Tuning the decay of sound in a viscous metamaterial.

Using analytical results for viscous dissipation in phononic crystals, we calculate the decay coefficient of a sound wave propagating at low frequencies through a two-dimensional phononic crystal with a viscous fluid background. It is demonstrated that the effective acoustic viscosity of the phononic crystal may exceed by two to four orders of magnitude the natural hydrodynamic viscosity of the background fluid. Moreover, the decay coefficient exhibits dependence on the direction of propagation; that is, a homogenized phononic crystal behaves like an anisotropic viscous fluid. Strong dependence on the filling fraction of solid scatterers offers the possibility of tuning the dissipative decay length of sound, which is an important characteristic of any acoustic device. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Nonreciprocal Linear Transmission of Sound in a Viscous Environment with Broken P Symmetry.

Reciprocity is a fundamental property of the wave equation in a linear medium that originates from time-reversal symmetry, or T symmetry. For electromagnetic waves, reciprocity can be violated by an external magnetic field. It is much harder to realize nonreciprocity for acoustic waves. Here we report the first experimental observation of linear nonreciprocal transmission of ultrasound through a water-submerged phononic crystal consisting of asymmetric rods. Viscosity of water is the factor that breaks the T symmetry. Asymmetry, or broken P symmetry along the direction of sound propagation, is the second necessary factor for nonreciprocity. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. Our study demonstrates that a medium with broken PT symmetry is acoustically nonreciprocal. The proposed passive nonreciprocal device is cheap, robust, and does not require an energy source.

Transport properties and enhanced figure of merit of quantum dot-based spintronic thermoelectric device.

Transport properties of quantum dot-based thermoelectric device with magnetic leads placed in external magnetic field are considered. The exact expressions for the thermoelectric coefficients are obtained by the equation of motion method, assuming noninteracting electrons. It is shown that at the maximum power mode the figure of merit of the proposed spintronic device is several times higher than that of a device with unpolarized electrons. The influence of electron-electron interaction on the figure of merit is analyzed and it is shown that in the limit of strong Coulomb repulsion the optimal thermoelectric performance predicted for noninteracting electrons is restored.

Iterative method for generating correlated binary sequences.

We propose an efficient iterative method for generating random correlated binary sequences with a prescribed correlation function. The method is based on consecutive linear modulations of an initially uncorrelated sequence into a correlated one. Each step of modulation increases the correlations until the desired level has been reached. The robustness and efficiency of the proposed algorithm are tested by generating sequences with inverse power-law correlations. The substantial increase in the strength of correlation in the iterative method with respect to single-step filtering generation is shown for all studied correlation functions. Our results can be used for design of disordered superlattices, waveguides, and surfaces with selective transport properties.

Enhancement of localization in one-dimensional random potentials with long-range correlations.

We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single-mode waveguide with 100 tunable scatterers periodically inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the spacing between each pair of scatterers, we observe a strong decrease of the localization length when white-noise scatterers are replaced by a correlated arrangement of scatterers.

Generation of correlated binary sequences from white noise.

We suggest a method for generation of random binary sequences of elements 0 and 1, with prescribed correlation properties. It is based on a modification of the widely used convolution method of constructing continuous random processes. Using this method, a binary sequence with a power-law decaying pair correlator can be easily generated.

Dynamical origin of memory and renewal.

We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index theta = 1/2 . We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with 0 < theta < 1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots.

Homogenization of magnetodielectric photonic crystals.

We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity epsilon(r) and permeability micro(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, omega-->0 and epsilon--> infinity.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

Speed of sound in periodic elastic composites.

We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does.

Local and global control of high-period unstable orbits in reversible maps.

We study the nonlinear dynamics of a complex system, described by a two-dimensional reversible map. The phase space of this map exhibits elements typical of Hamiltonian systems (stability islands) as well as of dissipative systems (attractor). Due to the interaction between the stability islands and the attractor, the transition to chaos in this system occurs through the collapse of the stability island and stochastization of the limiting-cycles orbits. We show how to apply the method of discrete parametric control to stabilize unstable high-period orbits. To achieve highly efficient control we introduce the concepts of local and global control. These concepts are useful in situations where there are "dangerous" points on the target orbit, i.e., the points where the probability of breakdown of control is high. As a result, the dangerous points turn out to be much more sensitive to external noise than other points on the orbit, and only the dangerous points determine how effective the control is.

Effects of stochastic webs on chaotic electron transport in semiconductor superlattices.

We investigate chaotic electron transport in the lowest miniband of a semiconductor superlattice with a tilted magnetic field. This experimentally accessible non-Kolmogorov-Arnol'd-Moser system involves only stationary electric and magnetic fields, but is dynamically equivalent to a time-dependent kicked harmonic oscillator. The onset of chaos strongly delocalizes the electron orbits, thus raising the electrical conductivity. When the cyclotron and Bloch frequencies are commensurate, the phase space is threaded by a stochastic web, which produces a further resonant increase in the conductivity.