Related papers: Exact solution of Calogero model with competing lo…
We consider the large-N Calogero-Marchioro model in two dimensions in the Hamiltonian collective field approach based on the 1/N expansion. The Bogomol'nyi limit appears in the presence of the harmonic confinement. We investigate density…
It has been argued that despite remarkable success, existing random matrix theories are not adequate to describe disordered conductors in the metallic regime, due to the presence of certain two-body interactions in the effective Hamiltonian…
The analysis of equilibrium points in random games has been of great interest in evolutionary game theory, with important implications for understanding of complexity in a dynamical system, such as its behavioural, cultural or biological…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…
We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used…
This article introduces the "Goldilocks model" for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. The Goldilocks model shares features with two…
Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a…
We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin…
We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople…
It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as ``horizontal'' and construct new…
In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as…
We present exact results for the dynamical structure function, i.e.~the density-density correlations for the 1/r^2 system of interacting particles at three special values of the coupling constant. The results are interpreted in terms of…
We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero-Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the…
We study the large-scale dynamics of event chain Monte Carlo algorithms in one dimension, and their relation to the true self-avoiding walk. In particular, we study the influence of stress, and different forms of interaction on the…
A new concept of the available force in long-range interaction complex systems is proposed. The relationship between the available force in different time intervals and the interaction parameters of complex systems is described. It is found…
Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
We analyze the integrability of the ${\cal N}$-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair $\{L,A\}$ for this system, which properly reproduces all equations of motion. After adding a supersymmetric…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative…