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A description of many constituent (particle) systems with fuzzy initial conditions is proposed with the help of the field language. In this language correlation functions are defined and equations for them are derived in the free Fock…
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
Recent advances in operating and manipulating DNA have provided unique experimental possibilities in many fields of DNA research, especially in gene therapy. Researchers have deployed many techniques, experimental and theoretical, to study…
Cell-to-cell variability is inherent to numerous biological processes, including cell migration. Quantifying and characterizing the variability of migrating cells is challenging, as it requires monitoring many cells for long time windows…
A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius $R.$ When hard…
Systems in which particles can self-assemble into mono- or bilayers can form variety of stable and metastable structures on a nanometer length scale. For this reason confinement has a particularly strong effect on such systems. We discuss…
We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…
In this paper we produce evidence that confinement of colour is due to dual superconductivity of $QCD$ vacuum. To do that we put together results of old numerical simulations and results of more recent investigations. The starting point is…
The conceptual and dynamical aspects of decoherence are analyzed, while their consequences are discussed for several fundamental applications. This mechanism, which is based on a universal Schr\"odinger equation, is furthermore compared…
Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to…
The global $SU(3)$ color symmetry and its physical consequences are discussed. The N\"{o}ther current is actually governed by the conserved matter current of color charges if the color field generated by this charge is properly polarized.…
We give a brief overview of the problem of quark confinement in hadronic physics, and outline a few of the suggested explanations of the confining force.
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…
We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to…
The dynamics of few two-level atoms interacting with one cavity mode is described in master equation formalism. Two different configurations are considered: a transient one with all atoms initially in the excited state and a stationary one…
The theory of nucleation with depletion zones is discussed. The approach of stochastic effects of solitary droplet is analyzed. The negative features of a solution with fixed boundary are outlined. A new solution with effective fixed…
Morphologies of a vesicle confined in a spherical vesicle were explored experimentally by fast confocal laser microscopy and numerically by a dynamically-triangulated membrane model with area-difference elasticity. The confinement was found…
The mechanism of continuous set of different universes formation is elaborated. It provides tool to solve the problem of observed smallness of physical parameters. Solution of two puzzles - the hierarchy and the cosmological constant…
We discuss the issue of complementarity between the confining phase and the Higgs phase for gauge theories in which there are no light particles below the scale of confinement or spontaneous symmetry breaking. We show with a number of…