Quantum Monte Carlo
This group is led by Richard Needs, with research
performed by two subgroups:
Richard Needs working with
John Trail,
Neil Drummond,
Zoltan Radnai,
Pablo Lopez Rios,
Matthew Brown,
Alexander Badinski,
Graham Spink,
Gareth Conduit,
and Andrew Morris
Mike Towler working with
Andrea Ma.
The official Web page of the QMC group may be found
here.
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It may seem surprising at first, but random numbers can be used to
help solve complicated problems in physics. A simple example of one
such Monte Carlo technique (so-called because of the connection
with gambling!) is illustrated in the figure on the left. A series of
random numbers in the interval [-1,1] is generated, which are used in pairs
as the coordinates of a set of points. By counting the fraction of points
which lie inside the circle, which is just the ratio of the areas of
the circle and square, the value of  can be estimated.
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In quantum mechanics, the state of a system of N electrons is
described by a many-body wave-function which is a 3N-dimensional
quantity and is impossible to calculate exactly using
standard mathematical techniques. The Quantum Monte Carlo (QMC) method
offers an efficient computational approach which accurately describes
the interactions between electrons.
Over the last few years we have developed a general computer program to carry out QMC calculations, named `CASINO'.
With the fast parallel computers now available, CASINO provides a powerful and
flexible tool for applying the Quantum Monte Carlo method to real systems.
Electrons repel one another because they are charged and because they
must obey the Pauli exclusion principle. This results in a
`hole' being created around each electron, from which other electrons
are excluded. The figure on the right, which was created by Randy Hood, shows the hole created by an
electron in a real solid as calculated by QMC.
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One of the simplest many-body quantum system consists of a collection
of electrons in a uniform potential, yet even this `simple'
system exhibits a wide range of behaviour.
An accurate description of this behaviour (using both QMC and more traditional
methods) is an important step in understanding many-body phenomena.
At high densities these electrons adopt a fluid-like state, but at very
low densities they may form a `Wigner crystal'. The figure on the left, which was created by John Trail,
shows the electron density of a two dimensional crystal containing a vacancy. The
study of systems like this may provide insight into the melting of Wigner
crystals and possible realisations of quantum computers.
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