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We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat…
The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order.…
Quantum liquids in two dimensions represent interesting dynamical quantum systems for several reasons, among them the possibility of the existence of infinite hidden symmetries, such as conformal symmetry or the symmetry associated with…
Two-dimensional $\sigma$-models with $\mathbb{Z}_N$-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite…
The states of the physical algebra, namely the algebra generated by the operators involved in encoding and processing qubits, are considered instead of those of the whole system-algebra. If the physical algebra commutes with the interaction…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…
A prepotential approach to constructing the quantum systems with dynamical symmetry is proposed. As applications, we derive generalizations of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of…
We consider the six-dimensional dynamical system in three components introduced by Ryan to describe the scenario of Belinskii, Khalatnikov and Lifshitz to the cosmological singularity when the spatial metric tensor is not diagonal. Despite…
This paper is a continuation of [KS]. We develop the results of [KS] principally in two directions. First, we generalize the main result of [KS], the connection between the solutions of the classical dynamical Yang-Baxter equation and…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…