One-dimensional Hubbard model at quarter filling on periodic potentials

Using the Hubbard chain at quarter filling as a model system, we study the ground state properties of highly doped antiferromagnets. In particular, the Hubbard chain at quarter filling is unstable against 2k_F- and 4k_F-periodic potentials, leading to a large variety of charge and spin ordered ground states. Employing the density matrix renormalization group method, we compare the energy gain of the ground state induced by different periodic potentials. For interacting systems the lowest energy is found for a 2k_F-periodic magnetic field, resulting in a band insulator with spin gap. For strong interaction, the 4k_F-periodic potential leads to a half-filled Heisenberg chain and thus to a Mott insulating state without spin gap. This ground state is more stable than the band insulating state caused by any non-magnetic 2k_F-periodic potential. Adding more electrons, a cluster-like ordering is preferred.Comment: 8 pages, 5 figures, accepted by Phys. Rev.

Plasmon Evolution and Charge-Density Wave Suppression in Potassium Intercalated Tantalum Diselenide

We have investigated the influence of potassium intercalation on the formation of the charge-density wave (CDW) instability in 2H-tantalum diselenide by means of Electron Energy-Loss Spectroscopy and density functional theory. Our observations are consistent with a filling of the conduction band as indicated by a substantial decrease of the plasma frequency in experiment and theory. In addition, elastic scattering clearly points to a destruction of the CDW upon intercalation as can be seen by a vanishing of the corresponding superstructures. This is accompanied by a new superstructure, which can be attributed to the intercalated potassium. Based on the behavior of the c-axis upon intercalation we argue in favor of interlayer-sites for the alkali-metal and that the lattice remains in the 2H-modification

Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attaining steady state solutions is pointed out. Various routes to chaos and existence of hyperchaos even for low values of time delay which is evidenced by multiple positive Lyapunov exponents are brought out. The study is extended to the case of two coupled systems, one with delay and the other one without delay.Comment: 34 Pages, 14 Figure

Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement

Difference control schemes for controlling unstable fixed points become important if the exact position of the fixed point is unavailable or moving due to drifting parameters. We propose a memory difference control method for stabilization of a priori unknown unstable fixed points by introducing a memory term. If the amplitude of the control applied in the previous time step is added to the present control signal, fixed points with arbitrary Lyapunov numbers can be controlled. This method is also extended to compensate arbitrary time steps of measurement delay. We show that our method stabilizes orbits of the Chua circuit where ordinary difference control fails.Comment: 5 pages, 8 figures. See also chao-dyn/9810029 (Phys. Rev. E 70, 056225) and nlin.CD/0204031 (Phys. Rev. E 70, 046205

Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review

Stellar Populations in the Phoenix Dwarf (dIrr/dSph) Galaxy as Observed by HST/WFPC2

We present HST/WFPC2 photometry of the central regions of the Phoenix dwarf. Accurate photometry allows us to: 1) confirm the existence of the horizontal branch previously detected by ground-based observations, and use it to determine a distance to Phoenix, 2) clearly detect the existence of multiple ages in the stellar population of Phoenix, 3) determine a mean metallicity of the old red giant branch stars in Phoenix, and suggest that Phoenix has evolved chemically over its lifetime, 4) extract a rough star formation history for the central regions which suggests that Phoenix has been forming stars roughly continuously over its entire lifetime.Comment: Accepted by AJ, 22 pages including 6 figures + 1 figure in JPEG forma

Stability borders of feedback control of delayed measured systems

When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi and Yorke (OGY) has to be based on a measurement delayed by $\tau$ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Ljapunov number of $\lambda_{max}=1+\frac{1}{\tau}$. In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions have to be considered if one wants to stabilize fixed points with Ljapunov numbers above $\lambda_{max}$.Comment: 5 pages LaTeX using revtex and epsfig (4 figs included). Revised versio

Sierpinski signal generates 1/fα1/f^\alpha spectra

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for $1/f^\alpha$ spectra in a certain class of experimental and natural systems like catalytic reactions and mollusc patterns.Comment: 4 pages (4 figs included). Accepted for publication in Physical Review

Control of unstable steady states by time-delayed feedback methods

We show that time-delayed feedback methods, which have successfully been used to control unstable periodic ortbits, provide a tool to stabilize unstable steady states. We present an analytical investigation of the feedback scheme using the Lambert function and discuss effects of both a low-pass filter included in the control loop and non-zero latency times associated with the generation and injection of the feedback signal.Comment: 8 pages, 11 figure

Caby Photometry of the Hyades: Comparisons to the Field Stars

Intermediate-band photometry of the Hyades cluster on the Caby system is presented for dwarf stars ranging from spectral type A through late K. A mean hk, b-y relation is constructed using only single stars without anomalous atmospheres and compared to the field stars of the solar neighborhood. For the F dwarfs, the Hyades relation defines an approximate LOWER bound in the two-color diagram, consistent with an [Fe/H] between +0.10 and +0.15. These index-color diagrams follow the common convention of presenting stars with highest abundance at the bottom of the plot although the index values for the metal-rich stars are numerically larger. For field F dwarfs in the range [Fe/H] between +0.4 and -1.0, [Fe/H] = -5.6 delta-hk + 0.125, with no evidence for a color dependence in the slope. For the G and K dwarfs, the Hyades mean relation crosses the field star distribution in the two-color diagram, defining an approximate UPPER bound for the local disk stars. Stars found above the Hyades stars fall in at least one of three categories: [Fe/H] below -0.7, [Fe/H] above that of the Hyades, or chromospherically active. It is concluded that, contrary to the predictions of model atmospheres, the hk index for cool dwarfs at a given color hits a maximum value for stars below solar composition and, with increasing [Fe/H] above some critical value, declines. This trend is consistent, however, with the predictions from synthetic indices based upon much narrower Ca filters where the crossover is caused by the metallicity sensitivity of b-y.Comment: 13 pages, 9 eps figures, 1 tex table, 1 ascii tabl