Biomedical subjects

P B Wilkinson

Publications and source records attributed to P B Wilkinson.

6 recordsLinked to original sources

PubMed2002

Photonic Bloch oscillations and Wannier-Stark ladders in exponentially chirped Bragg gratings.

The formation of photonic Bloch oscillations and Wannier-Stark ladders is demonstrated in an exponentially chirped one-dimensional Bragg grating. The photonic Bloch oscillations are investigated using Hamiltonian optics, and direct analogies are made with electron dynamics in periodic potentials. The results of transfer matrix calculations are presented, which show the existence of a photonic Wannier-Stark ladder that should be detectable in experiments.

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PubMed2001

Compact fourth-order finite difference method for solving differential equations.

We present a fourth-order finite difference (FD) method for solving two-dimensional partial differential equations. The FD operator uses a compact nine-point stencil on a regular square grid. Despite the regular grid, Dirichlet boundary conditions can be applied on an arbitrarily shaped boundary without resorting to the usual stepped approximation. We demonstrate the superior convergence of the method over second-order techniques by solving the Schrödinger equation for an electron in a semiconductor quantum dot with a smoothly varying potential which generates classically chaotic dynamics.

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PubMed2001

Effects of geometrical ray chaos on the electromagnetic eigenmodes of a gradient index optical cavity.

Electromagnetic analogies of quantum chaos are investigated in two-dimensional optical cavities which have reflective surfaces and contain a gradient refractive index medium. As the shape of the cavity is transformed continuously from a rectangle to a parallelogram, the geometrical ray paths undergo a transition from stable to chaotic dynamics. In the chaotic regime, the spectral statistics of the cavity are accurately described by random matrix theory. In addition, the electromagnetic mode spectrum of the cavity is modulated by both real and ghost periodic ray paths. These paths also "scar" the electric field intensity distributions of regular subsets of cavity eigenmodes.

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PubMed2001

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.

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PubMed2001

Evolution of fractal patterns during a classical-quantum transition.

We investigate how fractals evolve into nonfractal behavior as the generation process is gradually suppressed. Fractals observed in the conductance of semiconductor billiards are of particular interest because the generation process is semiclassical and can be suppressed by transitions towards either fully classical or fully quantum-mechanical conduction. Investigating a range of billiards, we identify a "universal" behavior in the changeover from fractal to nonfractal conductance, which is described by a smooth evolution rather than deterioration in the fractal scaling properties.

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PubMed2001

Electromagnetic wave chaos in gradient refractive index optical cavities.

Electromagnetic wave chaos is investigated using two-dimensional optical cavities formed in a cylindrical gradient refractive index lens with reflective surfaces. When the planar ends of the lens are cut at an angle to its axis, the geometrical ray paths are chaotic. In this regime, the electromagnetic mode spectrum of the cavity is modulated by both real and ghost periodic ray paths, which also "scar" the electric field intensity distributions of many modes. When the cavity is coupled to waveguides, the eigenmodes generate complex series of resonant peaks in the electromagnetic transmission spectrum.

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