Related papers: Coupling and particle number intertwiners in the C…
For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice can be used to compute the ground state wave function and the dynamical…
The Kuramoto model with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions…
The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of…
Fractional Pontryagin's systems emerge in the study of a class of fractional optimal control problems but they are not resolvable in most cases. In this paper, we suggest a numerical approach for these fractional systems. Precisely, we…
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm…
An oscillator (IQuO) more elementary than the quantum one is formulated. This is expressed by quantum operators (a, a+), with two-components and it is composed of sub-oscillators, each with "semi-quanta" (1/2h). The commutation relation of…
We study the algebra $B_q(\ge)$ presented by Kashiwara and introduce intertwiners similar to $q$-vertex operators. We show that a matrix determined by 2-point functions of the intertwiners coincides with a quantum R-matrix (up to a diagonal…
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…
We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described…
There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an…
We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. For instance, in a 5-dimensional Kaluza-Klein manifold we argue that the motion of charged…
We present a controlled method for computing the exchange coupling in correlated one-dimensional electron systems based on the relation between the exchange constant and the pair-correlation function of spinless electrons. This relation is…
We identify a nontrivial yet tractable quantum field theory model with space/time anisotropic scale invariance, for which one can exactly compute certain four-point correlation functions and their decompositions via the operator-product…
Inverted hybrid inflation (in which the inflaton field slowly rolls away from the origin, giving a spectral index $n\lsim 1$) is an appealing variant of the more usually studied hybrid model. Analysing the model alongside the ordinary…
Quantum Liouville theory is analyzed in terms of the infinite dimensional representations of $U_Qsl(2,C)$ with q a root of unity. Making full use of characteristic features of the representations, we show that vertex operators in this…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
We compute the correlation functions of irregular Gaiotto states appearing in the colliding limit of the Liouville theory by using "regularizing" conformal transformations mapping the irregular (coherent) states to regular vertex operators…
In this paper we discuss a general strategy to construct vector coherent states of the Gazeau-Klauder type and we use them to built up examples of isospectral hamiltonians. For that we use a general strategy recently proposed by the author…
Explicit solutions for one completely-integrable system of Calogero-Moser type in external fields are found in case of three and four interacting particles. Relation between coupling constant, initial values of coordinates and time of…
Intertwiners between representations of Lie groups can be used to obtain relations for matrix elements. We apply this technique to obtain different identities for the wave functions of the open Toda chain, in particular raising operators…