Analysis of Possible Quantum Metastable States in Ballistic Graphene-based Josephson Junctions

Graphene is a relatively new material (2004) made of atomic layers of carbon arranged in a honeycomb lattice. Josephson junction devices are made from graphene by depositing two parallel superconducting leads on a graphene flake. These devices have hysteretic current-voltage characteristics with a supercurrent branch and Shapiro steps appear when irradiated with microwaves. These properties motivate us to investigate the presence of quantum metastable states similar to those found in conventional current-biased Josephson junctions. We present work investigating the nature of these metastable states for ballistic graphene Josephson junctions. We model the effective Washboard potential for these devices and estimate parameters, such as energy level spacing and critical currents, to deduce the design needed to observe metastable states. We propose devices consisting of a parallel on-chip capacitor and suspended graphene. The capacitor is needed to lower the energy level spacing down to the experimentally accessible range of 1-20 GHz. The suspended graphene helps reduce the noise that may otherwise come from two-level states in the insulating oxide layer. Moreover, back-gate voltage control of its critical current introduces another knob for quantum control. We will also report on current experimental progress in the area of fabrication of this proposed device.Comment: 4 pages, 5 figures, Accepted for publication in IEEE Transactions on Applied Superconductivity from ASC 2010. Additional figures, additional calculation

Discrete Dynamical Systems: A Brief Survey

Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization

Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models for nonlinear Luttinger liquids to the case of open boundary conditions. For integrable models, we show that boundary autocorrelations oscillate as a function of time with the same frequency as the corresponding bulk autocorrelations. This frequency can be identified as the band edge of elementary excitations. The amplitude of the oscillations decays as a power law with distinct exponents at the boundary and in the bulk, but boundary and bulk exponents are determined by the same coupling constant in the mobile impurity model. For nonintegrable models, we argue that the power-law decay of the oscillations is generic for autocorrelations in the bulk, but turns into an exponential decay at the boundary. Moreover, there is in general a nonuniversal shift of the boundary frequency in comparison with the band edge of bulk excitations. The predictions of our effective field theory are compared with numerical results obtained by time-dependent density matrix renormalization group (tDMRG) for both integrable and nonintegrable critical spin-$S$ chains with $S=1/2$, $1$ and $3/2$.Comment: 20 pages, 12 figure