Regular Article - Theoretical Physics
Gradient expansion technique for inhomogeneous, magnetized quark matter
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
Accepted: 25 May 2021
Published online: 6 July 2021
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 () in benchmark studies. It is found that the region of the -T plane (where is the chemical potential) occupied by the inhomogeneous phase expands, as H increases and T decreases.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021