20 citations · 58 across the 7 of their papers we have counts for
7 papers
Two-center problem with harmonic-like interactions: periodic orbits and non-integrability
A. M. Escobar Ruiz, L. Jiménez-Lara, J. Llibre +1
We study the classical planar two-center problem of a particle subjected to harmonic-like interactions with two fixed centers. For convenient values of the dimensionless parame…
On particular integrability for (co)symplectic and (co)contact Hamiltonian systems
R. Azuaje, A. M. Escobar-Ruiz
As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and…
Two-body neutral Coulomb system in a magnetic field at rest: from Hydrogen atom to positronium
J. C. del Valle, A. V. Turbiner, Adrian M Escobar Ruiz
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses and $(…
Three-body closed chain of interactive (an)harmonic oscillators and the algebra
Alexander V Turbiner, Willard Miller, Adrian M Escobar-Ruiz
In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative distances, , between particles. The…
The quantum n-body problem in dimension : ground state
Willard Miller, Alexander V. Turbiner, M Adrian Escobar Ruiz
We employ generalized Euler coordinates for the body system in dimensional space, which consists of the centre-of-mass vector, relative (mutual), mass-independent…
Quantum and thermal fluctuations in quantum mechanics and field theories from a new version of semiclassical theory
M. A. Escobar-Ruiz, E. Shuryak, A. V. Turbiner
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding endpoints, and proceed by identifying…
Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions
A. V. Turbiner, M. A. Escobar-Ruiz
The quantum mechanics of two Coulomb charges on a plane and subject to a constant magnetic field perpendicular to the plane is considered. Four integr…