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The single particle stability in a circular accelerator is of concern especially for operational regimes involving beam storage of hours. In the proximity to a resonance this stability domain shrinks, and the phase space fragments into a…
The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz $\gamma$-factor…
In this paper, we establish the pointwise upper and lower bounds of the gradients of solutions to a class of elliptic systems, including linear systems of elasticity, in a general narrow region and in all dimensions. This problem arises…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
A new way to define the operation of P-inversion in the theory with a magnetic charge is presented.
It is proposed that the equations of motion in periodic relativity which yielded major predictions of general relativity are exact in nature and can be applied to pulsars and inspiraling compact binaries for analyzing orbital period…
Random boundary conditions are one of the simplest realizations of quenched disorder. They have been used as an illustration of various conceptual issues in the theory of disordered spin systems. Here we review some of these results.
The presence of low-symmetry impurities or defect complexes in the zinc-blende direct-gap semiconductors (e.g. interstitials, DX-centers) results in a novel spin-orbit term in the effective Hamiltonian for the conduction band. The new…
We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
The problem concerning the form of the electrostatic field potential of the infinite charged metallic plane contacting with the metallic sphere is solved. The distributions of the surface charge densities both on the plane and the sphere…
The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
In this article we consider the problem of tether entanglement for tethered mobile robots. One of the main risks of using a tethered connection between a mobile robot and an anchor point is that the tether may get entangled with the…
We elaborate on a geometric characterization of the electromagnetic properties of matter. A fundamental complex quantity, z_{L}, is introduced to study the localization properties of extended quantum systems. z_L, which allows us to…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
We develop a framework to study the phase space of a system consisting of a scalar field rolling down an arbitrary potential with varying slope and a background fluid, in a cosmological setting. We give analytical approximate solutions of…
Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles.…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…