Results

**1 - 2**of**2**### Study of Instanton Physics in Lattice CD

, 1997

"... One of the most interesting parts of QCD dynamics is the non-perturbative region of long-range excitations and this thesis explores several semi-classical aspects of this region associated with in-stantons. The instanton distribution in lattice QCD has been calculated with and without internal fermi ..."

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One of the most interesting parts of QCD dynamics is the non-perturbative region of long-range excitations and this thesis explores several semi-classical aspects of this region associated with in-stantons. The instanton distribution in lattice QCD has been calculated with and without internal fermions and no statistically significant difference between the two distributions was found for a sea quark mass mq,:ti 10OMeV. Since the instanton distribution is observed by using a relaxation process, the effects of lattice artifacts and pair annihilation during relaxation are investigated. The role of the low-eigenvalue modes in the Hybrid Monte-Carlo dynamics has been studied and it is shown that the efficiency of this method can be significantly increased by using a few recent vectors to approximate the solution of the inverse Dirac operator. The algorithm to find the low-eigenvalue modes of the Dirac operator was developed and used to study the spectrum of the Dirac-Wilson operator on the lattice. Restricting the Dirac operator to the complement of the few lowest modes is shown to completely eliminate critical slowing down in the Conjugate Gradient method. Point-to-point correlation functions were calculated using the full propagator and the propagator

### Lattice Monte Carlo methods for systems far from equilibrium

, 2013

"... We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate the dynamics. As an example, these methods are applied to the ..."

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We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate the dynamics. As an example, these methods are applied to the random-force-driven one-dimensional Burgers ’ equation – a model for hydrody-namic turbulence. For a self-similar forcing acting on all scales the system is driven to a nonequi-librium steady state characterized by a Kolmogorov energy spectrum. We extract correlation functions of single- and multi-point quantities and determine their scaling spectrum displaying anomalous scaling for high-order moments. Varying the external forcing we are able to tune the system continuously from equilibrium, where the fluctuations are short-range correlated, to the case where the system is strongly driven in the infrared. In the latter case the nonequilibrium scaling of small-scale fluctuations are shown to be universal.