Multicenter McIntosh-Cisneros-Zwanziger-Kepler system, supersymmetry and integrability

Krivonos, S.; Nersessian, Armen; Ohanyan, Vadim

doi:10.1103/physrevd.75.085002

Cited by 30 publications

(67 citation statements)

References 23 publications

(16 reference statements)

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“…We could also view (2.17) as the conserved quantity related to oscillator-separability [represented by the first and the third terms], "corrected" by the middle one, required due to the Keplerian perturbation. We mention that our problem here can further be generalized by including magnetic charges [21].…”

Section: Resultsmentioning

confidence: 99%

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Separability and dynamical symmetry of Quantum Dots

et al. 2014

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The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonović et al. [1], is traced back to that of the perturbed Kepler problem. A large class of axially symmetric perturbing potentials which allow for separation in parabolic coordinates can easily be found. Apart of the 2:1 anisotropic harmonic trapping potential considered in [1], they include a constant electric field parallel to the magnetic field (Stark effect), the ring-shaped Hartmann potential, etc. The harmonic case is studied in detail.

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Section: Resultsmentioning

confidence: 99%

“…Translating into more familiar form, 21) allows us to interpret these quantities : (i) H is the perturbed Hamiltonian (2.8), as it should;…”

Section: )mentioning

confidence: 99%

Separability and dynamical symmetry of Quantum Dots

et al. 2014

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“…In the Ref. [16] it is shown that this Hamiltonian admits separation of variables in elliptic coordinates. Being presented in these coordinates, it has the following form:…”

Section: Paraboloidmentioning

confidence: 99%

“…For the construction of the Landau problem on ellipsoid and hyperboloid we use the so-called two-center MICZKepler system [16,17]. The system describes the charged particle with unit electric charge moving in the electric and magnetic fields of two dyons (electrically charged Dirac monopoles) with electric (magnetic) charges q 1,2 (g 1,2 ) which are fixed at the points with coordinates (0, 0, −a) and (0, 0, a) respectively.…”

Section: Paraboloidmentioning

confidence: 99%

“…Few years ago the two-center MICZ-Kepler systems were constructed, where the inclusion of monopoles yields, qualitatively, the same changes as in one-monopole MICZ-Kepler-like systems [16,17] (see also [18,19]). The main statement of those works is the following: let we have some one-particle three-dimensional system admitting separation of variables in elliptic coordinates.…”

Section: Introductionmentioning

confidence: 99%

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Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

et al. 2014

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We define the Landau problem on two-dimensional ellipsoid, hyperboloid and paraboloid of revolution. Starting form the two-center MICZ-Kepler system and making the reduction into these two-dimensional surfaces we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution in the magnetic field conserving the symmetry of the two-dimensional surface (Landau problem). For each case we figure out the values of parameter for which the qualitative character of the motion coincides with that of a free particle moving on the save two-dimensional surface. For the case of finite trajectories we construct the action-angle variables.

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Supergoop dynamics

Anninos

Anous

Denef

et al. 2013

J. High Energ. Phys.

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We initiate a systematic study of the dynamics of multi-particle systems with supersymmetric Van der Waals and electron-monopole type interactions. The static interaction allows a complex continuum of ground state configurations, while the Lorentz interaction tends to counteract this configurational fluidity by magnetic trapping, thus producing an exotic low temperature phase of matter aptly named supergoop. Such systems arise naturally in N = 2 gauge theories as monopole-dyon mixtures, and in string theory as collections of particles or black holes obtained by wrapping D-branes on internal space cycles. After discussing the general system and its relation to quiver quantum mechanics, we focus on the case of three particles. We give an exhaustive enumeration of the classical and quantum ground states of a probe in an arbitrary background with two fixed centers. We uncover a hidden conserved charge and show that the dynamics of the probe is classically integrable. In contrast, the dynamics of one heavy and two light particles moving on a line shows a nontrivial transition to chaos, which we exhibit by studying the Poincaré sections. Finally we explore the complex dynamics of a probe particle in a background with a large number of centers, observing hints of ergodicity breaking. We conclude by discussing possible implications in a holographic context.

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Multicenter McIntosh-Cisneros-Zwanziger-Kepler system, supersymmetry and integrability

Cited by 30 publications

References 23 publications

Separability and dynamical symmetry of Quantum Dots

Separability and dynamical symmetry of Quantum Dots

Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

Supergoop dynamics

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