Physics

The strong interaction of quarks and gluons is described theoretically within the framework of Quantum Chromodynamics (QCD). The most promising way to evaluate QCD for all energy ranges is to formulate the theory on a 4-dimensional Euclidean space-time grid, which allows for numerical simulations on state of the art supercomputers. We will review the status of lattice QCD calculations providing examples such as the hadron spectrum and the inner structure of nucleons. We will then point to problems that cannot be solved by conventional Monte Carlo simulation techniques, i.e. non-zero baryon density, the matter-antimatter asymmetry and real time simulations. It will be demonstrated at the example of the 1+1 dimensional Schwinger model that tensor network techniques are able to overcome these problems showing that with this approach --and eventual quantum simulations-- a path for solving QCD is opening up.

Energy and momentum are conserved in Newton's laws of gravitation.
Numerical integration of the equations of motion should comply to
these requirements in order to guarantee the correctness of a
solution, but this turns out to be insufficient.  The steady growth of
numerical errors and the exponential divergence, renders numerical
solutions over more than a dynamical time-scale meaningless.  Even
time reversibility is not a guarantee for finding the definitive
solution to the numerical few-body problem.  As a consequence,
numerical N-body simulations produce questionable results.  Using
brute force integrations to arbitrary numerical precision I will
demonstrate empirically that the statistics of an ensemble of resonant
3-body interactions is independent of the precision of the numerical
integration, and conclude that, although individual solutions using
common integration methods are unreliable, an ensemble of approximate
3-body solutions accurately represent the ensemble of true solutions.