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Astrophysical quantum matter: spinless charged particles on a magnetic dipole sphere


We consider the quantum mechanics of a spinless charged particle on a 2-dimensional sphere. When threaded with a magnetic monopole field, this is the well-known Haldane sphere that furnishes a translationally-invariant, incompressible quantum fluid state of a gas of electrons confined to the sphere. This letter presents the results of a novel variant of the Haldane solution where the monopole field is replaced by that of a dipole. We argue that this system is relevant to the physics on the surface of compact astrophysical objects like neutron stars.

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    While \(\sim 10^{14}\)T magnetic fields are achievable in heavy-ion collisions at, for example the LHC, these are out of equilibrium and too short-lived to be relevant for our purposes.

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    Although it must be pointed out that it is likely not pure dipole. Like the sun, there are multipole moments that decay rapidly with radius. We thank Bryan Gaensler for reminding us of this.


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We would like to thank Bryan Gaensler for very useful comments on the manuscript. JM is supported by the NRF of South Africa under Grant CSUR 114599. RPS is supported by a graduate fellowship from the National Institute for Theoretical Physics.

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Correspondence to Jeff Murugan.

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Murugan, J., Shock, J.P. & Slayen, R.P. Astrophysical quantum matter: spinless charged particles on a magnetic dipole sphere. Gen Relativ Gravit 53, 29 (2021).

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  • Magnetars
  • Quantum hall effect
  • Astrophysical quantum matter