Related papers: State space decomposition for nonautonomous dynami…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for…
We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
State space is widely used for modeling power systems and analyzing their dynamics but it is limited to representing causal and proper systems in which the number of zeros does not exceed the number of poles. In other words, the system…
The basic concepts of classical mechanics are given in the operator form. Then, the hybrid systems approach, with the operator formulation of both quantum and classical sector, is applied to the case of an ideal nonselective measurement. It…
Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in…
We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
We derive an integral convex combination of product states for a range of separable Werner states. Our method consists of expanding the sought-after local density operators in terms of Wigner operators. For dimension d=2, our decomposition…
In this paper, we are concerned with the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The asymptotic stability of the steady state with the…
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
The complete reducibility property for bipartite states reduced the separability problem to a proper subset of positive under partial transpose states and was used to prove several theorems inside and outside entanglement theory. So far…
We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
Klauder's recent generalization of the harmonic oscillator coherent states [J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems, requiring some additional structure if applied to systems with degeneracies. The author…