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Michael Wilkinson

Publications and source records attributed to Michael Wilkinson.

63 records · Page 4Linked to original sources
arXiv2006

Semilinear Response

We discuss the response of a quantum system to a time-dependent perturbation with spectrum Φ(ω). This is characterised by a rate constant D describing the diffusion of occupation probability between levels. We calculate the transition rates by first-order perturbation theory, so that multiplying Φ(ω) by a constant λchanges the diffusion constant to λD. However, we discuss circumstances where this linearity does notextend to the function space of intensities, so that if intensities Φ_i(ω) yield diffusion constants D_i, then the intensity \sum_i Φ_i(ω) does not result in a diffusion constant \sum_i D_i. This `semilinear' response can occur in the absorption of radiation by small metal particles.

cond-mat.dis-nn↗
arXiv2006

Caustic activation of rain showers

We show quantitatively how the collision rate of droplets of visible moisture in turbulent air increases very abruptly as the intensity of the turbulence passes a threshold, due to the formation of fold caustics in their velocity field. The formation of caustics is an activated process, in which a measure of the intensity of the turbulence, termed the Stokes number St, is analogous to temperature in a chemical reaction: the rate of collision contains a factor exp(-C/St). Our results are relevant to the long-standing problem of explaining the rapid onset of rainfall from convecting clouds. Our theory does not involve spatial clustering of particles.

cond-mat.dis-nn↗
arXiv2004

Screening of charged singularities of random fields

Many types of point singularity have a topological index, or 'charge', associated with them. For example the phase of a complex field depending on two variables can either increase or decrease on making a clockwise circuit around a simple zero, enabling the zeros to be assigned charges of plus or minus one. In random fields we can define a correlation function for the charge-weighted density of singularities. In many types of random fields, this correlation function satisfies an identity which shows that the singularities 'screen' each other perfectly: a positive singularity is surrounded by an excess of concentration of negatives which exactly cancel its charge, and vice-versa. This paper gives a simple and widely applicable derivation of this result. A counterexample where screening is incomplete is also exhibited.

cond-mat.dis-nn↗
arXiv2000

Absorption of Energy at a Metallic Surface due to a Normal Electric Field

The effect of an oscillating electric field normal to a metallic surface may be described by an effective potential. This induced potential is calculated using semiclassical variants of the random phase approximation (RPA). Results are obtained for both ballistic and diffusive electron motion, and for two and three dimensional systems. The potential induced within the surface causes absorption of energy. The results are applied to the absorption of radiation by small metal spheres and discs. They improve upon an earlier treatment which used the Thomas-Fermi approximation for the effective potential.

cond-mat.mes-hall↗
arXiv2000

Wannier Functions for Lattices in a Magnetic Field II: Extensions to Irrational Fields

This paper extends earlier work on the definition of Wannier functions for Bloch electrons in a magnetic field. Extensions to irrational as well as rational magnetic fields are defined, and their properties investigated. The results are used to give a generalisation of the Peierls effective Hamiltonian which is valid when the magnetic flux per unit cell is close to any rational number.

cond-mat↗
arXiv1999

Non-adiabatic transitions in multi-level systems

In a quantum system with a smoothly and slowly varying Hamiltonian, which approaches a constant operator at times $t\to \pm \infty$, the transition probabilities between adiabatic states are exponentially small. They are characterized by an exponent that depends on a phase integral along a path around a set of branch points connecting the energy level surfaces in complex time. Only certain sequences of branch points contribute. We propose that these sequences are determined by a topological rule involving the Stokes lines attached to the branch points. Our hypothesis is supported by theoretical arguments and results of numerical experiments.

quant-ph↗
arXiv1998

Band Distributions for Quantum Chaos on the Torus

Band distributions (BDs) are introduced describing quantization in a toral phase space. A BD is the uniform average of an eigenstate phase-space probability distribution over a band of toral boundary conditions. A general explicit expression for the Wigner BD is obtained. It is shown that the Wigner functions for {\em all} of the band eigenstates can be reproduced from the Wigner BD. Also, BDs are shown to be closer to classical distributions than eigenstate distributions. Generalized BDs, associated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum correspondence on the torus to arbitrary rational values of the scaled Planck constant.

chao-dyn↗
arXiv1996

Distribution of Oscillator Strengths for Recombination of Localised Excitons in Two Dimensions

We investigate the distribution of oscillator strengths for the recombination of excitons in a two dimensional sample, trapped in local minima of the confinement potential: the results are derived from a statistical topographic model of the potential. The predicted distribution of oscillator strengths is very different from the Porter-Thomas disribution which usually characterises disordered systems, and is notable for the fact that small oscillator strengths are extremely rare.

cond-mat.mes-hall↗