It is assumed that a convective zone with sunspots can be considered as a unique analog of a type... more It is assumed that a convective zone with sunspots can be considered as a unique analog of a type-II superconductor with the presence of magnetic vortices. The mathematical formalism of Ginzburg and Landau is used to describe superconductivity, and a particular form of the Lagrangian is proposed for modeling macrophenomena. Although its physical content is different from that used in microphysics, the fundamental topological properties implied by both models are identical. It is demonstrated that the sunspot's umbra is analogous to the core of a superconductor vortex, and the penumbra has its counterpart in the vortex region, where the 'supercurrent' flows. It is also shown that the total magnetic flux of stable sunspots can have discrete values only.
We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the ... more We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the classical Maxwellian term, the so-called Chern-Simons term generalized here in a gauge-invariant way. It is shown that it is namely this term which is responsible for the confinement of the spot's electromagnetic field into a finite-dimensional domain. We further demonstrate that besides the total magnetic flux it is also the spot's electric charge which is non-zero and that both quantities are topologically quantized, i.e. can acquire discrete values only. Finally, a cylindrically symmetric sunspot carryingp magnetic flux quanta,p being a positive integer, is revealed to possess a non-zero total angular momentum, the magnitude of which is proportional top2. The latter fact also implies the stability of rotating sunspots against their fragmentation (splitting).
It is assumed that a convective zone with sunspots can be considered as a unique analog of a type... more It is assumed that a convective zone with sunspots can be considered as a unique analog of a type-II superconductor with the presence of magnetic vortices. The mathematical formalism of Ginzburg and Landau is used to describe superconductivity, and a particular form of the Lagrangian is proposed for modeling macrophenomena. Although its physical content is different from that used in microphysics, the fundamental topological properties implied by both models are identical. It is demonstrated that the sunspot's umbra is analogous to the core of a superconductor vortex, and the penumbra has its counterpart in the vortex region, where the 'supercurrent' flows. It is also shown that the total magnetic flux of stable sunspots can have discrete values only.
We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the ... more We present a (2+1)-dimensional sunspot model whose Lagrange density contains, in addition to the classical Maxwellian term, the so-called Chern-Simons term generalized here in a gauge-invariant way. It is shown that it is namely this term which is responsible for the confinement of the spot's electromagnetic field into a finite-dimensional domain. We further demonstrate that besides the total magnetic flux it is also the spot's electric charge which is non-zero and that both quantities are topologically quantized, i.e. can acquire discrete values only. Finally, a cylindrically symmetric sunspot carryingp magnetic flux quanta,p being a positive integer, is revealed to possess a non-zero total angular momentum, the magnitude of which is proportional top2. The latter fact also implies the stability of rotating sunspots against their fragmentation (splitting).
For N ≥ 2, an N-qubit doily is a doily living in the N-qubit symplectic polar space. These doilie... more For N ≥ 2, an N-qubit doily is a doily living in the N-qubit symplectic polar space. These doilies are related to operator-based proofs of quantum contextuality. Following and extending the strategy of Saniga et al. (Mathematics 9 (2021) 2272) that focused exclusively on three-qubit doilies, we first bring forth several formulas giving the number of both linear and quadratic doilies for any N > 2. Then we present an effective algorithm for the generation of all N-qubit doilies. Using this algorithm for N = 4 and N = 5, we provide a classification of N-qubit doilies in terms of types of observables they feature and number of negative lines they are endowed with. We also list several distinguished findings about N-qubit doilies that are absent in the three-qubit case, point out a couple of specific features exhibited by linear doilies and outline some prospective extensions of our approach.
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Papers by Metod Saniga