Related papers: Symmetries in the many-body problems, a method to …
Short-range correlations in bosonic Helium clusters, composed of $^4$He atoms, are studied utilizing the generalized contact formalism. The emergence of universal $n$-body short range correlations is formulated and demonstrated numerically…
It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
A method has been developed for obtaining equivalent linear two-body equations (ELTBE) for the system of many ($N$) bosons using the variational principle. The method has been applied to the one-dimensional N-body problem with pair-wise…
Motivated by Xia-Zhou's recent work on applying symmetry groups to the N-body problem, we will study relative equilibria of the equilateral triangle and the square configurations under $\alpha$-homogeneous and quasi-homogeneous potentials…
The relativistic three-nucleon problem is formulated by constructing a dynamical unitary representation of the Poincar\'e group on the three-nucleon Hilbert space. Two-body interactions are included that preserve the Poincar\'e symmetry,…
We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed…
This work is devoted to the study of some exactly solvable quantum problems of four, five and six bodies moving on the line. We solve completely the corresponding stationary Schr\"odinger equation for these systems confined in an harmonic…
Time-symmetric initial data for two-body solutions in three dimensional anti-deSitter gravity are found. The spatial geometry has constant negative curvature and is constructed as a quotient of two-dimensional hyperbolic space. Apparent…
We consider a Pauli particle in a Coulomb field. The supersymmetric Hamiltonian is constructed, by explicitly giving the two supercharges $Q_{1}$ and $ Q_{2}$ in the full three-dimensional space and which together with the Hamiltonian, are…
Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
We lay down the {\em ab initio} many-body quantum theory of electrons and phonons in- and out-of-equilibrium at any temperature. We begin by addressing a fundamental issue concerning the {\em ab initio} Hamiltonian in the harmonic…
We study three sub-problems of the N-body problem that have two degrees of freedom, namely the n-pyramidal problem, the planar double-polygon problem, and the spatial double-polygon problem. We prove the existence of several families of…
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 $4$-body system with equal masses in {\it $d$}-dimensional space with…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension)…
We explore the application of generating symmetries, i.e. symmetries that depend on a parameter, to integrable hyperbolic third order equations, and in particular to consistent pairs of such equations as introduced by Adler and Shabat (AS).…
In this work we investigate small clusters of helium atoms using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ atoms with an inter-particle potential which does not present a strong repulsion at short distances.…
Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so…
General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…