenberg-like Hamiltonian from the potential-energy surfaces of the two lowest states of ethylene, it is possible to study the geometry of polyacetylene by minimization of the cohesive energy, using both variational-cluster and Rayleigh-Schrödinger perturbative expansions. The dimerization amplitude is satisfactorily reproduced. Optimizing the variational-cluster-expansion total energy with the equal-bond-length constraint, the barrier to reversal of alternation is obtained. The alternating-to-regular phase transition is treated from the Néel-state starting function and appears to be of second order.