Related papers: The Ruijsenaars-Schneider Model
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
We present a comparative analysis of current observational constraints on three recently discussed alternative models for explaining the low-redshift acceleration of the universe: the so-called steady-state torsion model, the generalized…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…
In this article, we are interested in studying locomotion strategies for a class of shape-changing bodies swimming in a fluid. This class consists of swimmers subject to a particular linear dynamics, which includes the two most investigated…
The classical (dynamical) $R$-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent…
We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal…
We present a graded-geometric approach to modular classes of Lie algebroids and their generalizations, introducing in this setting an idea of relative modular class of a Dirac structure for a certain type of Courant algebroids, called…
Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner…
Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss…
We provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the GRW model. We anticipate that the collapse operators of our class of…
After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson…
A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
We put forward the following, physically motivated premise for constructing a theory that underlies the standard model in four-dimensional space-time: The Euler-Lagrange equations of such a theory formally resemble some equations of motion…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
The subject of this paper is degenerate integrability in Hamiltonian mechanics. It starts with a short survey of degenerate integrability. The first section contains basic notions. It is followed by a number of examples which include the…
We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every…