Results

**1 - 3**of**3**### in Frankfurt am Main

, 2006

"... I derive a general effective theory for hot and/or dense quark matter. After introducing general projection operators for hard and soft quark and gluon degrees of freedom, I explicitly compute the functional integral for the hard quark and gluon modes in the QCD partition function. Upon appropriate ..."

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I derive a general effective theory for hot and/or dense quark matter. After introducing general projection operators for hard and soft quark and gluon degrees of freedom, I explicitly compute the functional integral for the hard quark and gluon modes in the QCD partition function. Upon appropriate choices for the projection operators one recovers various well-known effective theories such as the Hard Thermal Loop / Hard Dense Loop Effective Theories as well as the High Density Effective Theory by Hong and Schäfer. I then apply the effective theory to cold and dense quark matter and show how it can be utilized to simplify the weak-coupling solution of the color-superconducting gap equation. In general, one considers as relevant quark degrees of freedom those within a thin layer of width 2Λq around the Fermi surface and as relevant gluon degrees of freedom those with 3-momenta less than Λgl. It turns out that it is necessary to choose Λq ≪ Λgl, i.e., scattering of quarks along the Fermi surface is the dominant process. Moreover, this special choice of the two cut-off parameters Λq and Λgl facilitates the power-counting of the numerous contributions in the gap-equation. In addition, it is demonstrated that both the energy and the momentum dependence of the gap function has to be treated self-consistently in order to determine the imaginary part of the gap function. For quarks close to the Fermi surface the imaginary part is calculated explicitly and shown to be of sub-subleading order in the gap equation.

### Minimum search space and efficient methods for structural cluster optimization

, 2008

"... A novel unification for the problem of searching of optimal clusters (SOC) under pair potential functions is presented. My formulation introduce a unique lattice from where efficient methods can be build to address this problem. It is proved that exists a discrete lattice such the complexity of a co ..."

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A novel unification for the problem of searching of optimal clusters (SOC) under pair potential functions is presented. My formulation introduce a unique lattice from where efficient methods can be build to address this problem. It is proved that exists a discrete lattice such the complexity of a continuous and discrete ways of solving SOC is the same. As an numerical example of my formulation, two lattices IF (IF stands for a lattice that combines lattices IC and FC together) with 9483 and 1739 particles is presented with the property that they include all putative optimal clusters from 2 trough 1000 particles, even the difficult optimal Lennard-Jones (LJ) clusters, C ∗ 38, C ∗ 98, and the Ino’s decahedrons. Also with a greedy search method called modified peeling, I found news optimal LJ clusters. This novel formulation can be extended to other potential functions and it unifies the geometrical motifs of the optimal LJ clusters and gives new insight towards the understanding of the complexity of the NP problems.