Eur. Phys. J. A (2021) 57: 220
https://doi.org/10.1140/epja/s10050-021-00505-9

Regular Article - Theoretical Physics

Gradient expansion technique for inhomogeneous, magnetized quark matter

¹ School of Physics, University of Melbourne, 3010, Parkville, VIC, Australia
² Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), University of Melbourne, 3010, Parkville, VIC, Australia

^a fanzuini@student.unimelb.edu.au

Received: 14 February 2021
Accepted: 25 May 2021
Published online: 6 July 2021

Abstract

A quark-magnetic Ginzburg–Landau (qHGL) gradient expansion of the free energy of two-flavor inhomogeneous quark matter in a magnetic field H 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 ($T=0$) in benchmark studies. It is found that the region of the $\mu$-T plane (where $\mu$ is the chemical potential) occupied by the inhomogeneous phase expands, as H increases and T decreases.