Related papers: An algebraic solution of driven single band tight …
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
We provide a classification of all dynamical Lie algebras generated by 2-local spin interactions on undirected graphs. Building on our previous work where we provided such a classification for spin chains, here we consider the more general…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
We discuss how to construct a tight binding model Hamiltonan for the simplest possible solid, composed of hydrogen-like atoms. A single orbital per atom is not sufficient because the on-site electron-electron repulsion mixes in higher…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
A closed system of equations for the local Bloch vectors and spin correlation functions of three magnetic qudits, which are in an arbitrary, time-dependent, external magnetic field, is obtained using decomplexification of the Liouville-von…
It is shown that the rich algebraic structure of the standard $d$-dimensional Coulomb problem can be extended to its Dunkl counterpart. Replacing standard derivatives by Dunkl ones in the so($d+1$,2) dynamical algebra generators of the…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
Nonlinear systems of the reaction-diffusion type, including Gierer-Meinhardt models of autocatalysis, are studied by using Lie algebras coming from the prolongation structure. The consequences of this analytical approach, as the…
An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…
We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…
The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental…
We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic…
The issue of the parameterization of small-scale dynamics is addressed in the context of passive-scalar turbulence. The basic idea of our strategy is to identify dynamical equations for the coarse-grained scalar dynamics starting from…
In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed…
In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model…
We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the…
Brane model of universe is considered for zero-mass particle. Equation of Wheeler - de Witt type is obtained using variation principle from the well-known conservation laws inside the brane. This equation includes term accounting the…