0000000000537707
AUTHOR
Vladimir Stephanovich
The non-Gaussian distribution of galaxies gravitational fields
We perform a theoretical analysis of the observational dependence between angular momentum of the galaxy clusters and their mass (richness), based on the method introduced in our previous paper. For that we obtain the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal interaction. Within the statistical method of Chandrasekhar we are able to show that the distribution function is determined by the form of interaction between objects and for multipole (tidal) interaction it is never Gaussian. Our calculation permits to demonstrate how the alignment of galaxies angular momenta depend on the cluster richn…
Superharmonic double-well systems with zero-energy ground states: Relevance for diffusive relaxation scenarios
Relaxation properties (specifically time-rates) of the Smoluchowski diffusion process on a line, in a confining potential $ U(x) \sim x^m$, $m=2n \geq 2$, can be spectrally quantified by means of the affiliated Schr\"{o}dinger semigroup $\exp (-t\hat{H})$, $t\geq 0$. The inferred (dimensionally rescaled) motion generator $\hat{H}= - \Delta + {\cal{V}}(x)$ involves a potential function ${\cal{V}}(x)= ax^{2m-2} - bx^{m-2}$, $a=a(m), b=b(m) >0$, which for $m>2$ has a conspicuous higher degree (superharmonic) double-well form. For each value of $m>2$, $ \hat{H}$ has the zero-energy ground state eigenfunction $\rho _*^{1/2}(x)$, where $\rho _*(x) \sim \exp -[U(x)]$ stands for the Boltzmann equil…
Influence of Dirac cone warping and tilting on the Friedel oscillations in a topological insulator
We calculate the Ruderman-Kittel-Kasuya-Yosida interaction between impurity spins, localized at the surface of an imperfect topological insulator (TI). Namely, we consider the warping and tilting of a TI Dirac cone. We show that the warping and tilting addition to the initial Rashba spin-orbit interaction (SOI) yields a highly anisotropic response to the localized spin rotation. Also, the Friedel oscillation strength of such an imperfect TI depends on the direction in its plane. Latter dependence, parametrized by Lissajous curves of spin-response components, can serve as a “fingerprint” of the initial Dirac cone distortion in the TI. The ensuing unusual dynamics is due to the interplay of S…
The influence of stellar objects mass distribution on their gravitational fields
We study the influence of the astronomical objects masses randomness on the distribution function of their gravitational fields. Based on purely theoretical arguments and comparison with extensive data, collected from observations and numerical simulations, we have shown that while mass randomness does not alter the non-Gaussian character of the gravitational fields distribution, it changes the dependencies of mean angular momenta of galaxies and clusters on their richness. The specific form of above dependence is determined by the interplay of mass distribution character and different assumptions about cluster morphology. We trace the influence of masses distribution on the time evolution …
The distribution of galaxies gravitational field stemming from their tidal interaction
We calculate the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal in- teraction. For that we apply the statistical method of Chandrasekhar (1943), used there to calculate famous Holtzmark distribution. We show that in our approach the distribution function is never Gaussian, its form being dictated by the potential of interaction between objects. This calculation permits us to perform a theoretical analysis of the relation between angular momentum and mass (richness) of the galaxy clusters. To do so, we follow the idea of Catelan & Theuns (1996) and Heavens & Peacock (1988). The main differen…
Dynamics of confined Levy flights in terms of (Levy) semigroups
The master equation for a probability density function (pdf) driven by L\'{e}vy noise, if conditioned to conform with the principle of detailed balance, admits a transformation to a contractive strongly continuous semigroup dynamics. Given a priori a functional form of the semigroup potential, we address the ground-state reconstruction problem for generic L\'{e}vy-stable semigroups, for {\em all} values of the stability index $\mu \in (0,2)$. That is known to resolve an invariant pdf for confined L\'{e}vy flights (e.g. the former jump-type process). Jeopardies of the procedure are discussed, with a focus on: (i) when an invariant pdf actually is an asymptotic one, (ii) subtleties of the pdf…
Electron spectra in double quantum wells of different shapes
We suggest a method for calculating electronic spectra in ordered and disordered semiconductor structures (superlattices) forming double quantum wells (QW). In our method, we represent the solution of Schr\"odinger equation for QW potential with the help of the solution of the corresponding diffusion equation. This is because the diffusion is the mechanism, which is primarily responsible for amorphization (disordering) of the QW structure, leading to so-called interface mixing. We show that the electron spectrum in such a structure depends on the shape of the quantum well, which, in turn, corresponds to an ordered or disordered structure. Namely, in a disordered substance, QW typically has …
Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity
AbstractWe study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal diffe…
THE INFLUENCE OF THE MASS DISTRIBUTION OF STELLAR OBJECTS ON THEIR GRAVITATIONAL FIELDS
We study the influence of the mass randomness of astronomical objects on the distribution function of their gravitational fields. Based on purely theoretical arguments and on a comparison with extensive data collected from observations and numerical simulations, we show that while mass randomness does not alter the non-Gaussian character of the gravitational field distribution, it does changes the dependencies of mean angular momenta of galaxies and clusters on their richness. The specific form of such dependencies is determined by the interplay of the character of the mass distributions and different assumptions about cluster morphology. We trace the influence of the mass distribution on t…