Related papers: Calogero Models for Distinguishable Particles
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
We completely solve the problem of classifying all one-dimensional quantum potentials with nearest- and next-to-nearest-neighbors interactions whose ground state is Jastrow-like, i.e., of Jastrow type but depending only on differences of…
We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i -…
A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number…
The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic…
The purpose of this paper is to develop a simplified model as the modeling of the magnetized plasmas. The starting point is an assumption that the distribution of the ensemble of charged particles in the same species is homogeneous over…
We discuss several aspects of multiparticle mixed state entanglement and its experimental detection. First we consider entanglement between two particles which is robust against disposals of other particles. To completely detect these kinds…
We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the…
We study an extension of one dimensional Calogero model involving strongly coupled and electrically charged particles. Besides Calogero term $\frac{g}{% 2x^{2}}$, there is an extra factor described by a Yukawa like coupling modeling short…
As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine…
We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a…
For systems consisting of distinguishable particles, there exists an agreed upon notion of entanglement which is fundamentally based on the possibility of addressing individually each one of the constituent parties. Instead, the…
We present a kind of construction for a class of special matrices with at most two different eigenvalues, in terms of some interesting multiplicators which are very useful in calculating eigenvalue polynomials of these matrices. This class…
This thesis investigates the entanglement of distinguishable and indistinguishable particles, introducing a new error model for Hardy's test, experimentally verified using superconducting qubits. We address challenges in implementing…
We introduce a class of particle models in one dimension involving exchange interactions that have scattering properties satisfying the Yang-Baxter consistency condition. A subclass of these models exhibits reflectionless scattering, in…
We have obtained the solutions of two dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability…
This work presents a comprehensive study of the exotic Landau model in a two-dimensional noncommutative plane. Beginning with the classical formulation where two conserved quantities $\mathcal{P}_i$ and $\mathcal{K}_i$ are derived, we…
A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$…
One of the challenges of collider physics is to unambiguously associate detector based objects with the corresponding elementary physics objects. A particular example is the association of calorimeter-based objects such as "jets",…
We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3. These solitons behave like particles with relativistic properties like Lorentz contraction and…