Related papers: Geometries of Maximal Acceleration
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
We consider a model in which accelerated particles experience line--elements with maximal acceleration corrections that are introduced by means of successive approximations. It is shown that approximations higher than the first need not be…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…
The consideration of the N-body gravitational problem equations can give to us some class of boundary-value problems defined on the "beem's" construction. One can considere it as weak or so-called finite element method's approximation with…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
The paper gives an overview of the principles of particle accelerators and their historical development. After introducing the basic concepts, the main emphasis is on sketching the layout of modern storage rings and discussing their…
The concepts of relative velocity and acceleration, deviation velocity and acceleration and relative momentum of point particles in spaces (manifolds), the tangent bundle of which is equipped with a transport along paths, are introduced. If…
We investigate the point-particle limit of the equations of motion valid for a system of extended bodies in a scalar alternative theory of gravitation: the size of one of the bodies being a small parameter xi, we calculate the limit, as xi…
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and…
We determine transformations between coordinate systems which are mutually in linear accelerated motion. In case of the symmetrical linear mutual acceleration, we immediately get the maximal acceleration limit which was derived by…
The paper gives a short overview of the principles of particle accelerators, their historical development and the typical performance limitations. After an introduction to the basic concepts, the main emphasis is to sketch the layout of…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
For the stochastic six-vertex model on the quadrant $\mathbb{Z}_{\geq0}\times\mathbb{Z}_{\geq0}$ with step initial conditions and a single second-class particle at the origin, we show almost sure convergence of the speed of the second-class…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
Recently we have presented a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration Relativity principle in phase spaces . The maximal proper-acceleration bound is $a = c^2/…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…