Paul graduated from the University of London in 1977 and went on to Lancaster University to carry out Ph.D research, producing a thesis entitled "Electrons in the Heavy rare Earth Metals". This was followed by a Postdoctoral position associated with Collaborative Computer Project 9 on the electronic structure of complex materials based at Bristol University and an independent SERC (now EPSRC) fellowship to pursue research on relativistic effects in materials.
Following a brief period as a Research fellow at the Rutherford-Appleton Laboratory he was appointed to a lectureship at Keele University in 1989. He was promoted to senior lecturer in 1993 and Professor of Theoretical Physics in 2001.
In 2005 Paul moved to the University of Kent to become Head of the School of Physical Sciences.
Paul is a member of the College of the Engineering and Physical Sciences Research Council and has been on the organising committees of a number of major conferences. From December 2000 to December 2006 he was secretary of the condensed matter division of the Institute of Physics and is currently the Institutes representative on the Materials Research Forum of the Royal Society of Chemistry. He is on the steering panel of CCP9 and is also on the Peer Review Panel for the XMAS beamline at the European Synchrotron in Grenoble. He also holds an honorary scientist position at Daresbury Laboratory.
Room 219, Ingram Building
Also view these in the Kent Academic Repository
My research interests centre on Theoretical and Computational Physics. My primary interest is in mathematical physics. Within this theme I have several topics on which I have done a lot of work. These are enumerated below. A secondary interest involves investigating the properties of materials using first principles techniques, particularly materials containing rare earth elements.
Relativistic Quantum Mechanics
Relativistic quantum mechanics is a very mathematical subject that is well established, but that can still generate astonishing results. In particular where this subject borders non-relativistic quantum theory and optics can lead to unexpected consequences. We perform model calculations to illustrate such phenomena and to predict new ones. We are also looking towards applications of the theory in optics and condensed matter physics. Examples include relativistic quantum revivals, knots in the zeroes of quantum wave-packets, quantum mechanics for observers in accelerating frames of reference and the nature of particle spin.
This topic overlaps with the relativistic quantum mechanics above. The addition of many discrete waves with well-defined phase relations, such as the field near diffraction gratings or time-dependent quantum mechanics of periodic waves frequently yields striking interference phenomena. In particular elaborate quantum carpet-like structures as a function of space (Talbot effect) or time (quantum revivals) occur. We have recently examined relativistic extensions of this theory and currently we are considering various generalisations of such phenomena.
The basic equations of electromagnetism are known as Maxwells equations. The solutions of these equations in a vacuum are well-known to be electromagnetic waves, or light. However these are not the only solutions and combining physics with topology a number of other solutions have been found where the light behaves in very unusual ways, including not travelling in a straight line and knotting round itself. We are investigating these solutions and looking at the implications for the nature of charge and how such electromagnetic knots would interact with dielectric materials.
Super-oscillations are now well-established oscillations of wave-packets where the oscillation rate is faster than that of the fastest Fourier component of the wave-packet. A good understanding of super-oscillations in non-relativistic quantum wave-packets exists. We have found that super-oscillations in relativistic wave-packets behave very differently and we are currently developing the relativistic theory and trying to align it with the non-relativistic theory. The GIF below shows super-oscillations (plotted as a logarithm) for a free particle on the left and a harmonic oscillator on the right. (click image for bigger size)
Relativistic Effects in Solids
Contrary to popular belief Einsteins theory of relativity plays a role in many everyday phenomena. A unification of quantum theory and relativity is necessary to understand materials properties such as the dependence of the reflection of light on its polarisation and the position of the north and south poles of a magnet. My work takes this one step further to ask (and attempt to answer) what the dependence of the reflection/absorption of light as a function of energy and polarisation tells us about the material at the atomic level.
Rare Earth Materials
The rare earth metals are a series of fourteen elements (atomic numbers 58 to 71) that have some extraordinary properties such as exotic forms of magnetism, unusual superconductivity, fluctuating charges on the atoms in the solid and some of their compounds (called heavy fermions) have the extraordinary property that it takes thousands of times more energy to raise their temperature by one degree than standard metals like copper. Gaining a full understanding of such materials is a huge challenge to theoretical physics. Working with colleagues I have developed techniques that enable us to calculate and predict some of these properties using first principles that are consistent with Einsteins relativity.
