AI 中文总结
本文研究非均匀磁场中是否存在手征孤子晶格（CSL），利用QCD低能有效场论，解析得到无质量极限下的CSL态，数值结果表明弯曲磁场下CSL类基态仍存在，还绘制了均匀磁场有限体积QCD相图中CSL相的位置。
AI 中文摘要
已知在足够强的均匀磁场中，量子色动力学（QCD）的基态支持空间调制的中性π介子凝聚体，被称为手征孤子晶格（CSL）。本文研究当外磁场非均匀时是否存在类似的有序基态，这一问题对重离子碰撞和中子星等唯象学应用具有重要意义。为此，我们采用QCD的低能有效场论，限制中性π介子作为强磁场中唯一的低能自由度。在π介子质量为零的极限下，我们完整刻画了支持CSL类基态的磁场；此外，对于一类简单的无穷多磁场，我们解析得到了对应的CSL态。偏离无质量极限则需要对能量泛函进行完整的数值最小化，我们在此给出了一些数值样本结果，重点关注与均匀磁场或零π介子质量情况的定性差异。主要结论保持不变：虽然弯曲磁场通常会降低中性π介子凝聚带来的能量增益，但CSL型基态仍然存在。作为附带结果，我们绘制了有限体积、均匀磁场下QCD相图中CSL相的位置。
英文摘要
It has been known that in sufficiently strong uniform magnetic fields, the ground state of quantum chromodynamics (QCD) supports a spatially modulated condensate of neutral pions, dubbed chiral soliton lattice (CSL). In this paper, we investigate whether a similar ordered ground state might exist when the external magnetic field is nonuniform, as appropriate for potential phenomenological applications, including heavy-ion collisions and neutron stars. To that end, we use the low-energy effective field theory of QCD, restricted to the neutral pions as the sole low-energy degrees of freedom in strong magnetic fields. In the limit of vanishing pion mass, we achieve a complete characterization of magnetic fields supporting a CSL-like ground state. Moreover, for a simple but infinite family of magnetic fields, we find the corresponding CSL state analytically. Going away from the massless limit requires full numerical minimization of the energy functional. Here we provide some sample numerical results, focusing on the qualitative differences as compared to the situations with a uniform magnetic field or a vanishing pion mass. The main conclusion remains unchanged: while bending the magnetic field typically reduces the energy gain due to the neutral pion condensation, a CSL-type ground state is still possible. As a byproduct of our work, we map the location of the CSL phase in the phase diagram of QCD in a uniform magnetic field and finite volume.
Comments17 pages, 7 figures
