# Quantum Magnetic Collapse In Neutron Star Binary Systems

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Quantum magnetic collapse is a phenomenon that corresponds to the collapsing of stars due to the generation of high magnetic field. Such stars are highly magnetized objects (such as neutron stars) where the particle processes take place in the presence of very high external magnetic field B. When the magnetic energy inside the star exceeds the internal energy of electrons and/or positrons fluids it will lead to breaking of hydrostatic equilibrium. In the astrophysical context, this will occur when B corresponding to electron mass (10^13 Gauss). At this energy, there is a collapse of the neutral matter with a magnetic moment since the pressure transverse to the magnetic field vanishes. Typically, we would calculate the magnetization and particle number N of this system using derivatives of the thermodynamic potential Ω with respect to magnetic field and chemical potential, but this can be difficult since Ω diverges. Additionally, for neutron stars, we would like to consider how these quantities may change as electrons are accreted onto the neutron star. We develop a method for calculating the particle number N in the static case, then extend this to the accreting system to calculate the dynamical particle number density with the orientation of using this result for calculating the magnetization as it changes in time.