20 citations · 124 across the 24 of their papers we have counts for
24 papers
Wolfes model aka -rational integrable model: hidden algebras and quartic polynomial algebra of integrals
J C Lopez Vieyra, A V Turbiner
One-dimensional 3-body Wolfes model with 2- and 3-body interactions also known as -rational integrable model of the Hamiltonian reduction is exactly-solvable and superinte…
Ultra-Compact accurate wave functions for He-like iso-electronic sequences and variational calculus. IV. Spin-singlet states family of the Helium sequence
J. C. Lopez Vieyra, A. V. Turbiner
As a continuation of Parts I \cite{Part-1:2020}, II \cite{Part-2:2021}, III \cite{Part-3:2022}, where ultra-compact wave functions were constructed for a few low-lying states of He…
Polynomial Integrable System: Different Faces of the 3-Body/ Elliptic Calogero Model
Alexander V. Turbiner, Juan Carlos Lopez Vieyra, Miguel Ayala
It is shown that the polynomial integrable system, introduced by Sokolov-Turbiner in [arXiv:1409.7439], is equivalent to the quantum Euler-Arn…
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence
D. J. Nader, J. C. del Valle, J. C. Lopez Vieyra +1
As a continuation of Part I, dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges , and Part II, dedicated to two excited sta…
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. II. Spin-singlet (excited) and spin-triplet (lowest) states of the Helium sequence
A. V. Turbiner, J. C. Lopez Vieyra, J. C. del Valle +1
As a continuation of Part I \cite{Part-1:2020} (Int. Journal of Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences fo…
The molecule in a strong magnetic field revisited
D. J. Nader, A. V. Turbiner, J. C. López Vieyra
A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state of the hydrogen m…
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. I. Ground state
A. V. Turbiner, J. C. Lopez Vieyra, J. C. del Valle +1
Several ultra-compact accurate wave functions in the form of generalized Hylleraas-Kinoshita functions and Guevara-Harris-Turbiner functions, which describe the domain of applicabi…
The He molecular ion and the He atomic ion in strong magnetic fields
J. C. Lopez Vieyra, A. V. Turbiner
We study the question about existence i.e. stability with respect to dissociation of the spin-quartet, permutation- and reflection-symmetric () state…
Three-body quantum Coulomb problem: analytic continuation
A. V. Turbiner, J. C. Lopez Vieyra, H. Olivares Pilon
The second (unphysical) critical charge in the 3-body quantum Coulomb system of a nucleus of positive charge and mass , and two electrons, predicted by F~Stillinger has be…
Cross-over in non-standard random-matrix spectral fluctuations without unfolding
G. Torres Vargas, R. Fossion, J. A. Méndez-Bermúdez +1
Recently, the singular value decomposition (SVD) was applied to standard Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale invariance in the spectral fluctuat…
Quantum Integrable, rational and trigonometric models: space-of-orbits view
A. V. Turbiner, J. C. López Vieyra
Algebraic-rational nature of the four-dimensional, -invariant integrable quantum Hamiltonians, both rational and trigonometric, is revealed and reviewed. It was shown that bei…
On 1/Z expansion for two-electron systems
J. C. Lopez Vieyra, A. V. Turbiner
The -expansion for the Coulomb system of infinitely massive center of charge Z and two electrons is discussed. Numerical deficiency in Baker et al, {\em Phys. Rev. \bf A41}, 1…
Stable He can exist in a strong magnetic field
A. V. Turbiner, J. C. Lopez Vieyra
The existence of bound states of the system $(\al,e,e,e)$ in a magnetic field is studied using the variational method. It is shown that for this sy…
The ground state of the molecular ion: physics behind
A. V. Turbiner, J. C. Lopez Vieyra
Five physics mechanisms of interaction leading to the binding of the molecular ion are identified. They are realized in a form of variational trial functions and thei…
A note about the ground state of the hydrogen molecular ion
J. C. Lopez Vieyra, A. V. Turbiner, H. Medel Cobaxin
Three simple parametric trial functions for the molecular ion are presented. Each of them provides subsequently the most accurate approximation for t…
Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials. III. case
K. G. Boreskov, A. V. Turbiner, J. C. López Vieyra +1
It is shown that the trigonometric Olshanetsky-Perelomov Hamiltonian, when written in terms of the Fundamental Trigonometric Invariants (FTI), is in algebraic form, i.e., has…
One-electron atomic-molecular ions containing Lithium in a strong magnetic field
H. Olivares Pilón, D. Baye, A. V. Turbiner +1
The one-electron Li-containing Coulomb systems of atomic type and molecular type , and are studied in the presence of a strong magn…
Charged Hydrogenic, Helium and Helium-Hydrogenic Molecular Chains in a Strong Magnetic Field
A. V. Turbiner, N. L. Guevara, J. C. Lopez Vieyra
A non-relativistic classification of charged molecular hydrogenic, helium and mixed helium-hydrogenic chains with one or two electrons which can exist in a strong magnetic field $B…
Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariable Polynomials. II. case
J. C. López Vieyra, M. A. G. García, A. V. Turbiner
It is shown that the trigonometric Olshanetsky-Perelomov Hamiltonian, when written in terms of the Fundamental Trigonometric Invariants (FTI), is in algebraic form, i.e., has…
Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials
K. G. Boreskov, A. V. Turbiner, J. C. Lopez Vieyra
It is conjectured that any trigonometric Olshanetsky-Perelomov Hamiltonian written in Fundamental Trigonometric Invariants (FTI) as coordinates takes an algebraic form and preserve…
H_3^{++}$ molecular ion in a strong magnetic field: triangular configuration
J. C. Lopez Vieyra, A. V. Turbiner
The existence of the molecular ion in a magnetic field in a triangular configuration is revised. Variational method with an optimization of the form of the vector potent…
Bound States from Regge Trajectories in a Scalar Model
A. Weber, J. C. Lopez Vieyra, C. R. Stephens +2
The calculation of bound state properties using renormalization group techniques to compute the corresponding Regge trajectories is presented. In particular, we investigate the bou…
Quantum Field Theory in the Limit x << 1
C. R. Stephens, A. Weber, J. C. Lopez Vieyra +1
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Part…
Regge Behaviour from an Environmentally Friendly Renormalization Group
C. R. Stephens, J. C. Lopez Vieyra, A. Weber +1
The asymptotic behaviour of cubic field theories is investigated in the Regge limit using the techniques of environmentally friendly renormalization, environmentally friendly in th…