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Simulation specifics

Quantum mechanically, the system can be simulated by the Metropolis algorithm. This involves constructing a wavefunction, and then moving particles by a small amount with a probability governed by the wavefunction. [1] describes the results of such a program.

This simulation is of the classical counter part. Unlike for QED, there is no classical physics corresponding to QCD. QCD is a purely quantum mechanical system. This project's goal is to simulate of a classical system of particles obeying a similar potential function.

Classically, the negative gradient of the potential energy gives the force that a particle experiences. This means that particles will be attracted towards a common centre of mass.

The total energy is linearly proportional to the total distance, the first derivative of a linear function is a constant, thus the attractive force is attractive, but not a function of distance. This should be contrasted to the electromagnetic and gravitational forces where .

A further point of difference is that this flux-tube force is does not obey superposition: the force is strictly between pairs or triplets rather than between all particles.

This simulation deals only with mesonic rather than baryonic matter, so only two particles (quark and anti-quark) will be discussed from this point onwards.