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We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
We consider a space with noncommutativity of coordinates and noncommutativity of momenta. It is shown that coordinates in noncommutative phase space depend on mass therefore they can not be considered as kinematic variables. Also,…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system coupling operator. A general stability result is given for a class of perturbations to the system…
A modification of general relativity is presented in which Newton's constant and the cosmological constant become a conjugate pair of dynamical variables.
We prove that the stability problem of a vertical uniform rotation of a heavy top is completely solved by using the linearization method and the conserved quantities of the differential system which describe the rotation of the heavy top.
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
We describe the space-time model of a uniformly rotating frame of reference satisfying the Helmholtz free mobility postulate, as we implemented it in a preceding article \cite{Bel1}, and we discuss the implications of this model as it…
I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…
de Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss…
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent, generic approaches suggest the presence of many-body…
Describing dynamics in a gravitational universe with positive cosmological constant, such as de Sitter space, is a conceptually challenging problem. We propose a principle for constructing a quantum system that can potentially be used to…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…