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Harry C. Shaw

Publications and source records attributed to Harry C. Shaw.

7 recordsLinked to original sources

Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points

We construct an infinite family of quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ with no quadratic points, for all primes $p\neq 2$. This answers a question of Colliot--Th\'el\`ene, Creutz and Viray in the negative, which asks whether every quartic del Pezzo surface has quadratic points over $C_2$ fields. We exhibit a Brauer--Manin obstruction on the variety parametrising lines associated to the quartic del Pezzo surface.

math.NT

Stability of the Kato-Kuzumaki's properties under field extensions

In 1986, Kato and Kuzumaki introduced some Diophantine properties of fields, called the $C_i^q$ properties, and they hoped they would provide a good characterization of the cohomological dimension of fields. In this paper, we study the stability of some variants of the $C_i^q$ properties under transcendental and algebraic extensions. As an application, we obtain the $C_n^1$ property for the field $\mathbf{F}_p(x_1,\cdots,x_n)$.

math.NT

Deep learning for enhanced free-space optical communications

Atmospheric effects, such as turbulence and background thermal noise, inhibit the propagation of coherent light used in ON-OFF keying free-space optical communication. Here we present and experimentally validate a convolutional neural network to reduce the bit error rate of free-space optical communication in post-processing that is significantly simpler and cheaper than existing solutions based on advanced optics. Our approach consists of two neural networks, the first determining the presence of coherent bit sequences in thermal noise and turbulence and the second demodulating the coherent bit sequences. All data used for training and testing our network is obtained experimentally by generating ON-OFF keying bit streams of coherent light, combining these with thermal light, and passing the resultant light through a turbulent water tank which we have verified mimics turbulence in the air to a high degree of accuracy. Our convolutional neural network improves detection accuracy over threshold classification schemes and has the capability to be integrated with current demodulation and error correction schemes.

cs.LG

Generation of polarization entanglement via the quantum Zeno effect

The quantum Zeno effect reveals that the continuous observation of a quantum system can result in significant alterations to its evolution. Here, we present a method for establishing polarization entanglement between two initially unentangled photons in coupled waveguides via the quantum Zeno effect. We support our analytical investigation with numerical simulations of the underlying Schrodinger equation describing the system. Further, we extend our technique to three coupled waveguides in a planar configuration and determine the parameter regime required to generate three-qubit W-states. Our findings offer a powerful quantum state engineering approach for photonic quantum information technologies.

quant-ph

Nonlinear dynamic interpretation of quantum spin

In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body, anti-ferromagnetic ordering, highly coupled quantum spin and a semi-classical interpretation of the torque on a spin magnetic moment in the presence of a magnetic field. The deterministic nonlinear differential coupling equation is used to introduce chaos, which is necessary to reproduce the correct statistical quantum results.

quant-ph

Electronic and Structural Characteristics of Zinc-Blende Wurtzite Biphasic Homostructure GaN Nanowires

We report a new biphasic crystalline wurtzite/zinc-blende homostructure in gallium nitride nanowires. Cathodoluminescence was used to quantitatively measure the wurtzite and zinc-blende band gaps. High resolution transmission electron microscopy was used to identify distinct wurtzite and zinc-blende crystalline phases within single nanowires through the use of selected area electron diffraction, electron dispersive spectroscopy, electron energy loss spectroscopy, and fast Fourier transform techniques. A mechanism for growth is identified.

cond-mat.mtrl-sci