Related papers: Integrability of the n-centre problem at high ener…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
The superconformal properties of N=4 Yang-Mills theory are most naturally studied using the formalism of harmonic superspace. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant…
The conservation of energy, linear momentum and angular momentum are important drivers for our physical understanding of the evolution of the Universe. These quantities are also conserved in Newton's laws of motion under gravity…
The higher-order superintegrability of separable potentials is studied. It is proved that these potentials possess (in addition to the two quadratic integrals) a third integral of higher-order in the momenta that can be obtained as the…
We revise critically existing approaches to evaluation of thermodynamic potentials within the Green's function calculations at finite electronic temperatures. We focus on the entropy and show that usual technical problems related to the…
We show that there exist an upper bound and a lower bound for the number of non-degenerate central configurations of the n-body problem in the plane with a homogeneous potential. In particular, both bounds are independent of the homogeneous…
We consider some random iterated function systems on the interval and show that the invariant measure has density in $\mathcal{C}^\infty$. To prove this we use some techniques for contractions in cone metrics, applied to the transfer…
The potential group method is applied to the n-dimensional Coulomb-Rosochatius potential, whose bound states and scattering states are worked out in detail. As far as scattering is concerned, the S-matrix elements are computed by the method…
This paper aims at completing and clarifying a delicate step in the proof of Theorem 5.3 of our paper \cite{ST}, where it was used the differentiability of a function $F$, which a priori can appear not necessarily differentiable.
We carried out numerical calculations by an extended-Hueckel program in order to check the analytical results reported in the preceding Part I and Part II. We typically consider alkali halide clusters composed of some tens of constituent…
Chaplygin proved the integrability by quadratures of a round sphere, rolling without slipping on a horizontal plane, with center of mass at the center of the sphere, but with arbitrary moments of inertia. Although the system is integrable…
We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the…
Kinetic energy functionals of the electronic density are used to model large systems in the context of density functional theory, without the need to obtain electronic wavefunctions. We discuss the problems associated with the application…
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several…
We consider the problem of characterizing, for certain natural number $m$, the local $\mathcal{C}^m$-non-integrability near elliptic fixed points of smooth planar measure preserving maps. Our criterion relates this non-integrability with…
Scattering of particles with different masses and energy in the gravitational field of rotating black holes is considered as outside as inside the black hole. Expressions for scattering energy of particles in the centre of mass system are…
In a large class of factorizing scattering models, we construct candidates for the local energy density on the one-particle level starting from first principles, namely from the abstract properties of the energy density. We find that the…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
An in-principle exact working equation to compute electronic affinity and ionization Fukui functions is derived within the $N$-centered (Nc) ensemble extension of density functional theory (DFT). It circumvents the kernel derivative…