Gradient expansion technique for inhomogeneous, magnetized quark matter
arXiv:2106.04744 · doi:10.1140/epja/s10050-021-00505-9
Abstract
A quark-magnetic Ginzburg-Landau (qHGL) gradient expansion of the free energy of two-flavor inhomogeneous quark matter in a magnetic field is derived analytically. It can be applied away from the Lifshitz point, generalizing standard Ginzburg-Landau techniques. The thermodynamic potential is written as a sum of the thermal contribution, the non-thermal lowest Landau level contribution, and the non-thermal qHGL functional, which handles any arbitrary position-dependent periodic modulation of the chiral condensate as an input. The qHGL approximation has two main practical features: (1) it is fast to compute; (2) it applies to non-plane-wave modulations such as solitons even when the amplitude of the condensate and its gradients are large (unlike standard Ginzburg-Landau techniques). It agrees with the output of numerical techniques based on standard regularization schemes and reduces to known results at zero temperature () in benchmark studies. It is found that the region of the - plane (where is the chemical potential) occupied by the inhomogeneous phase expands, as increases and decreases.
arXiv comment16 pages, 5 figures. Accepted for publication in EPJA
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