Superintegrability of the Fock-Darwin system

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Drigho-Filho E., KURU Ş., Negro J., Nieto L. M.

ANNALS OF PHYSICS, cilt.383, ss.101-119, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 383
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1016/j.aop.2017.05.003
  • Dergi Adı: ANNALS OF PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.101-119
  • Anahtar Kelimeler: Fock-Darwin system, Quantum dot, Superintegrability, Factorization, Higher-order symmetry, Coherent state, ANISOTROPIC QUANTUM DOTS, MAGNETIC-FIELD, COHERENT STATES, CHARGED-PARTICLE, ACCIDENTAL DEGENERACIES, HARMONIC-OSCILLATOR, SYMMETRY GROUP, EQUATION
  • Ankara Üniversitesi Adresli: Evet

Özet

The Fock-Darwin system is analyzed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one. (C) 2017 Elsevier Inc. All rights reserved.