Universal criterion for the breakup of invariant tori in dissipative systems

The transition from quasiperiodicity to chaos is studied in a two-dimensional dissipative map with the inverse golden mean rotation number. On the basis of a decimation scheme, it is argued that the (minimal) slope of the critical iterated circle map is proportional to the effective Jacobian determinant. Approaching the zero-Jacobian-determinant limit, the factor of proportion becomes a universal constant. Numerical investigation on the dissipative standard map suggests that this universal number could become observable in experiments. The decimation technique introduced in this paper is readily applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page

Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper

Dimer decimation scheme is introduced in order to study the kicked quantum systems exhibiting localization transition. The tight-binding representation of the model is mapped to a vectorized dimer where an asymptotic dissociation of the dimer is shown to correspond to the vanishing of the transmission coefficient thru the system. The method unveils an intricate nesting of extended and localized phases in two-dimensional parameter space. In addition to computing transport characteristics with extremely high precision, the renormalization tools also provide a new method to compute quasienergy spectrum.Comment: There are five postscript figures. Only half of the figure (3) is shown to reduce file size. However, missing part is the mirror image of the part show

The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian

We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower bounds for its fractal dimension in the large coupling regime. These bounds show that as $\lambda \to \infty$, $\dim (\sigma(H_\lambda)) \cdot \log \lambda$ converges to an explicit constant ($\approx 0.88137$). We also discuss consequences of these results for the rate of propagation of a wavepacket that evolves according to Schr\"odinger dynamics generated by the Fibonacci Hamiltonian.Comment: 23 page

Light Induced Melting of Colloidal Crystals in Two Dimensions

We demonstrate that particles confined to two dimensions (2d) and subjected to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with both ``locked floating solids'' and smectic phases. The resulting phases and phase transitions are studied as a function of temperature and potential strength. We find reentrant melting as a function of the potential strength. Our results lead to universal predictions consistent with recent experiments on 2d colloids in the presence of a laser-induced 1d periodic potential.Comment: 4 pages, 3 figures, also available at http://cmtw.harvard.edu/~fre

Glassiness Vs. Order in Densely Frustrated Josephson Arrays

We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the uniformly frustrated two dimensional XY model, for a sequence of frustrations f converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp first order equilibrium phase transition to an ordered vortex structure at a T_c which varies only slightly with f. This ordered vortex structure remains in general phase incoherent until a lower pinning transition T_p(f) that varies with f. We argue that the glassy behaviors reported for this model in earlier simulations are dynamic effects.Comment: 4 pages, 4 eps figure

Anything You Can Do, You Can Do Better: Neural Substrates of Incentive-Based Performance Enhancement

Performance-based pay schemes in many organizations share the fundamental assumption that the performance level for a given task will increase as a function of the amount of incentive provided. Consistent with this notion, psychological studies have demonstrated that expectations of reward can improve performance on a plethora of different cognitive and physical tasks, ranging from problem solving to the voluntary regulation of heart rate. However, much less is understood about the neural mechanisms of incentivized performance enhancement. In particular, it is still an open question how brain areas that encode expectations about reward are able to translate incentives into improved performance across fundamentally different cognitive and physical task requirements

Disturbance spreading in incommensurate and quasiperiodic systems

The propagation of an initially localized excitation in one dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances $\sigma^2(t)$ of atom displacements depends on the initial condition. For the initial condition with nonzero momentum, $\sigma^2(t)$ goes as $t^\alpha$ with $\alpha=1$ and 0 for incommensurate Frenkel-Kontorova (FK) model at $V$ below and above $V_c$ respectively; and $\alpha=1$ for uniform, quasiperiodic and random chains. It is also found that $\alpha=1-\beta$ with $\beta$ the exponent of distribution function of frequency at zero frequency, i.e., $\rho(\omega)\sim \omega^{\beta}$ (as $\omega\to 0$). For the initial condition with zero momentum, $\alpha=0$ for all systems studied. The underlying physical meaning of this diffusive behavior is discussed.Comment: 8 Revtex Pages, 5 PS figures included, to appear in Phys. Rev. B April 200

Role of phason-defects on the conductance of a 1-d quasicrystal

We have studied the influence of a particular kind of phason-defect on the Landauer resistance of a Fibonacci chain. Depending on parameters, we sometimes find the resistance to decrease upon introduction of defect or temperature, a behavior that also appears in real quasicrystalline materials. We demonstrate essential differences between a standard tight-binding model and a full continuous model. In the continuous case, we study the conductance in relation to the underlying chaotic map and its invariant. Close to conducting points, where the invariant vanishes, and in the majority of cases studied, the resistance is found to decrease upon introduction of a defect. Subtle interference effects between a sudden phason-change in the structure and the phase of the wavefunction are also found, and these give rise to resistive behaviors that produce exceedingly simple and regular patterns.Comment: 12 pages, special macros jnl.tex,reforder.tex, eqnorder.tex. arXiv admin note: original tex thoroughly broken, figures missing. Modified so that tex compiles, original renamed .tex.orig in source

Physical nature of critical wave functions in Fibonacci systems

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of these critical wave functions and the quasiperiodic order of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in Phys. Rev. Let

Hidden dimers and the matrix maps: Fibonacci chains re-visited

The existence of cycles of the matrix maps in Fibonacci class of lattices is well established. We show that such cycles are intimately connected with the presence of interesting positional correlations among the constituent `atoms' in a one dimensional quasiperiodic lattice. We particularly address the transfer model of the classic golden mean Fibonacci chain where a six cycle of the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys. Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far been provided, to the best of our knowledge. In addition, we show that our prescription leads to a determination of other energy values for a mixed model of the Fibonacci chain, for which the full matrix map may have similar cyclic behaviour. Apart from the standard transfer-model of a golden mean Fibonacci chain, we address a variant of it and the silver mean lattice, where the existence of four cycles of the matrix map is already known to exist. The underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review