34 citations · 136 across the 13 of their papers we have counts for
13 papers
Four-body (an)harmonic oscillator in -dimensional space: -states, (quasi)-exact-solvability, hidden algebra
M. A. Escobar-Ruiz, Alexander V. Turbiner, Willard Miller
As a generalization and extension of our previous paper {\it J. Phys. A: Math. Theor. 53 055302} \cite{AME2020}, in this work we study a quantum 4-body system in ($d…
From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics
Alexander V Turbiner, Willard Miller, M. Adrian Escobar-Ruiz
It is shown that planar quantum dynamics can be related to 3-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case…
Four-body problem in d-dimensional space: ground state, (quasi)-exact-solvability. IV
M. A. Escobar-Ruiz, Willard Miller, Alexander V. Turbiner
Due to its great importance for applications, we generalize and extend the approach of our previous papers to study aspects of the quantum and classical dynamics of a -body syst…
Three charges on a plane in a magnetic field: Special trajectories
M. A. Escobar-Ruiz, C. A. Escobar
As a generalization and extension of JMP 54 (2013) 022901, the classical dynamics of three non-relativistic Coulomb charges , and on the plane…
Three-body problem in -dimensional space: ground state, (quasi)-exact-solvability
Alexander V Turbiner, Willard Miller, M. A. Escobar-Ruiz
As a straightforward generalization and extension of our previous paper, J. Phys. A50 (2017) 215201 we study aspects of the quantum and classical dynamics of a -body system with…
Fluctuations in quantum mechanics and field theories from a new version of semiclassical theory. II
M. A. Escobar-Ruiz, E. Shuryak, A. V. Turbiner
This is the second paper on semiclassical approach based on the density matrix given by the Euclidean time path integral with fixed coinciding endpoints. The classical path, interp…
Separation equations for 2D superintegrable systems on constant curvature spaces
M. A. Escobar-Ruiz, E. G. Kalnins, W. Miller
Second-order conformal quantum superintegrable systems in 2 dimensions are Laplace equations on a manifold with an added scalar potential and independent 2nd order conformal sy…
Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces
M. A. Escobar-Ruiz, Willard Miller
2nd-order conformal superintegrable systems in dimensions are Laplace equations on a manifold with an added scalar potential and independent 2nd order conformal symmet…
Three-loop Correction to the Instanton Density. II. The Sine-Gordon potential
M. A. Escobar-Ruiz, E. Shuryak, A. V. Turbiner
In this second paper on quantum fluctuations near the classical instanton configurations, see {\em Phys. Rev. D \bf 92}, 025046 (2015) and arXiv:1501.03993, we focus on another wel…
Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential
M. A. Escobar-Ruiz, E. Shuryak, A. V. Turbiner
This paper deals with quantum fluctuations near the classical instanton configuration. Feynman diagrams in the instanton background are used for the calculation of the tunneling am…
Two charges on plane in a magnetic field: III. ion
M. A. Escobar-Ruiz
The ion on a plane subject to a constant magnetic field perpendicular to the plane is considered taking into account the finite nuclear mass. Factorization of eigenfunct…
Two charges on plane in a magnetic field I. "Quasi-equal" charges and neutral quantum system at rest cases
M. A. Escobar-Ruiz, A. V. Turbiner
Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field perpendicular to the plane are considered. Major…
Two charges on plane in a magnetic field: special trajectories
M. A. Escobar-Ruiz, A. V. Turbiner
A classical mechanics of two Coulomb charges on a plane and subject to a constant magnetic field perpendicular to a plane is considered. Special "superint…