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Register a new userSymmetric and anti-symmetric Landau parameters and magnetic properties of dense quark matter
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We calculate the dimensionless Fermi liquid parameters (FLPs), $F_{0,1}^{sym}$ and $F_{0,1}^{asym}$, for spin asymmetric dense quark matter. In general, the FLPs are infrared divergent due to the exchange of massless gluons. To remove such divergences, the Hard Density Loop (HDL) corrected gluon propagator is used. The FLPs so determined are then invoked to calculate magnetic properties such as magnetization $langle Mrangle$ and magnetic susceptibility $chi_M$ of spin polarized quark matter. Finally, we investigate the possibility of magnetic instability by studying the density dependence of $langle Mrangle$ and $chi_M$.
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We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy $epsilon$. While the approximation still suffers from curse of dimensionality, to the best of our knowledge, these are first results in the literature with explicit error bounds. Moreover, we also discuss neural network architecture that can be suitable for approximating symmetric and anti-symmetric functions.
We apply Ginzburg-Landau theory to determine BCS pairing in a strongly-coupled uniform superfluid of three-flavor massless quarks in flavor equilibrium. We elucidate the phase diagram near the critical temperature in the space of the parameters characterizing the thermodynamic potential terms of fourth order in the pairing gap. Within the color and flavor antisymmetric channel with zero total angular momentum, the phase diagram contains an isoscalar (IS) color-antitriplet phase and a color-flavor-locked (CFL) phase, reached by a second order transition from the normal state, as well as states reached by a first order transition. We complement the general Ginzburg-Landau approach by deriving the high-density asymptotic form of the Ginzburg-Landau free energy from the weak-coupling gap equation. The dynamically-screened, long-range color magnetic interactions are taken into account in solving the gap equation. We find that in the limit of weak coupling, the IS phase is less favorable near the transition temperature than the CFL phase. In view of the fact that deconfined quark matter must be color charge neutral, we incorporate the constraint of overall color neutrality into the Ginzburg-Landau theory and the gap equation. This constraint yields a disparity in the chemical potential between colors and reduces the size of the gap, in the presence of the anisotropy of the order parameters in color space. In comparison with the case in which there are no chemical potential differences between colors and hence the superfluid generally has nonzero net color charge, we find that while the constraint of color neutrality has only negligible effects on the gap in the weak coupling regime, it appreciably destabilizes the IS phase in the strong coupling regime without affecting the CFL phase.
We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 lesssim T lesssim 1 , {rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.
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