Integrability and Superintegrability of Hamiltonian Systems
- with M. A. Quiroz-Juarez, J. L. Del Rio-Correa and N. Aquino, Classical harmonic three-body system: an experimental electronic realization, Scientific Reports volume 12, 13346 (2022)
- with I. Yurdusen and Irlanda Meza y Palma, Doubly Exotic Nth-order Order Superintegrable Classical Systems Separating in Cartesian Coordinates, SIGMA 18 (2022), 039, 20 pages
- with R. Linares, P. Winternitz, New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates, accepted manuscript to appear in J. Phys. A: Math. Theor. (2020)
- with A. V. Turbiner, W. Miller Jr., From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics, J. Phys. A: Math. Theor. 54 (2020) 015204
- with A. V. Turbiner, W. Miller Jr., Three-body closed chain of interactive (an)harmonic oscillators and the algebra sl(4;R), J. Phys. A: Math. Theor. 53 (2020) 055302
- with P. P. Goldstein, A. M. Grundland, The su(2) spin s representations via CP^{2s} sigma models, J. Phys. Commun. 4 (2020) 105006
- with J. C. Ndogmo, Equivalence classes and Linearization of the Riccati and Abel chain, Journal of Mathematical Analysis and Applications, 475 (2019) 1818-1830
- with P. Winternitz, _I. Yurdusen General Nth-order superintegrable systems separating in polar coordinates, J. Phys. A: Math. Theor. 51 (2018) 40LT01
- with J. C. López Vieyra, P. Winternitz, _I. Yurdusen Fourth order superintegrable systems separating in Polar Coordinates. II. Standard Potentials, J. Phys. A: Math. Theor. 51 (2018) 455202
- with J. C. López Vieyra, P. Winternitz, Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials, J. Phys. A: Math. Theor. 50 (2017) 495206
- with W. Miller Jr., E. Subag, Contractions of degenerate quadratic algebras, abstract and geometric, SIGMA 13 (2017) 099
- with E. G. Kalnins, W. Miller Jr., Separation equations for 2D superintegrable systems on constant curvature spaces, J. Phys. A: Math. Theor. 50 (2017) 385202
- with E. G. Kalnins, W. Miller Jr., E. Subag, Bôcher and abstract contractions of 2nd order quadratic algebras, SIGMA 13 (2017) 013
- with W. Miller Jr., Toward a classification of semidegenerate 3D superintegrable systems, J. Phys. A: Math. Theor. 50 (2017) 095203
- with W. Miller Jr., Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces, J. Phys. A: Math. Theor. 49, (2016), 305202
Many body problem
- with Alexander V. Turbiner, Classical n-body system in volume variables II: Four-body case, International Journal of Modern Physics A 37 (2022) 2250209
- with R. Linares, Alexander V. Turbiner and Willard Miller Jr., Classical n-body system in geometrical and volume variables I: Three-body case, International Journal of Modern Physics A 36 (2021) 2150140
- with W. Miller Jr., A. V. Turbiner, Four-body (an)harmonic oscillator in d-dimensional space: S-states, (quasi)-exact-solvability, hidden algebra sl(7), Journal of Math Physics 62 (2021) 072103
- with W. Miller Jr., A. V. Turbiner, Four-body problem in d-dimensional space: ground state, (quasi)-exact-solvability. IV, Journal of Math Physics 60 (2019) 062101
- with W. Miller Jr., A. V. Turbiner, The quantum n-body problem in dimension d > n – 1: ground state, J. Phys. A: Math. Theor. 51 (2018) 205201
- with A. V. Turbiner, W. Miller Jr., Three-body problem in d-dimensional space: ground state, (quasi)-exact-solvability, Journal of Math Physics 59 (2018) 022108
- with C. A. Escobar Three charges on a plane in a magnetic field: Special trajectories, Journal of Math Physics 59 (2018) 102901
- with A. V. Turbiner, W. Miller Jr., Three-body problem in 3D space: ground state, (quasi)-exact-solvability, J. Phys. A: Math. Theor. 50 (2017) 215201
Path integral (instanton calculus)
- with E. Shuryak, A. V. Turbiner, Fluctuations in quantum mechanics and field theories from a new version of semiclassical theory. II, Phys. Rev. D 96 (2017) 045005
- with E. Shuryak, A. V. Turbiner, Quantum and thermal uctuations in quantum mechanics and field theories from a new version of semiclassical theory, Phys. Rev. D 93 (2016) 105039
- with E. Shuryak, A. V. Turbiner, Three-loop correction to the instanton density. II. The sine-Gordon potential, Phys. Rev. D 92 (2015) 025047
- with E. Shuryak, A. V. Turbiner, Three-loop correction to the instanton density. I. The quartic double well potential, Phys. Rev. D 92 (2015) 025046
Perturbative and variational methods in quantum mechanics
- with H Olivares-Pilón and F Montoya Molina, Three-body harmonic molecule, J. Phys. B: At. Mol. Opt. Phys. 56 075002 (2023)
- with Fidel Montoya, Generalized three-body oscillator system: ground state, Acta Polytechnica 62(1):50–55, (2022)
- with H. Olivares-Pilón, N. Aquino and S. A. Cruz, Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions, J. Phys. B: At. Mol. Opt. Phys. 54 235002 (2022)
- with J.C. del Valle, A. V. Turbiner, Two-body neutral Coulomb system in a magnetic field at rest: From hydrogen atom to positronium, Physical Review A 103 (2021) 032820
- Two charges on plane in a magnetic field: III. He+ ion, Annals of Physics 351 (2014) 714-726
- with A. V. Turbiner, Two charges on a plane in a magnetic field II: Moving neutral quantum system across magnetic field, Annals of Physics 359 (2014) 405-418
- with A. V. Turbiner, Two charges on a plane in a magnetic field I: Quasi-equal charges and neutral quantum system at rest cases, Annals of Physics 340 (2014) 37-59
- with A. V. Turbiner, Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions, J. Phys. A: Math. Theor. 46 (2013) 295204
- with A. V. Turbiner, Two charges on a plane in a magnetic field: special trajectories, Journal of Math Physics 54 (2013) 022901
- Electrostatic models of charged hydrogenic chains in a strong magnetic field, Rev. Mex. Fis. 57 (3) (2011) 193-203
Casimir Effect
- with A. Martín-Ruiz, C.A. Escobar., O.J. Franca, Lorentz violating scalar Casimir effect for a D-dimensional sphere, Phys. Rev. D 102 (2020) 015027
- with A. Martín-Ruiz, C.A. Escobar., R. Linares, Scalar Casimir effect for a conducting cylinder in a Lorentz violating background, International Modern Physics A Vol. 36 No. 23 (2021) 2150168
- with A. Martín-Ruiz, C.A. Escobar., R. Linares, Testing the scalar sector of the standard-model extension with neutron gravity experiments, Eur. Phys. J. Plus 137, 1186 (2022)
Corrigendum
- with J. C. López Vieyra, P. Winternitz, Corrigendum: Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials (J. Phys. A: Math. Theor. 50 495206), J. Phys. A: Math. Theor., 52 (2019) 019501
- with E. Shuryak, A. V. Turbiner, Erratum Three-loop correction to the instanton density. I. The quartic double well potential [Phys. Rev. D 92, 025046 (2015)], Phys. Rev. D 92 (2015) 089902