Conductivity of a quasiperiodic system in two and three dimensions

A generalization of the Aubry-Andre model in two and three dimensions is introduced which allows for quasiperiodic hopping terms in addition to the quasiperiodic site potentials. This corresponds to an array of interstitial impurities within the periodic host crystal. The resulting model is exactly solvable and I compute the density of states and the ac-conductivity. There is no mobility edge as in completely disordered systems but the regular ac-conductivity and the strongly reduced Drude weight indicate a precursor of the Anderson transition as the Fermi energy goes from the center to the band edges.Comment: 4 pages,6 figures, references adde

Computing periodic orbits using the anti-integrable limit

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Henon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the well-known bound of Devaney and Nitecki. We also reformulate the popular method for finding periodic orbits introduced by Biham and Wenzel. Near an anti-integrable limit, we show that this method is guaranteed to converge. This formulation puts the choice of symbolic dynamics, required for the algorithm, on a firm foundation.Comment: 11 Pages Latex2e + 1 Figure (eps). Accepted for publication in Physics Lettes

Bosons in one-dimensional incommensurate superlattices

We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices L. Fallani et al., Phys. Rev. Lett. 98, 130404, (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasi-period) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasi-periodic potential, both for hardcore and softcore bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover we discuss the validity of the local-density approximation in presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasi-periodic potential; and we discuss the ab-initio derivation of the Bose-Hubbard Hamiltonian with quasi-periodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.Comment: 22 pages, 28 figure

Controlling Mixing Inside a Droplet by Time Dependent Rigid-body Rotation

The use of microscopic discrete fluid volumes (i.e., droplets) as microreactors for digital microfluidic applications often requires mixing enhancement and control within droplets. In this work, we consider a translating spherical liquid droplet to which we impose a time periodic rigid-body rotation which we model using the superposition of a Hill vortex and an unsteady rigid body rotation. This perturbation in the form of a rotation not only creates a three-dimensional chaotic mixing region, which operates through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of the mixing. Such a control is achieved by judiciously adjusting the three parameters that characterize the rotation, i.e., the rotation amplitude, frequency and orientation of the rotation. As the size of the mixing region is increased, complete mixing within the drop is obtained.Comment: 6 pages, 6 figure

Correlated bosons in a one-dimensional optical lattice: Effects of the trapping potential and of quasiperiodic disorder

We investigate the effect of the trapping potential on the quantum phases of strongly correlated ultracold bosons in one-dimensional periodic and quasiperiodic optical lattices. By means of a decoupling meanfield approach, we characterize the ground state of the system and its behavior under variation of the harmonic trapping, as a function of the total number of atoms. For a small atom number the system shows an incompressible Mott-insulating phase, as the size of the cloud remains unaffected when the trapping potential is varied. When the quasiperiodic potential is added the system develops a metastable-disordered phase which is neither compressible nor Mott insulating. This state is characteristic of quasidisorder in the presence of a strong trapping potential.Comment: Accepted for publication in PR

Rician MIMO Channel- and Jamming-Aware Decision Fusion

In this manuscript we study channel-aware decision fusion (DF) in a wireless sensor network (WSN) where: (i) the sensors transmit their decisions simultaneously for spectral efficiency purposes and the DF center (DFC) is equipped with multiple antennas; (ii) each sensor-DFC channel is described via a Rician model. As opposed to the existing literature, in order to account for stringent energy constraints in the WSN, only statistical channel information is assumed for the non-line-of sight (scattered) fading terms. For such a scenario, sub-optimal fusion rules are developed in order to deal with the exponential complexity of the likelihood ratio test (LRT) and impractical (complete) system knowledge. Furthermore, the considered model is extended to the case of (partially unknown) jamming-originated interference. Then the obtained fusion rules are modified with the use of composite hypothesis testing framework and generalized LRT. Coincidence and statistical equivalence among them are also investigated under some relevant simplified scenarios. Numerical results compare the proposed rules and highlight their jammingsuppression capability.Comment: Accepted in IEEE Transactions on Signal Processing 201

Localization in one-dimensional incommensurate lattices beyond the Aubry-Andr\'e model

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schr\"odinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.Comment: 5 pages, 6 figure

Order in extremal trajectories

Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker's map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or quasiperiodic. We discuss what the relevance of this calculation may be for dynamical systems and for glasses

Asymptotic energy profile of a wavepacket in disordered chains

We investigate the long time behavior of a wavepacket initially localized at a single site $n_0$ in translationally invariant harmonic and anharmonic chains with random interactions. In the harmonic case, the energy profile $\bar{< e_n(t)>}$ averaged on time and disorder decays for large $|n-n_0|$ as a power law $\bar{}\approx C|n-n_0|^{-\eta}$ where $\eta=5/2$ and 3/2 for initial displacement and momentum excitations, respectively. The prefactor $C$ depends on the probability distribution of the harmonic coupling constants and diverges in the limit of weak disorder. As a consequence, the moments $< m_{\nu}(t)>$ of the energy distribution averaged with respect to disorder diverge in time as $t^{\beta(\nu)}$ for $\nu \geq 2$, where $\beta=\nu+1-\eta$ for $\nu>\eta-1$. Molecular dynamics simulations yield good agreement with these theoretical predictions. Therefore, in this system, the second moment of the wavepacket diverges as a function of time despite the wavepacket is not spreading. Thus, this only criteria often considered earlier as proving the spreading of a wave packet, cannot be considered as sufficient in any model. The anharmonic case is investigated numerically. It is found for intermediate disorder, that the tail of the energy profile becomes very close to those of the harmonic case. For weak and strong disorder, our results suggest that the crossover to the harmonic behavior occurs at much larger $|n-n_0|$ and larger time.Comment: To appear in Phys. Rev.

Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let