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Crystalline phases by an improved gradient expansion technique

机译：通过改进的梯度扩展技术获得结晶相

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We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion of the order parameter. We apply this method to quark matter at vanishing temperature and large chemical potential, which is expected to be relevant for astrophysical considerations. The method is remarkably reliable and fast as compared to performing the full numerical diagonalization of the quark Hamiltonian in momentum space and is designed to improve the standard Ginzburg-Landau expansion close to the phase transition points. For definiteness, we focus on inhomogeneous chiral symmetry breaking, accurately reproducing known results for one-dimensional and two-dimensional modulations and examining novel crystalline structures, as well. Consistently with previous results, we find that the energetically favored modulation is the so-called one-dimensional real-kink crystal. We propose a qualitative description of the pairing mechanism to motivate this result.
机译：我们开发了一种创新技术，用于研究具有自发破碎对称性的不均匀相。该方法依赖于在均匀相中自由能的确切形式的知识以及阶数参数的特定梯度扩展。我们将这种方法应用于在消失温度和大化学势下的夸克物质，这有望与天文学有关。与在动量空间中对夸克哈密顿量进行完全数值对角化相比，该方法具有显着的可靠性和快速性，旨在改善接近相变点的标准Ginzburg-Landau展开。为了确定性，我们集中在不均匀的手性对称性断裂上，准确地再现一维和二维调制的已知结果，并检查新颖的晶体结构。与以前的结果一致，我们发现在能量上受人喜爱的调制是所谓的一维实扭结晶体。我们提出了配对机制的定性描述，以激发这一结果。

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