The fuzzy onion scalar field theory shows three fuzzy-sphere-like phases with aligned layers, dynamical phase transitions that blur boundaries, and two fitted phase-boundary curves of the form |b| = k1 + k2 sqrt(c).
Fuzzy Onion as a Matrix Model
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We propose a matrix model realisation of a three-dimensional quantum space. It has an onion-like structure composed of concentric fuzzy spheres of increasing radius. The angular part of the Laplace operator is inherited from that of the fuzzy sphere. The radial part is constructed using operators that relate matrices of various sizes using the matrix harmonic expansion. As an example of this approach, we produce a numerical simulation of a scalar quantum field theory, the classical heat transfer, study the quantum mechanical hydrogen atom, and consider some analytical aspects of the scalar field theory on this space.
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Numerical Study of Scalar Field Theory on the Fuzzy Onion
The fuzzy onion scalar field theory shows three fuzzy-sphere-like phases with aligned layers, dynamical phase transitions that blur boundaries, and two fitted phase-boundary curves of the form |b| = k1 + k2 sqrt(c).