High density effective theory

COLOR SUPERCONDUCTIVITY AND HIGH DENSITY EFFECTIVE THEORY... 

At low temperature or energy, most degrees of freedom of quark matter are irrelevant due to Pauli blocking. Only quasi-quarks near the Fermi surface are excited. Therefore, relevant modes for quark matter are quasi-quarks near the Fermi surface and the physical properties of quark matter like the symmetry of the ground state are determined by those modes. High density effective theory (HDET) [7, 8] of QCD is an effective theory for such modes to describe the low-energy dynamics of quark matter. 

Color superconductivity and high density effective theory... 

In order to accurately describe such oscillations, which have been the center of attention of modern liquid state theory, two major requirements need be fulfilled. The first has already been discussed above, i.e., the need to accurately resolve the nonlocal interactions, in particular the repulsive interactions. The second is the need to accurately resolve the mechanisms of the equation of state of the bulk fluid. Thus we need a mechanistically accurate bulk equation of state in order to create a free energy functional which can accurately resolve nonuniform fluid phenomena related to the nonlocality of interactions. So far we have only discussed the original van der Waals form of equation of state and its slight modification by choosing a high-density estimate for the excluded volume, vq = for a fluid with effective hard sphere diameter a, instead of the low-density estimate vq = suggested by van der Waals. These two estimates really suggest... 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

Equilibrium properties are surprisingly accurately predicted by molecular-level SCF calculations. MC simulations help us to understand why the SCF theory works so well for these densely packed layers. In effect, the high density screens the correlations for chain packing and chain conformation effects to such a large extent that the properties of a single chain in an external field are rather accurate. Cooperative fluctuations, such as undulations, are not included in the SCF approach. Also, undulations cannot easily develop in an MD box. To see undulations, one needs to perform molecularly realistic simulations on very large membrane systems, which are extremely expensive in terms of computation time. 

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