Related papers: Relativistic phase space: dimensional recurrences
In the case of one extra dimension, well known Newton's potential $\phi (r_3)=-G_N m/r_3$ is generalized to compact and elegant formula $\phi(r_3,\xi)=-(G_N m/r_3)\sinh(2\pi r_3/a)[\cosh(2\pi r_3/a)-\cos(2\pi\xi/a)]^{-1}$ if…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…
Two-term recurrence relations are supplied for indefinite integrals of functions that involve factors of the types ${P_2}^n$, ${P_3}^n$, ${P_4}^n$, ${P_1}^m {Q_1}^n$, $E_1 {P_1}^n$, ${P_1}^m {Q_2}^n$, $E_1 {P_2}^n$, ${P_2}^m {Q_2}^n$,…
Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…
We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…
For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the…
We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study…
The quantum-phase-field concept of matter is revisited with special emphasis on the introverted view of space. Extroverted space surrounds physical objects, while introverted space lies in between physical objects. Space between objects…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
We formulate analytically the reflection of a one dimensional, expanding free wave-packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule and a classical object. We derive a threshold…
We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards…
The force fields of interior boundaries of matters are calculated as superposition of fields of modified Sierpinski carpet. The long-range effect interaction in irradiated crystals is introduced as various manifestations of second order…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.
TeV size extra dimensions introduce domain walls. Such walls are inconsistent with CMB anisotropies. Either inflationary dynamics washes them out, or the reheating temperature is lower then the temperature at which the walls start forming…
Broad classes of plasma phenomena can be understood in terms of phase-space rearrangements. For example, the net effect of a wave-particle interaction may consist of moving populations of particles from one region of phase space to another.…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
It is shown that if our visible universe is a thin trapped shell in a five-dimensional universe, all matter in it may be connected almost instantaneously through the fifth dimension. What appears to be action at a distance is then…