Related papers: An algebraic solution of driven single band tight …
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
A dynamical study of the generalised scalar-tensor theory in the empty Bianchi type I model is made. We use a method from which we derive the sign of the first and second derivatives of the metric functions and examine three different…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
In the single band tight-binding approximation, we consider the transport properties of an electron in a homogeneous static electric field. We show that repeated interactions of the electron with two-level systems in thermal equilibrium…
A connection of a variety of tight-binding models of noninteracting electrons on a rectangular lattice in a magnetic field with theta functions is established. A new spectrum generating symmetry is discovered which essentialy reduces the…
In this article we propose an algebraic system, which is an abelian group $(A,+)$ with a family of non-associative and non-(left)distributive multiplications $\{\cdot_{\lambda}\}_{\lambda\in H}$. We call this algebraic system dynamical…
Tight-binding (TB) molecular dynamics (MD) has emerged as a powerful method for investigating the atomic-scale structure of materials --- in particular the interplay between structural and electronic properties --- bridging the gap between…
We introduce the marked Brauer algebra and the marked Brauer category. These generalize the analogous constructions for the ordinary Brauer algebra to the setting of a homogeneous bilinear form on a $\mathbb{Z}_2$-graded vector space. We…
Lattice models are abundant in theoretical and condensed-matter physics. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here,…
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent…
In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
The centralizer algebra of the action of the unitary group on the real tensor powers of its natural module, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with…
We study a notion of tight inclusions of C*- and W*-dynamical systems which is meant to capture a tension between topological and measurable rigidity of boundary actions. An important case of such inclusions are $C(X)\subset L^\infty(X,…
We first review the application of Dirac's method to the dynamics of a classical particle constrained to a circle and its subsequent quantization. Then, we extend the analysis to a particle constrained to move on an ellipse. Particularly,…
This paper is mainly concerned with the robustly stable adaptive control of single-input single-output impulse-free linear time-invariant singular dynamic systems of known order and unknown parameterizations subject to single external point…
Newtonian dynamical systems which accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor…
We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…