Quantifying coherence

We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining conditions for measures of coherence we identify classes of functionals that satisfy these conditions and other, at first glance natural quantities, that do not qualify as coherence measures. We conclude with an outline of the questions that remain to be answered to complete the theory of coherence as a resource

A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states

We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or mixed - which have to satisfy merely weak conditions concerning the decay of correlations. The considered setting is a proven instance of a situation where dynamically evolving closed quantum systems locally appear as if they had truly relaxed, to maximum entropy states for fixed second moments. This furthers the understanding of relaxation in suddenly quenched quantum many-body systems. The proof features a non-commutative central limit theorem for non-i.i.d. random variables, showing convergence to Gaussian characteristic functions, giving rise to trace-norm closeness. We briefly relate our findings to ideas of typicality and concentration of measure.Comment: 27 pages, final versio

Exact relaxation in a class of non-equilibrium quantum lattice systems

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we study a setting where relaxation to a steady state is exact, namely for the Bose-Hubbard model where the system is quenched from a Mott quantum phase to the strong superfluid regime. We find that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments, maximizing the entanglement, to a state which is different from the thermal state of the new Hamiltonian. Remarkably, in the infinite system limit this relaxation is true for all large times, and no time average is necessary. For large but finite system size we give a time interval for which the system locally "looks relaxed" up to a prescribed error. Our argument includes a central limit theorem for harmonic systems and exploits the finite speed of sound. Additionally, we show that for all periodic initial configurations, reminiscent of charge density waves, the system relaxes locally. We sketch experimentally accessible signatures in optical lattices as well as implications for the foundations of quantum statistical mechanics.Comment: 8 pages, 3 figures, replaced with final versio

Scalable reconstruction of density matrices

Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently by tailored reconstruction schemes. Here, we discuss a scalable method to reconstruct mixed states that are well approximated by matrix product operators. The reconstruction scheme only requires local information about the state, giving rise to a reconstruction technique that is scalable in the system size. It is based on a constructive proof that generic matrix product operators are fully determined by their local reductions. We discuss applications of this scheme for simulated data and experimental data obtained in an ion trap experiment.Comment: 9 pages, 5 figures, replaced with published versio

Mode-Based Sensing and Actuation Techniques for Multi-Objective Flexible Aircraft Control

Intelligent sensing and actuation designs are explored as a means to improve performance of a gust load alleviation control design for a flexible wing aircraft equipped with wing-shaping control surfaces. The proposed techniques rely on identification of the dominant structural modes during specified flight conditions and uses them as a basis for sensor placement and actuator utilization. Specifically, a strategy for sensor placement is discussed that uses target mode shape capture as a mean to improve state estimation quality. A second strategy that reduces the number of wing-shaping control inputs using mode and objective-based shape functions as virtual input channels is also presented. Both techniques are demonstrated in simulation of a flexible wing transport aircraft utilizing a multi-objective control system designed to suppress flexible motion, minimize gust and maneuver load, and reduce drag

Investigation of Anti-Phase Asymmetric Quiet Rotor Technology

The future of urban air mobility has a well-known tall pole challenge in the form of community acceptance which largely comes from the noise. This paper presents a proposed anti-phase rotor technology that could reduce noise sources such as blade vortex interaction noise. The anti-phase rotor technology includes a rotor design with various anti-phase alternating trailing edge patterns and a rotor design with an asymmetric blade tip. Four small-scale anti-phase rotors are fabricated by 3D printing for acoustic measurements conducted in a low-speed open-circuit wind tunnel to assess the effectiveness of the proposed anti-phase rotor technology. Preliminary test results appear to be promising and indicate that the anti-phase rotor designs could be a practical means of reducing blade vortex interactions and noise. The four tested anti-phase rotor designs have peak acoustic performance depending on the RPM and thrust which suggests improved performance through design optimization could be achieved for specific mission requirements

Unsteady Crack Motion and Branching in a Phase-Field Model of Brittle Fracture

Crack propagation is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability at a fraction of the wave speed.Comment: 11 pages, 4 figure