Related papers: Properties of a Two-Sphere Singularity
We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter $w=p/\rho$, there exist…
Wave and particle are two fundamental properties of Nature. The wave-particle duality has indicated that a quantum object may exhibit the behaviours of both wave and particle, depending upon the circumstances of the experiment. The major…
We study a model of quantum cosmology originating from a classical model of gravitation where a self interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical…
The ground state of a classical two-dimensional (2D) system with finite number of charged particles, trapped by two positive impurities charges localized at a distance (zo) from the 2D plane and separated from each other by a distance xp…
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the…
Suppose that $\theta_1,\theta_2,\dots,\theta_n$ are positive numbers and $n\ge 3$. Does there exist a sphere with a spherical metric with $n$ conical singularities of angles $2\pi\theta_1,2\pi\theta_2,\dots,2\pi\theta_n$? A sufficient…
Classical secular theory can be a powerful tool to describe the qualitative character of multi-planet systems and offer insight into their histories. The eigenmodes of the secular behavior, rather than current orbital elements, can help…
Coupling of angular motion to a spin degree of freedom gives rise to various transport phenomena in quantum systems that are beyond the standard paradigms of classical physics. Here, we discuss features of spin-orbit dynamics that can be…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
Indistinguishability of particles is normally considered to be an inherently quantum property which cannot be possessed by a classical theory. However, Saunders has argued that this is incorrect, and that classically indistinguishable…
Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…
We consider spinfoam quantum gravity. We show in a simple case that the amplitude projects over a nontrivial (curved) classical geometry. This suggests that, at least for spinfoams without bubbles and for large values of the boundary spins,…
On the basis of an alternative approach to micro-cat states (Found. of Phys., 41, No. 9, p.1502 (2011)) we develop a new model of the two-slit experiment. It explains both this particular experiment and how the wave properties of any…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as…
Wave-particle duality and the superposition of quantum mechanical states furnish quantum mechanics with unique features which distinguishes it from classical mechanics and give it the apparently counter-intuition interpretation. The two…
In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transform of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the…
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…