Related papers: Calogero-Sutherland Particles as Quasisemions
The structure of the moduli space of N=1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge invariant composite fields of…
The notion of quasi-unit has been introduced by Yosida in unital Riesz spaces. Later on, a fruitful potential theoretic generalization was obtained by Arsove and Leutwiler. Due to the work of Eriksson and Leutwiler, this notion also turned…
The Calogero-Sutherland model is a paradigmatic integrable system describing one-dimensional non-relativistic particles with inverse-square interactions. At interaction strength $\lambda=2$, the CSM exhibits a deep connection to anyon…
We show that in quantum dots the physical quantities probed by local tunneling spectroscopies, namely the quasi-particle wavefunctions of interacting electrons, can considerably deviate from their single-particle counterparts as an effect…
A novel realization is provided for the scattering states of the $N$-particle Calogero-Moser Hamiltonian. They are explicitly shown to be the coherent states of the singular oscillators of the Calogero-Sutherland model. Our algebraic…
We investigate a quantum many-body system with particles moving on a circle and subject to two-body and three-body potentials. In this new class of models, that extrapolates from the celebrated Calogero-Sutherland model and a system with…
A similarity transformation is constructed through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension, can be mapped identically, to a set of free harmonic oscillators. This…
The Schr\"odinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have…
We briefly review a recently developed semiclassical theory for quantum oscillations in the spatial (particle and kinetic energy) densities of finite fermion systems and present some examples of its results. We then discuss the inclusion of…
We discuss various algebraic quantum structures associated to monotone Lagrangian submanifolds and we present a number of applications, computations and examples.
Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also…
Relying on rays, we search for submodules of a module V over a supertropical semiring on which a given anisotropic quadratic form is quasilinear. Rays are classes of a certain equivalence relation on V, that carry a notion of convexity,…
Being ubiquitous, solitons have particle-like properties, exhibiting behaviour often associated with atoms. Bound solitons emulate dynamics of molecules, though solitonic analogues of polymeric materials have not been considered yet. Here…
We report on the new approach to constructing superconformal extensions of the Calogero-type systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-abelian isometries of some supersymmetric…
For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids.…
We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the…
We extend the study on the algebraic structure of the $su(n)$ color Calogero-Sutherland models to the case of $gl(n|m)$ color CS model and show that the generators of the super-Yangian $Y(gl(n|m))$ can be obtained from two $gl(n|m)$ loop…
Chameleons are scalar fields that couple directly to ordinary matter with gravitational strength, but which nevertheless evade the stringent constraints on tests of gravity because of properties they acquire in the presence of high ambient…
In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor…
We show that a particular many-matrix model gives rise, upon hamiltonian reduction, to a multidimensional version of the Calogero-Sutherland model and its spin generalizations. Some simple solutions of these models are demonstrated by…