Related papers: q-Orthogonal dualities for asymmetric particle sys…
We address some properties of the quadrupole-quadrupole ($Q \cdot Q$) interaction in nuclear studies. We first consider how to restore $SU(3)$ symmetry even though we use only coordinate and not momentum terms. Using the Hamiltonian…
In this paper we will report on a one-dimensional, non-separable quantum many-particle system introduced in [arXiv:1504.08283,arXiv:1604.06693]. It consists of two (distinguishable) particles moving on the half-line being subjected to two…
The concept of wave-particle duality holds significant importance in the field of quantum mechanics, as it elucidates the dual nature encompassing both wave-like and particle-like properties exhibited by microscopic particles. In this…
The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological…
We study the dynamics of a symmetric two-level system strongly coupled to a broadened harmonic mode. Upon mapping the problem onto a spin-boson model with peaked spectral density, we show how analytic solutions can be obtained, at arbitrary…
We develop the algebraic approach to duality, more precisely to intertwinings, within the context of particle systems in general spaces, focusing on the $\mathfrak{su}(1,1)$ current algebra. We introduce raising, lowering, and neutral…
We present the complete azimuthal asymmetries at leading twist in terms of fragmentation functions in dihadron production semi-inclusive electron positron annihilation process. When the non-trivial $\theta$ vacuum is taken into…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
One-dimensional asymmetric simple exclusion processes (ASEPs) which are coupled to external reservoirs via diffusive transport are studied. These ASEPs consist of active compartments characterized by directed movements of the particles and…
In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.
The goal of this article is to display a $Q$-polynomial structure for the Attenuated Space poset $\mathcal A_q(N,M)$. The poset $\mathcal A_q(N,M)$ is briefly described as follows. Start with an $(N+M)$-dimensional vector space $H$ over a…
We consider a system of stochastic interacting particles with general diffusion coefficient and drift functions and we study the types of collisions that arise in them. In particular, interactions between particles are inversely…
Anisotropic pseudopotential relevant to collisions of two particles polarized by external field is rigorously derived and its properties are investigated. Such low-energy pseudopotential may be useful in describing collective properties of…
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to…
We consider the totally asymmetric exclusion process in discrete time with generalized updating rules. We introduce a control parameter into the interaction between particles. Two particular values of the parameter correspond to known…
We give an exact expression for the distribution of the position X(t) of a single second class particle in the asymmetric simple exclusion process (ASEP) where initially the second class particle is located at the origin and the first class…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We investigate the total asymmetric exclusion process by analyzing the dynamics of the shock. Within this approach we are able to calculate the fluctuations of the number of particles and density profiles not only in the stationary state…
The multi-component density functional theory is faced with the challenge of capturing various types of inter- and intra-particle exchange-correlation effects beyond those introduced by the conventional electronic exchange-correlation…
A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect…