Metric-space analysis of systems immersed in a magnetic field

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• Irene d'Amico, York
• Thursday 14 January 2016, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

Understanding the behavior of quantum systems subject to magnetic fields is of fundamental importance and underpins quantum technologies. However, modeling these systems is a complex task, because of many-body interactions and because many-body approaches such as density-functional theory get complicated by the presence of a vector potential into the system Hamiltonian. We use the metric-space approach to quantum mechanics [1, 2] to study the effects of varying the magnetic vector potential on quantum systems [3]. The application of this technique to model systems in the ground state provides insight into the fundamental mapping at the core of current density-functional theory, which relates the many-body wave function, particle density, and paramagnetic current density. We show that the role of the paramagnetic current density in this relationship becomes crucial when considering states with different magnetic quantum numbers m. Additionally, varying the magnetic field uncovers a richer complexity for the “band structure” present in ground-state metric spaces, as compared to previous studies varying scalar potentials. We go beyond ground-state properties and apply this approach to excited states. The results suggest that, under specific conditions, a universal behavior may exist for the relationships between the physical quantities defining the system. [1] I. D’Amico, J. P. Coe, V. V. Franc¸a, and K. Capelle, Quantum mechanics in metric space: Wave functions and their densities, Phys. Rev. Lett. 106, 050401 (2011) [2] P. M. Sharp and I. D’Amico, Metric space formulation of quantum mechanical conservation laws, Phys. Rev. B 89 , 115137 (2014). [3] P. M. Sharp and I. D’Amico, PRA 92 , 032509 (2015)

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