Berry's phase and the anomalous velocity of Bloch wavepackets

The semiclassical equations of motion for a Bloch electron include an anomalous velocity term analogous to a $k$-space "Lorentz force", with the Berry connection playing the role of a vector potential. By examining the adiabatic evolution of Bloch states in a monotonically-increasing vector potential, I show that the anomalous velocity can be explained as the difference in the Berry's phase acquired by adjacent Bloch states within a wavepacket.Comment: 2 pages, 1 figur

Some notions of decentralization and coordination in large-scale dynamic systems

Some notions of decentralization and coordination in the control of large-scale dynamic systems are discussed. Decentralization and coordination have always been important concepts in the study of large systems. Roughly speaking decentralization is the process of dividing a large problem into subproblems so that it can be handled more easily. Coordination is the manipulation of the subproblem so that the original problem is solved. The various types of decentralization and coordination that have been used to control dynamic systems are discussed. The emphasis was to distinguish between on-line and off-line operations to understand the results available by indicating the aspects of the problem which are decentralized

Coherent optical control of polarization with a critical metasurface

We describe the mechanism by which a metamaterial surface can act as an ideal phase-controlled rotatable linear polarizer. With equal-power linearly polarized beams incident on each side of the surface, varying the relative phase rotates the polarization angles of the output beams, while keeping the polarization exactly linear. The explanation is based on coupled-mode theory and the idea of coherent perfect absorption into auxiliary polarization channels. The polarization-rotating behavior occurs at a critical point of the coupled-mode theory, which can be associated with the exceptional point of a parity-time (PT) symmetric effective Hamiltonian

Dark-State Polaritons in Single- and Double-Λ\Lambda Media

We derive the properties of polaritons in single-$\Lambda$ and double-$\Lambda$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\Lambda$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.Comment: 7 pages, 6 figure

Pseudo-Hermitian Hamiltonians Generating Waveguide Mode Evolution

We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians defined in this way are non-Hermitian, but satisfy symmetry properties that have previously been identified in the literature as "pseudo Hermiticity" and "anti-PT symmetry". We show how simple one-channel and two-channel models exhibit transitions between real, imaginary, and complex eigenvalue pairs.Comment: 7 pages, 2 figure

Optical Resonator Analog of a Two-Dimensional Topological Insulator

A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes.Comment: 10 pages, 9 figure

PID control system analysis and design

With its three-term functionality offering treatment of both transient and steady-state responses, proportional-integral-derivative (PID) control provides a generic and efficient solution to realworld control problems. The wide application of PID control has stimulated and sustained research and development to "get the best out of PID", and "the search is on to find the next key technology or methodology for PID tuning". This article presents remedies for problems involving the integral and derivative terms. PID design objectives, methods, and future directions are discussed. Subsequently, a computerized, simulation-based approach is presented, together with illustrative design results for first-order, higher order, and nonlinear plants. Finally, we discuss differences between academic research and industrial practice, so as to motivate new research directions in PID control

PID control system analysis, design, and technology

Designing and tuning a proportional-integral-derivative (PID) controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs obtained by all means need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. This stimulates the development of "intelligent" tools that can assist engineers to achieve the best overall PID control for the entire operating envelope. This development has further led to the incorporation of some advanced tuning algorithms into PID hardware modules. Corresponding to these developments, this paper presents a modern overview of functionalities and tuning methods in patents, software packages and commercial hardware modules. It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging. The inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree. This should also assist future development of "plug-and-play" PID controllers that are widely applicable and can be set up easily and operate optimally for enhanced productivity, improved quality and reduced maintenance requirements

Hidden Black: Coherent Enhancement of Absorption in Strongly-scattering Media

We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results from random matrix theory imply that the reflectivity of the medium can be suppressed by a factor ~(l_a/lN^2), where N is the number of incident channels and l,l_a are the elastic and absorption mean free paths respectively. It is thus possible to increase absorption from a few percent to > 99%. For a localized weak absorber buried in a non-absorbing scattering medium, we find a large but bounded enhancement.Comment: 4 pages, 4 figure