相关论文: An algebraic solution of driven single band tight …

We develop a new method for solving minimization problems on the Stiefel Manifold using damped dynamical systems. The constraints are satisfied in the limit by an additional damped dynamical system. The method is illustrated by numerical…

Motivated by work of Kucharczyk and Scholze, we use sheafified rational Witt vectors to attach a new ringed space $W_{\mathrm{rat}} (X)$ to every scheme $X$. We also define $R$-valued points $W_{\mathrm{rat}} (X) (R)$ of $W_{\mathrm{rat}}…

In this paper, a new method to determine the complete set of dynamically balanced planar four-bar mechanims is presented. Using complex variables to model the kinematics of the mechanism, the dynamic balancing constraints are written as…

This paper addresses a class of impulsive systems defined by a mix of continuous-time and discrete-time switched linear dynamics. We first analyze a related class of weighted discrete-time switched systems for which we establish a…

A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

We propose a generalization of spin algebra using multi-index objects, and a dynamical system analogous to matrix theory. The system has a solution described by generalized spin representation matrices and possesses a symmetry similar to…

Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we…

Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…

Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…

The classical and the quantal problem of a particle interacting in one-dimension with an external time-dependent quadratic potential and a constant inverse square potential is studied from the Lie-algebraic point of view. The integrability…

We introduce algebraic approach for superoperators that might be useful tool for investigation of quantum (bosonic) multi-mode systems and its dynamics. In order to demonstrate potential of proposed method we consider multi-mode Liouvillian…

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…

We develop a categorical approach to the dynamical Yang-Baxter equation (DYBE) for arbitrary Hopf algebras. In particular, we introduce the notion of a dynamical extension of a monoidal category, which provides a natural environment for…

We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…

This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…

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…

Under certain conditions, the dynamics of a nonlinear mechanical system can be represented by a single nonlinear modal oscillator. The properties of the modal oscillator can be determined by computational or experimental nonlinear modal…