Theory of charge fluctuations and domain relocation times in semiconductor superlattices

Shot noise affects differently the nonlinear electron transport in semiconductor superlattices depending on the strength of the coupling among the superlattice quantum wells. Strongly coupled superlattices can be described by a miniband Boltzmann-Langevin equation from which a stochastic drift-diffusion equation is derived by means of a consistent Chapman-Enskog method. Similarly, shot noise in weakly coupled, highly doped semiconductor superlattices is described by a stochastic discrete drift-diffusion model. The current-voltage characteristics of the corresponding deterministic model consist of a number of stable branches corresponding to electric field profiles displaying two domains separated by a domain wall. If the initial state corresponds to a voltage on the middle of a stable branch and is suddenly switched to a final voltage corresponding to the next branch, the domains relocate after a certain delay time, called relocation time. The possible scalings of this mean relocation time are discussed using bifurcation theory and the classical results for escape of a Brownian particle from a potential well.Comment: 14 pages, 2 figure

Axisymmetric pulse recycling and motion in bulk semiconductors

The Kroemer model for the Gunn effect in a circular geometry (Corbino disks) has been numerically solved. The results have been interpreted by means of asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric pulses of the electric field are periodically shed by an inner circular cathode. These pulses decay as they move towards the outer anode, which they may not reach. As a pulse advances, the external current increases continuously until a new pulse is generated. Then the current abruptly decreases, in agreement with existing experimental results. Depending on the bias, more complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure

Aging in the Linear Harmonic Oscillator

The low temperature Monte Carlo dynamics of an ensemble of linear harmonic oscillators shows some entropic barriers related to the difficulty of finding the directions in configurational space which decrease the energy. This mechanism is enough to observe some typical non-equilibrium features of glassy systems like activated-type behavior and aging in the correlation function and in the response function. Due to the absence of interactions the model only displays a one-step relaxation process.Comment: 6 pages revtex including 3 figures in postscrip

Kinetics of helium bubble formation in nuclear materials

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modelled by a discrete kinetic equations for the number densities of bubbles having $k$ atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (i) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (ii) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present boundary layer theory for discrete equations is compared to the numerical solution of the full kinetic model and to previous approximation of Schaldach and Wolfer involving a truncated system of moment equations.Comment: 24 pages, 6 figures, to appear in Physica

Synchronization in populations of globally coupled oscillators with inertial effects

A model for synchronization of globally coupled phase oscillators including ``inertial'' effects is analyzed. In such a model, both oscillator frequencies and phases evolve in time. Stationary solutions include incoherent (unsynchronized) and synchronized states of the oscillator population. Assuming a Lorentzian distribution of oscillator natural frequencies, $g(\Omega)$, both larger inertia or larger frequency spread stabilize the incoherent solution, thereby making harder to synchronize the population. In the limiting case $g(\Omega)=\delta(\Omega)$, the critical coupling becomes independent of inertia. A richer phenomenology is found for bimodal distributions. For instance, inertial effects may destabilize incoherence, giving rise to bifurcating synchronized standing wave states. Inertia tends to harden the bifurcation from incoherence to synchronized states: at zero inertia, this bifurcation is supercritical (soft), but it tends to become subcritical (hard) as inertia increases. Nonlinear stability is investigated in the limit of high natural frequencies.Comment: Revtex, 36 pages, submit to Phys. Rev.

Time-periodic phases in populations of nonlinearly coupled oscillators with bimodal frequency distributions

The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to synchronization to phases with a time periodic order parameter. The richest behavior is found near the tricritical point were the incoherent, stationarily synchronized, ``traveling wave'' and ``standing wave'' phases coexist. The behavior near the tricritical point can be extrapolated to the rest of the phase diagram. Direct Brownian simulation of the model confirms our findings.Comment: Revtex,16 pag.,10 fig., submitted to Physica

Sawtooth patterns in force-extension curves of biomolecules: An equilibrium-statistical-mechanics theory

We analyze the force-extension curve for a general class of systems, which are described at the mesoscopic level by a free energy depending on the extension of its components. Similarly to what is done in real experiments, the total length of the system is the controlled parameter. This imposes a global constraint in the minimization procedure leading to the equilibrium values of the extensions. As a consequence, the force-extension curve has multiple branches in a certain range of forces. The stability of these branches is governed by the free energy: there are a series of first-order phase transitions at certain values of the total length, in which the free energy itself is continuous but its first derivative, the force, has a finite jump. This behavior is completely similar to that observed in real experiments with biomolecules like proteins and with other complex systemsEspaña Ministerio de Economía y Competitividad Grants No. FIS2011- 24460 (A.P.), No. FIS2011-28838-C02-0

Fronts in lattices

Simple models of defect motion in lattices identify dislocations [1] and cracks [8,9] with discrete traveling waves [4,10]. In overdamped limits, such lattice models often become discrete bistable equations [3,5], similar to the ones encountered in biology (to describe nerve propagation [7], for instance). In this talk, we will review recent results on front propagation in spatially discrete models, discussing existence of stationary and travelling wave fronts [2,5,6] together with strategies to predict their speeds and the thresholds for propagation failure [3]

Switching-on and -off dynamics of MQW structures with bistable electro-optical absorption

In this work we have studied the dynamics of switch-on and switch-off processes in biased MQW structures where every well shows optical bistability in a light intensity range (Il ,Ih). We have analyzed in detail MQW structures with negligible inter-well transport. We have found that the switch-on mechanism consists of a time sequence where every QW jumps into the high-absorption state. Therefore a step-like switching wave propagates through the structure. The switch-off process resembles a reverse wave propagating in the opposite direction and step-like processes in the plasma concentration decay. These effects can be used for conversion of an analog optical signal to digital (optical and electrical) signal(s).В роботі досліджена динаміка включення-виключення у несиметричних (зміщенних) БКЯ структурах, де кожна яма показує оптичну бістабільність у області інтенсивностей світла ( Il , Ih ). Детально проаналізовано БКЯ структури з незначним переносом між ямами. Знайдено, що механізм включення складається з часової послідовності , коли кожна квантова яма (КЯ) переходить в сильнопоглинаючий стан. Таким чином, в структурі розповсюджується ступінчата хвиля. Процесс виключення нагадує зворотню хвилю, яка розповсюджується в протилежному напрямку и ступінчати процеси у спаді концентрації плазми. Ці ефекти можуть бути використані для перетворення аналового оптичного сигналу у цифровий (оптичний та електричний).В настоящей работе исследована динамика включения-выключения в несимметричных (смещенных) МКЯ структурах где каждая яма обнаруживает оптическую бистабильность в области интенсивностей света ( Il , Ih ). Детально проанализированы МКЯ структуры с незначительным переносом между ямами. Обнаружено, что механизм включения состоит из временной последовательности, когда каждая квантовая яма (КЯ) переходит в сильнопоглощающее состояние. Таким образом, в структуре распространяется ступенчатая волна. Процесс выключения напоминает обратную волну, распространяющуюся в противоположном направлении и ступенчатые процессы в спаде концентрации плазмы. Эти эффекты могут быть использованы для преобразования аналогового оптического сигнала в цифровой (оптический и электрический)