Author: "Popov, Todor" / Publisher: american institute of physics - Searchworks@Jio Institute Digital Library Search Results

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Start Over Author "Popov, Todor" Publisher american institute of physics

Author: Dereli, Tekin and Popov, Todor
Subjects: *BLOCH waves, *TRANSLATING & interpreting, *MAGNETIC flux density, *TORUS, *QUANTUM optics, *GEOMETRIC quantization, *NONCOMMUTATIVE algebras
Abstract: We review the Landau problem of an electron in a constant uniform magnetic field. The magnetic translations are the invariant transformations of the free Hamiltonian. A Kähler polarization of the plane has been used for the geometric quantization. Under the assumption of quasi-periodicity of the wavefunction, the Zak's magnetic translations in the Bravais lattice generate a non-commutative quantum torus. We concentrate on the case when the magnetic flux density is a rational number. The Bloch wavefunctions form a finite-dimensional module of the noncommutative torus of magnetic translations as well as of its commutant, which is the non-commutative torus of magnetic translations in the dual Bravais lattice. The bi-module structure of the Bloch waves is shown to be the connecting link between two Morita equivalent non-commutative tori. The main focus of our review is the Kähler structure on the Hilbert space of Bloch waves and its inherent quantum toric geometry. We reveal that the metaplectic group M p (2 , R) of the automorphisms of magnetic translation algebras is represented by the quantum optics squeezing operators. [ABSTRACT FROM AUTHOR]
Published: 2021
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Author: Popov, Todor
Subjects: *JORDAN algebras, *HYDROGEN atom, *SPACE-time symmetries, *POINCARE conjecture, *MINKOWSKI space
Abstract: It has been realized long ago that the 15 dimensional conformal group, extending the Poincaré group with dilations and conformal inversions is a symmetry of the Maxwell equations. Conformal action yields a special mass-zero representation preserving the causal structure of Minkowski spacetime. On the other hand in the seventies in the works of Barut and others the conformal group emerged as a dynamical symmetry of the hydrogen atom. In this note we show that the conformal symmetry of Minkowski spacetime and the hydrogen atom dynamical symmetry are actually the coordinate and momentum space representation of the conformal group of the Euclidean Jordan algebra of Pauli matrices. [ABSTRACT FROM AUTHOR]
Published: 2019
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Author: Popivanov, Nedyu and Popov, Todor
Subjects: *WAVE equation, *MATHEMATICAL singularities, *BOUNDARY value problems, *TRANSONIC flow, *THEORY of wave motion, *GENERALIZABILITY theory
Abstract: We study four-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of Darboux problems on the plane. They were formulated by M.H.Protter in connection with BVPs for mixed type equations that model transonic flow phenomena. It is known that the unique generalized solution of Protter's problem may have singularity at only one point. This singularity is isolated at the vertex O of the boundary light characteristic cone and does not propagate along the cone. We present some conditions on the smooth right-hand side functions that are sufficient for existence of generalized solutions and give some a priori estimates for its singularity at O. [ABSTRACT FROM AUTHOR]
Published: 2014
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Author: Popivanov, Nedyu, Popov, Todor, and Tesdall, Allen
Subjects: *FREDHOLM equations, *ASYMPTOTIC expansions, *WAVE equation, *BOUNDARY value problems, *DARBOUX transformations, *APRIORI algorithm, *CARTESIAN coordinates
Abstract: We study four-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of Darboux problems on the plane. It is known that the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex O of the boundary light characteristic cone and does not propagate along the cone. We find asymptotic expansion of the generalized solutions in negative powers of the distance to O. Necessary and sufficient conditions for existence of bounded solutions are derived and additionally some a priori estimates for the singular solutions are given. [ABSTRACT FROM AUTHOR]
Published: 2013
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Author: Loday, Jean-Louis and Popov, Todor
Subjects: *YOUNG tableaux, *PARTITIONS (Mathematics), *NUMBER theory, *HALL polynomials, *WARING'S problem
Abstract: We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics. [ABSTRACT FROM AUTHOR]
Published: 2010
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