F. Palmero

Charge Transport in Poly(dG)-Poly(dC) and Poly(dA)-Poly(dT) DNA Polymers.

We investigate the charge transport in synthetic DNA polymers built up from single type of base pairs. In the context of a polaronlike model, for which an electronic tight-binding system and bond vibrations of the double helix are coupled, we present estimates for the electron-vibration coupling strengths utilizing a quantum-chemical procedure. Subsequent studies concerning the mobility of polaron solutions, representing the state of a localized charge in unison with its associated helix deformation, show that the system for poly(dG)–poly(dC) and poly(dA)–poly(dT) DNA polymers, respectively possess quantitatively distinct transport properties. While the former supports unidirectionally moving electron breathers attributed to highly efficient long-range conductivity, the breather mobility in the latter case is comparatively restrained, inhibiting charge transport. Our results are in agreement with recent experimental results demonstrating that poly(dG)–poly(dC) DNA molecules acts as a semiconducting nanowire and exhibit better conductance than poly(dA)–poly(dT) ones.

Moving discrete breathers in a Klein?Gordon chain with an impurity

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein?Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.

TAMING CHAOS IN A DRIVEN JOSEPHSON JUNCTION

We present analytical and numerical results concerning the inhibition of chaos in a single driven Josephson junction by means of an additional weak resonant perturbation. From Melnikov analysis, we theoretically find parameter-space regions, associated with the chaos-suppressing perturbation, where chaotic states can be suppressed. In particular, we test analytical expressions for the intervals of initial phase difference between the two excitations for which chaotic dynamics can be eliminated. All the theoretical predictions are in overall good agreement with numerical results obtained by simulation.

Effect of base-pair inhomogeneities on charge transport along the DNA molecule, mediated by twist and radial polarons

Some recent results for a three-dimensional, semi-classical, tight-binding model for DNA show that there are two types of polarons, namely radial and twist polarons, which can transport charge along the DNA molecule. However, the existence of two types of base pairs in real DNA makes it crucial to find out if charge transport also exists in DNA chains with different base pairs. In this paper, we address this problem in its simple case, a homogeneous chain except for a single different base pair, which we call a base-pair inhomogeneity, and its effect on charge transport. Radial polarons experience either reflection or trapping. However, twist polarons are good candidates for charge transport along real DNA. This transport is also very robust with respect to weak parametric and diagonal disorder.

Moving breathers in a bent DNA model

We study the properties of moving breathers in a bent DNA model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bonds within each base pair. We show that the movement of a breather is hindered by the bending of the chain analogously to a particle in a potential barrier.

Discrete breathers in a nonlinear electric line: Modeling, computation, and experiment

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where n-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of n-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary n-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki-Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.

Aharonov-Bohm effect for an exciton in a finite-width nanoring

We study the Aharonov-Bohm effect for an exciton on a nano-ring using a 2D attractive fermionic Hubbard model. We extend previous results obtained for a 1D ring in which only azimuthal motion is considered, to a more general case of 2D annular lattices. In general, we show that the existence of the localization effect, increased by the nonlinearity, makes the phenomenon in the 2D system similar to the 1D case. However, the introduction of radial motion introduces extra frequencies, different from the original isolated frequency corresponding to the excitonic Aharonov- Bohm oscillations. If the circumference of the system becomes large enough, the Aharonov-Bohm effect is suppressed.

Energy thresholds for the existence of breather solutions and travelling waves on lattices

We discuss the existence of breathers and of energy thresholds for their formation in DNLS lattices with linear and nonlinear impurities. In the case of linear impurities, we present some new results concerning important differences between the attractive and repulsive impurity which is interplaying with a power nonlinearity. These differences concern the coexistence or the existence of staggered and unstaggered breather profile patterns. We also distinguish between the excitation threshold (the positive minimum of the power observed when the dimension of the lattice is greater or equal to some critical value) and explicit analytical lower bounds on the power (predicting the smallest value of the power a discrete breather one-parameter family), which are valid for any dimension. Extended numerical studies in one-, two- and three-dimensional lattices justify that the theoretical bounds can be considered as thresholds for the existence of the frequency parameterized families. The discussion reviews and extends the issue of the excitation threshold in lattices with nonlinear impurities while lower bounds, with respect to the kinetic energy, are also discussed for travelling waves in FPU periodic lattices.

Nonlinear localized modes in two-dimensional electrical lattices.

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and moving self-localized modes were generated experimentally and theoretically in a family of two-dimensional square as well as honeycomb lattices composed of 6 × 6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILMs), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introducing additional capacitors into the unit cell, these lattices can controllably induce mobile discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness, and wave interactions generates a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results and confirm that these phenomena qualitatively carry over to larger lattice sizes.