Finite Element Analysis of Strain Effects on Electronic and Transport Properties in Quantum Dots and Wires

Lattice mismatch in layered semiconductor structures with submicron length scales leads to extremely high nonuniform strains. This paper presents a finite element technique for incorporating the effects of the nonuniform strain into an analysis of the electronic properties of SiGe quantum structures. Strain fields are calculated using a standard structural mechanics finite element package and the effects are included as a nonuniform potential directly in the time independent Schrodinger equation; a k-p Hamiltonian is used to model the effects of multiple valence subband coupling. A variational statement of the equation is formulated and solved using the finite element method. This technique is applied to resonant tunneling diode quantum dots and wires; the resulting densities of states confined to the quantum well layers of the devices are compared to experimental current-voltage I(V) curves.Comment: 17 pages (LaTex), 18 figures (JPEG), submitted to Journal of Applied Physic

Divergence of the Chaotic Layer Width and Strong Acceleration of the Spatial Chaotic Transport in Periodic Systems Driven by an Adiabatic ac Force

We show for the first time that a {\it weak} perturbation in a Hamiltonian system may lead to an arbitrarily {\it wide} chaotic layer and {\it fast} chaotic transport. This {\it generic} effect occurs in any spatially periodic Hamiltonian system subject to a sufficiently slow ac force. We explain it and develop an explicit theory for the layer width, verified in simulations. Chaotic spatial transport as well as applications to the diffusion of particles on surfaces, threshold devices and others are discussed.Comment: 4 pages including 3 EPS figures, this is an improved version of the paper (accepted to PRL, 2005

Targeted mixing in an array of alternating vortices

Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip boundary conditions for the flow

Poincare recurrences and transient chaos in systems with leaks

In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient chaos. This expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble. With a subtle choice of the initial ensemble, we obtain an equivalence to the classical problem of Poincare recurrences in closed systems, which is treated in the same framework. Finally, we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle in hyperbolic and nonhyperbolic components, related, respectively, to the intermediate exponential and asymptotic power-law decays of the survival probability.Comment: Corrected version, as published. 12 pages, 9 figure

Dynamic instabilities in resonant tunneling induced by a magnetic field

We show that the addition of a magnetic field parallel to the current induces self sustained intrinsic current oscillations in an asymmetric double barrier structure. The oscillations are attributed to the nonlinear dynamic coupling of the current to the charge trapped in the well, and the effect of the external field over the local density of states across the system. Our results show that the system bifurcates as the field is increased, and may transit to chaos at large enough fields.Comment: 4 pages, 3 figures, accepted in Phys. Rev. Letter

On the influence of noise on chaos in nearly Hamiltonian systems

The simultaneous influence of small damping and white noise on Hamiltonian systems with chaotic motion is studied on the model of periodically kicked rotor. In the region of parameters where damping alone turns the motion into regular, the level of noise that can restore the chaos is studied. This restoration is created by two mechanisms: by fluctuation induced transfer of the phase trajectory to domains of local instability, that can be described by the averaging of the local instability index, and by destabilization of motion within the islands of stability by fluctuation induced parametric modulation of the stability matrix, that can be described by the methods developed in the theory of Anderson localization in one-dimensional systems.Comment: 10 pages REVTEX, 9 figures EP

Kolmogorov-Sinai entropy in field line diffusion by anisotropic magnetic turbulence

The Kolmogorov-Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the KS entropy is shown to deviate considerably from the earlier predicted scaling relations [Rev. Mod. Phys. {\bf 64}, 961 (1992)]. In particular, a slowing down logarithmic behavior versus the so-called Kubo number $R\gg 1$ ($R = (\delta B / B_0) (\xi_\| / \xi_\bot)$, where $\delta B / B_0$ is the ratio of the rms magnetic fluctuation field to the magnetic field strength, and $\xi_\bot$ and $\xi_\|$ are the correlation lengths in respective dimensions) is found instead of a power-law dependence. These discrepancies are explained from general principles of Hamiltonian dynamics. We discuss the implication of Hamiltonian properties in governing the paradigmatic "percolation" transport, characterized by $R\to\infty$, associating it with the concept of pseudochaos (random non-chaotic dynamics with zero Lyapunov exponents). Applications of this study pertain to both fusion and astrophysical plasma and by mathematical analogy to problems outside the plasma physics. This research article is dedicated to the memory of Professor George M. ZaslavskyComment: 15 pages, 2 figures. Accepted for publication on Plasma Physics and Controlled Fusio

Out of Equilibrium Solutions in the XYXY-Hamiltonian Mean Field model

Out of equilibrium magnetised solutions of the $XY$-Hamiltonian Mean Field ($XY$-HMF) model are build using an ensemble of integrable uncoupled pendula. Using these solutions we display an out-of equilibrium phase transition using a specific reduced set of the magnetised solutions