Other topics in which I take a professional interest include Atmospheric Optics and Analytic Number Theory (the properties of numbers). I am the author of a book entitled Relativistic Quantum Mechanics: with applications in atomic and condensed matter physics published by Cambridge University Press.back to top
- PH588 - Mathematical Techniques for Physical Sciences
- PH605 - Thermal and Statistical Physics
- PH722 - Quantum Mechanics
I tend to teach at the more theoretical/mathematical end of Physics and have delivered modules in quantum mechanics at all levels, mathematics, electromagnetism, relativity, condensed matter physics. At present I teach quantum mechanics to second year students and problem solving to the final year. I also supervise undergraduate projects.back to top
I have most bitterly regretted that I didn't study physics when I was at school, because it is the key to the most exciting research and discoveries of our time, and physicists are the adventurers and the risk takers. Young people who study physics can expect to find themselves at the frontier of human thought.
Science may set limits to knowledge, but should not set limits to imagination.
James Clerk Maxwell
Happy is the man who can recognise in the work of today a connected portion of the work of eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of infinity. He strenuously works out his daily enterprises, because the present is given him for a possession.
Charles Mees(Research director, Kodak)
The best person to decide what research shall be done is the one doing the research. The next best is the head of the department. After that you leave the field of best persons and meet increasingly worse groups. The first of these is the research director, who is probably wrong more than half the time. Then comes a committee which is wrong most of the time. Finally there is a committee of company vice-presidents, which is wrong all the time.
It is inexcusable for scientists to torture animals; let them make their experiments on journalists and politicians.
An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: What does happen is that the opponents gradually die out.
Thomas Browne (1605-82)
No one should approach the temple of science with the soul of a money changer.
The Prophet Muhammed
Seek knowledge from the cradle to the grave.
The ink of the scholar is more sacred than the blood of the martyr.
Physics should be made as simple as possible, but not simpler. (attributed; after hearing a philosopher lecturing on relativity)
Science is a wonderful thing if one doesn’t have to earn one’s living at it.
Wernher von Braun
Crash programs fail because they are based on theory that, with nine women pregnant, you can get a baby in a month.
Research is what I'm doing when I don't know what I'm doing.
Should we force science down the throats of those that have no taste for it? Is it our duty to drag them kicking and screaming into the twenty-first century? I am afraid that it is.
There are in fact two things, science and opinion; the former begets knowledge, the latter ignorance.
As an adolescent I aspired to lasting fame, I craved factual certainty, and I thirsted for a meaningful vision of human life - so I became a scientist. This is like becoming an archbishop so you can meet girls.
Knowledge is boring, it’s what you don’t know that’s not boring.
Quantum Mechanics: The dreams stuff is made of.
Anyone who is not shocked by quantum theory has not understood a single word
Physics is like sex: sure, it may give some practical results, but that's not why we do it.
The doubter is a true man of science; he doubts only himself and his interpretations, but he believes in science.
In physics, you don't have to go around making trouble for yourself - nature does it for you.
Those who invest in science invest in the future, those who cut science hope for the best.
Thomas Watson (Chairman of IBM) in 1943
I think there is a world market for maybe five computers
Popular Mechanics Magazine in 1949
Computers in the future may weigh no more than 1.5 tons
Attributed to the Business Books Editor, prentice-Hall 1957
I have travelled the length and breadth of this country and talked with the best people and I can assure you that data processing is a fad that won’t last out the year
Ken Olson (President of DEC) in 1977
There is no reason anyone would want a computer in their own home
Bill Gates in 1981
640K ought to be enough for anyone
Laws of Science
- Discoveries are rarely attributed to the right person. (Arnold's Law)
- Nothing is ever discovered for the first time. (Michael Berry)
- Everything of importance has been said before by someone who did not discover it. (Whitehead’s Law)
- When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong. (Clark’s 1st Law)
- The limits of the possible can only be defined by going beyond them into the impossible. (Clark’s 2nd Law)
- Any sufficiently advanced science is indistinguishable from magic. (Clark’s 3rd Law)
- If an experiment works, something has gone wrong. (Finagles 1st Law)
- No matter what the experiment's result, there will always be someone eager to: (a) misinterpret it. (b) fake it. or (c) believe it supports his own pet theory. (Finagle’s 2nd Law).
- In any collection of data, the figure most obviously correct, beyond all need of checking, is the mistake. (Finagle’s 3rd Law).
- Once a job is fouled up, anything done to improve it only makes it worse. (Finagle’s 4th Law)
- A few months in the laboratory can save a few hours in the library. (Westheimer’s Law)
- No experiment is reproducible. (Wyszowski’s Law)
- Whenever a system becomes completely defined, someone discovers something which either abolishes the system or expands it beyond recognition. (Brooke’s Law).
- An object in motion will be heading in the wrong direction. (Gerrold’s 1st Law)
- An object at rest will be in the wrong place. (Gerrold’s 2nd Law)
- 2 is not equal to 3 - not even for very large values of 2. (Grable’s Law)
- Variables won’t, constants aren’t. (Osborn’s Law)