J. J. Mazo

Superconducting persistent-current qubit

We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nanoscale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a superconducting quantum interference device, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence. @S0163-1829~99!00746-8#

Dissipative dynamics of the Frenkel-Kontorova model

The aim of this review article is to present recent advances in the theory of the dynamics of modulated phases in the Frenkel-Kontorova model. This theory is motivated through two specific condensed matter systems: charge-density wave conductors and Josephson junction arrays. The presentation tries to integrate the existing results into the perspective of the equilibrium theory of the model, which is summarized in the beginning. The issues of defectibility, metastability, pinning and synchronization are discussed in connection with the underlying interplay of continuum and discrete descriptions. Special emphasis is placed on the different transitions between dynamical phases; namely depinning transition, unlocking transition and dynamical Aubry transition.

Ratchet potential for fluxons in Josephson-junction arrays

We propose a simple configuration of a one-dimensional parallel array of Josephson junctions in which the pinning potential for trapped fluxons lacks inversion symmetry (ratchet potential). This system can be modelised by a set of non-linear pendula with alternating lenghts and asymmetric harmonic couplings. We show, by molecular dynamics simulation, that fluxons behave as single particles in which the predictions for overdamped thermal ratchets can be easily verified.

Thermal and mechanical properties of a DNA model with solvation barrier

We study the thermal and mechanical behaviors of DNA denaturation in the frame of the mesoscopic Peyrard-Bishop-Dauxois model with the inclusion of solvent interaction. By analyzing the melting transition of a homogeneous A-T sequence, we are able to set suitable values of the parameters of the model and study the formation and stability of bubbles in the system. Then, we focus on the case of the P5 promoter sequence and use the principal component analysis of the trajectories to extract the main information on the dynamical behavior of the system. We find that this analysis method gives an excellent agreement with previous biological results.

Discrete breathers in Josephson ladders

We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups [Phys. Rev. Lett. 84 (2000) 741; Phys. Rev. Lett. 84 (2000) 745; Phys. Rev. E 62 (2000) 2858]. We review the experiments made by Trias et al. [Phys. Rev. Lett. 84 (2000) 741]. We report the detection of different single-site and multi-site breather states and study the dynamics when changing the array bias current. By changing the temperature we can control the value of the damping (the Stewart–McCumber parameter) in the array, thus allowing an experimental study at different array parameters. We propose a simple DC circuit model to understand most of the features of the detected states. We have also compared this model and the experiments with simulations of the dynamics of the array. We show that the study of the resonances in the ladder and the use of harmonic balance techniques allow for understanding of most of the numerical results. We have computed existence diagrams of breather solutions in our arrays, found resonant localized solutions and described the localized states in terms of vortex and antivortex motion.

Josephson junction ladders: Ground state and relaxation phenomena

This paper considers a Josephson junction array with the geometry of a ladder and anisotropy in the Josephson couplings. The ground-state problem for the ladder corresponds to the one for the one-dimensional chiral {ital XY} model in a twofold anisotropy field, which allows for a rigorous characterization of the ground-state phase diagram and the relevant elementary excitations for the system. The approach to equilibrium, which we study using Langevin dynamics, shows slow relaxation, typical of systems whose energy landscape in the configuration space consists of a wealth of metastable states, dynamically disconnected.

Model for hand-over-hand motion of molecular motors.

A simple flashing ratchet model in two dimensions is proposed to simulate the hand-over-hand motion of two head molecular motors such as kinesin. Extensive Langevin simulations of the model are performed. Good qualitative agreement with the expected behavior is observed. We discuss different regimes of motion and efficiency depending on model parameters.

Decoherence of the Superconducting Persistent Current Qubit

Decoherence of a solid state based qubit can be caused by coupling to microscopic degrees of freedom in the solid. We lay out a simple theory and use it to estimate decoherence for a recently proposed superconducting persistent current design. All considered sources of decoherence are found to be quite weak, leading to a high quality factor for this qubit.

Josephson-junction ladder: a benchmark for nonlinear concepts

The theoretical analysis of the ground state properties and dissipative dynamics of an anisotropic ladder of Josephson junctions has revealed interesting features associated to the nonlinear character of the Josephson effect, combined with the inherent discreteness of the system and the peculiarities of the ladder geometry. We analyse some aspects of its underdamped dynamics when spatially homogeneous time-periodic currents are injected into the islands, and predict the existence of attracting time-periodic spatially localised modes, for some ranges of junction characteristic parameters. These elementary dynamical excitations are of two different types, associated to oscillatory and rotating motion of a few superconducting island phases, respectively, revealing a dynamical mechanism of creation of vortex‐antivortex pairs. These results are physical applications of recent advances in the theory of nonlinear dynamics of discrete macroscopic systems. Their experimental confirmation would probe the physical relevance of localisation in superconducting devices. Copyright

Translocation time of periodically forced polymer chains

In this work we study the presence of both a minimum and clear oscillations in the frequency dependence of the translocation time of a polymer described as a unidimensional Rouse chain driven by a spatially localized oscillating linear potential. The observed oscillations of the mean translocation time arise from the synchronization between the very mean translocation time and the period of the external force. We have checked the robustness of the frequency value for the minimum translocation time by changing the damping parameter, finding a very simple relationship between this frequency and the correspondent translocation time. The translocation time as a function of the polymer length has been also evaluated, finding a precise L2 scaling. Furthermore, the role played by the thermal fluctuations described as a gaussian uncorrelated noise has been also investigated, and the analogies with the resonant activation phenomenon are commented.