We have produced ultrathin epitaxial graphite films which show remarkable 2D electron gas (2DEG) behavior. The films, composed of typically 3 graphene sheets, were grown by thermal decomposition on the (0001) surface of 6H-SiC, and characterized by surface-science techniques. The low-temperature conductance spans a range of localization regimes according to the structural state (square resistance 1.5 kOhm to 225 kOhm at 4 K, with positive magnetoconductance). Low resistance samples show characteristics of weak-localization in two dimensions, from which we estimate elastic and inelastic mean free paths. At low field, the Hall resistance is linear up to 4.5 T, which is well-explained by n-type carriers of density 10^{12} cm^{-2} per graphene sheet. The most highly-ordered sample exhibits Shubnikov - de Haas oscillations which correspond to nonlinearities observed in the Hall resistance, indicating a potential new quantum Hall system. We show that the high-mobility films can be patterned via conventional lithographic techniques, and we demonstrate modulation of the film conductance using a top-gate electrode. These key elements suggest electronic device applications based on nano-patterned epitaxial graphene (NPEG), with the potential for large-scale integration.

Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics

A localized and a propagating component appear when an ultracold atomic gas expands in a disordered optical potential. Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. We observe three-dimensional AL of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential. A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component. We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy. These measurements provide a benchmark for more sophisticated theories of AL.

http://absimage.aps.org/image/DAMOP12/MWS_DAMOP12-2012-000016.pdf

Three-Dimensional Anderson Localization of Ultracold Matter

Bubbles in DNA are related to fundamental processes such as duplication and transcription. Using a new ensemble technique to trap intermediate states, we present direct measurements of the average length of the denaturation bubble and the statistical weights of the bubble states in the temperature-driven melting of DNA oligomers. For a bubble flanked by double-stranded regions, we find a nucleation size of approximately 20 bases, and a broad distribution of bubble sizes. However, for bubbles opening at the ends of the molecule there is no nucleation threshold. The measured statistical weights of different conformations agree with the predictions of the thermodynamic models in the case of unzipping from the ends; however, internal bubble states are not completely described by the models. The measurements further show that, due to end effects, the melting transition becomes a two-state process only in the limit of a molecule length L approximately 1 bp.

Bubble nucleation and cooperativity in DNA melting

Wavelet theory has been proved to be a useful tool in the study of time series. Specifically, the scalogram allows the detection of the most representative scales (or frequencies) of a signal. In this work, we present the scalogram as a tool for studying some aspects of a given signal. Firstly, we introduce a parameter called scale index, interpreted as a measure of the degree of the signal’s non-periodicity. In this way, it can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. Secondly, we introduce a method for comparing different scalograms. This can be applied for determining if two time series follow similar patterns.

The Wavelet Scalogram in the Study of Time Series

The nonlinear dynamics of a shape memory oscillator (SMO) subjected to an ideal or nonideal excitation is studied. The restoring force of the oscillator is provided by a shape memory device (SMD), described by a thermomechanical model capable of reproducing the hysteretic behavior via the evolution of a suitable internal variable. Due to nonlinearities in the model, the SMO can exhibit periodic or non-periodic behaviors. The effects of the external sources on the response of SMO are studied through the scalogram analysis of continuous wavelet transform by using a new measure, called the Scale index (Benitez R, Bolos VJ and Ramirez ME. A wavelet-based tool for studying non-periodicity. Comput Math Appl 2010; 60: 634–641). Numerical results show that the Scale index can successfully detect the behavior of the system when the signal is periodic or nonperiodic, and distinguish between them in a way consistent with the indications provided by the alternative 0-1 test.

Characterizing the nonlinear behavior of a pseudoelastic oscillator via the wavelet transform

Controlling charge current through a DNA based molecular transistor

Molecule-based transistors have attracted much attention due to their exclusive properties. Creation of a molecular transistor as well as engineering its structure have become one of the greatest aims of scientists. We have focused on the environmental dependent behavior of a DNA-templated transistor. Using the statistical distribution of the energy levels, we were able to distinguish the delocalized states of charge carriers and the transition between the localized and delocalized behaviors. On the other hand, we can determine the stability conditions of our quantum dynamical system. The results are verified by the inverse participation ratio method. Therefore, the most appropriate parameters for designing the DNA transistor are chosen. The DNA sequence is an important factor for its transport properties, but the results have shown that in the presence of the bath, the bath parameters are important, too. As is shown, it is possible that via the adjustment of bath parameters, one can design a conductivity...

Engineering DNA Molecule Bridge between Metal Electrodes for High-Performance Molecular Transistor: An Environmental Dependent Approach.

The emergence of second-harmonic generation (SHG) is a pivotal issue to the development of nano-optical devices and interfaces. Here, we perform a quantum analysis of the spectral statistics of the SHG resonances with the aim of determining the instability of this process. We compute different independent statistical properties to being chaotic. We find that the short-range fluctuations of the resonances at electric fields with different intensities are in agreement with random matrix theory (RMT) predictions. We conclude that although in low intensities of electric field the SHG dynamics follows Poisson statistics, in high intensities the dynamics is chaotic (ergodic). On the other hand, a study of the singularity spectrum of eigenstates provides additional evidence supporting RMT predictions. We also analyze the inverse participation ratio of eigenstates and find that it equals $$\sim$$
 0.5 in localized phase, and approaches to $$1/dim(\mathcal {H})$$
 in delocalized (chaotic) phase.

An electric field induced delocalization transition in second-harmonic generation effect

The study of cardiac dynamics by mathematical models has a long history that has been started by using nonlinear oscillators to generate such rhythms. Since cardiac rhythms may exhibit chaotic behaviors, the chaos theory as a powerful tool in studying nonlinear dynamical systems, can be used for analyzing cardiac system. In this paper, based on Grudzinski and Zebrowski's model, the effects of external factors on pacemaker rhythms were studied using a new measure, called the scale index. Obtained results showed that the scale index can detect special behaviors in the action potential whereas the Lyapunov exponent is not capable of uncovering them. Moreover, it was found that the non-periodicity of pacemaker rhythms in the presence of external periodic force is not high. Finally, it was discovered that the scale index can provide a non-invasive assessment of the heart in real-life conditions.

/pdf/a-new-approach-to-the-study-of-heartbeat-dynamics-based-on-2ass8at0qx.pdf

A new approach to the study of heartbeat dynamics based on mathematical model

Tailoring the propagation of light in an arbitrarily manner has motivated a great of interest on nanophotonics. As a new mechanism for this purpose, the generation of an effective magnetic field leading to a Lorentz force for photons is recently proposed in a photonic resonator lattice. Here, we consider a photonic resonator lattice with a harmonically modulated phase and with an interface splitting the lattice into two magnetically different regions. Considering this lattice, we try to explore the impact of phase and the location of interface on the localization of Hamiltonian eigenstates by applying level spacing distribution as a cornerstone of random matrix theory. The obtained results show that while the location of interface has no effect on the appearance of localized states in weak phases, in strong phases it is found a threshold value for location of interface above which all eigenstates are delocalized. As a result, level spacing distribution and so random matrix theory is capable of characterizing the behavior of a photon in regions with different magnetic properties.

J. Ziaei

Papers

Controlling charge current through a DNA based molecular transistor

Engineering DNA Molecule Bridge between Metal Electrodes for High-Performance Molecular Transistor: An Environmental Dependent Approach.

An electric field induced delocalization transition in second-harmonic generation effect

A new approach to the study of heartbeat dynamics based on mathematical model

Quantum chaos analysis for characterizing a photonic resonator lattice