Related papers: Algebraic treatment of three-body problems
We consider an algebraic treatment of a three-body system. We develop the formalism for a system of three identical objects and show that it provides a simultaneous description of the vibrational and rotational excitations of an oblate…
A new spectrum generating algebra for a unified description of rotations and vibrations in polyatomic molecules is introduced. An application to nonlinear X$_3$ molecules shows that this model (i) incorporates exactly the relevant point…
Three-body clusters are studied in the algebraic cluster model. Particular attention is paid to the case of three identical particles. It is shown in a geometrical analysis that the harmonic oscillator, the deformed oscillator and the…
We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and…
A new method is introduced to study three-body clusters. Triangular configurations with ${\cal D}_{3h}$ point-group symmetry are analyzed. The spectrum, transition form factors and $B(E\lambda)$ values of $^{12}$C are investigated. It is…
We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of…
We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have…
The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U(2) algebra and the…
A completely algebraic treatment of the six-dimensional hypercoulomb problem is discussed in terms of an oscillator realization of the dynamical algebra of SO(7,2). Closed expressions are derived for the energy spectrum and form factors.
We investigate symmetry-breaking phenomena in semilinear elliptic systems on the unit ball in $\mathbb{R}^3$, focusing on the emergence of non-radial solution branches with prescribed spatial and internal symmetries. Extending previous…
We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and…
We performed bound state calculations to obtain the first few vibrational states for the Ar_3 molecular system. The equations used are of Faddeev-type and are solved directly as three-dimensional equations in configuration space, i.e.…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed…
We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…
In this work it is shown that there are symmetries beyond the Euclidean group $E\left(3\right)$ in 3-body problem, and by extension in many-body problem, with inverse squared distance inter particle force. The symmetries in 3-body problem…
In this contribution, I discuss an algebraic treatment of alpha-cluster nuclei based on the introduction of a spectrum generating algebra for the relative motion of the alpha-clusters. Particular attention is paid to the discrete symmetry…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…