Related papers: Internal variables and dynamic degrees of freedom
Integrodifference equations are versatile models in theoretical ecology for the spatial dispersal of species evolving in non-overlapping generations. The dynamics of these infinite-dimensional discrete dynamical systems is often illustrated…
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
In this paper we give an explanation of a number of observations relating to degree growth of birational mappings of the plane and their deautonomisation by singularity confinement. These observations are of a link between two a priori…
The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement…
Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the…
We consider the dynamics of lattices which have constrained constitutive units flexible in only their mutual orientations. A continuum description is derived through which it is shown that the models have zero shear velocity, free-particle…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
We quantize a classically stable system of a harmonic oscillator polynomially coupled to a ghost with negative kinetic energy. We prove that due to an integral of motion with a positive discrete spectrum: i) the Hamiltonian has a pure point…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…
Usually, bilevel optimization problems need to be transformed into single-level ones in order to derive optimality conditions and solution algorithms. Among the available approaches, the replacement of the lower-level problem by means of…
This paper investigates disentanglement as a result of evolution according to a class of master equations which include dissipation and interparticle interactions. Generalizing an earlier result of Di\'{o}si, the time taken for complete…
We investigate some classical evolution model in the discrete 2+1 space-time. A map, giving an one-step time evolution, may be derived as the compatibility condition for some systems of linear equations for a set of auxiliary linear…
It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the…
We study the non-equilibrium dissipative dynamics of the center of mass of a particle coupled to a field via its internal degrees of freedom. We model the internal and external degrees of freedom of the particle as quantum harmonic…
Unambiguous identification of the rewards driving behaviours of entities operating in complex open-ended real-world environments is difficult, partly because goals and associated behaviours emerge endogenously and are dynamically updated as…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…