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The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…
Oscillatory media can exhibit the coexistence of synchronized and desynchronized regions, so-called chimera states, for uniform parameters and symmetrical coupling. In a phase-balanced chimera state, where the totals of synchronized and…
First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but…
It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial derivative of the state. This higher spatial derivative (termed…
In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all exotic potentials with a third or a fourth order integrals,…
Topological phases characterized by non-Abelian charges have garnered increasing attention recently. Although Floquet (periodic-driving) higher-order topological phases have been explored at the single-particle level, the role of…
Off-diagonal mixed state phases based upon a concept of orthogonality adapted to unitary evolution and a proper normalisation condition are introduced. Some particular instances are analysed and parallel transport leading to the…
We consider a problem of geometric phase generation in a system of two interacting bosons confined in a narrow ring potential with a localized defect. Geometric phase emerges from variation of parameters of the defect. Particle interaction…
We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model…
We study cosmological solutions in nonlocal teleparallel gravity or $f(T)$ theory, where $T$ is the torsion scalar in teleparallel gravity. This is a natural extenstion of the usual teleparallel gravity with nonlocal terms. In this work the…
We discuss the self-consistent dynamics of plasmas by means of hamiltonian formalism for a system of $N$ near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the…
We note that the non-orthogonality of states and their coincidence at the degeneracy point are both admitted by nonlinear Hermitian systems and linear non-Hermitian systems. These striking characteristics motivate us to re-investigate the…
In the present paper which is a sequel to [N.B. Volkov and A.M. Iskoldsky The dynamics of vortex structures and states of current: 1;[1]], the dynamics of non-equilibrium phase transitions and states of current in electrophysical systems…
We evaluate theoretically the interaction of the open bottom and strange systems $\bar B\bar K$, $\bar B^* \bar K$, $\bar B\bar K^*$ and $\bar B^*\bar K^*$ to look for possible bound states which could correspond to exotic…
We report on a remarkable spectral phenomenon in a generic type of quantum lattice gas model. As the interaction strength increases, eigenstates spontaneously reorganize and lead to plateaus of the interaction energy, with gaps opening akin…
We present a comprehensive overview of different types of parametric interactions in nonlinear optics which are associated with simultaneous phase-matching of several optical processes in quadratic nonlinear media, the so-called multistep…
Labyrinthine patterns arise in two-dimensional physical systems submitted to competing interactions, ranging from the fields of solid-state physics to hydrodynamics. For systems of interacting particles, labyrinthine and stripe phases were…
We study dynamics of a phase boundary in a one-dimensional lattice gas, which is initially put into a non-equilibrium configuration and then is let to evolve in time by particles performing nearest-neighbor random walks constrained by…
A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…
In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…