On the Mean Value of the Potential and Kinetic Energy of an Electron in a Hydrogenlike Atom

Russian Physics Journal - The mean values of the potential $$ \left\langle \hat{\varPi}\right\rangle $$ and kinetic $$ \left\langle \hat{\mathrm{T}}\right\rangle $$ energy of an electron in a...     

On Realization of an Extremely Small Shift of MR Frequency in a Wide Range of Operating Temperatures in Rubidium Atomic Clock on 87 Rb Cell with Two Anti-Relaxation Components (Coating + Inert Gas, 40 Ar)

One of the most important problems in achieving daily frequency instability $$\sigma _{y} < 5 \cdot 10^{{ - 14}}$$ of on-board rubidium atomic clocks on absorption cell with working 87Rb atoms and mixture of buffer gases is realization of the TFS parameter — of temperature frequency shift $$\delta \nu \left( T \right)$$ at the level of $$\ \le 3 \cdot 10^{{ - 12}} /\, {^\circ } {\text{C}}.$$ The temperature dependence of the microwave “0–0” transition frequency $$\nu \left( T \right)$$ has an extremum with a small flat top ∆T ~ 0.5 °C to which the 87Rb-cell operating temperature is tuned. Significant difficulties arise in maintaining the high stability of this small ∆T zone under conditions of increased 87Rb cell operating temperature, $$T>70\, ^\circ{\rm C}$$, with an accuracy of < 0.005 °C for a day or more. To solve this problem, authors proposed a new type of 87Rb absorption cell with two dissimilar anti-relaxation (AR) components (wall coating + buffer gas, 40Ar) and created a special physical setup for optical spin pumping of 87Rb atoms at the microwave magnetic resonance frequency, $$\nu \sim \;6.834\,\;{\text{GHz}}$$, with a resolution $$0.01 \,\mathrm{H}\mathrm{z}$$. Investigations have shown TFS $$\sim 1.4 \cdot 10^{{ - 12}} /\;{{^\circ }} {\text{C}}$$ in significantly expanded (by an order of magnitude) zone, $$\Delta T$$ ≃ $$5 \left(\pm 1\right)\,\, ^\circ{\rm C} ,$$ in the operating temperature range of $$\left( {35 \div 41} \right)\;^{ \circ } {\text{C}},$$ which is ensured inside a satellite, for example. The simultaneous effect of AR-components causes the maximum mutual compensation of temperature frequency shifts in the extended ∆T zone. The experimental data show the possibility realizing daily frequency instability $$\sigma _{y} \sim 1 \cdot 10^{{ - 14}}$$ of the on-board atomic clock on 87Rb cell with two dissimilar AR-components (wall coating + inert gas, 40Ar).     

Lifshitz Tails for the Fractional Anderson Model

Journal of Statistical Physics - We consider the d-dimensional fractional Anderson model $$(-\Delta )^\alpha + V_\omega $$ on $$\ell ^2({\mathbb {Z}}^d)$$ where $$0&lt;\alpha \leqslant 1$$....     

On a homotopy version of the Duflo isomorphism

Letters in Mathematical Physics - For a finite-dimensional Lie algebra $$\mathfrak {g}$$, the Duflo map $$S\mathfrak {g}\rightarrow U\mathfrak {g}$$ defines an isomorphism of $$\mathfrak...     

Hopf Bifurcations,Drops in the Lid-Driven Square Cavity Flow

The lid-driven square cavity flow is investigated by numerical experiments. It is found that from $ \mathrm{Re} $$=$ $5,000 $ to $ \mathrm{Re} $$=$$ 7,307.75 $ the solution is stationary, but at $ \mathrm{Re}$$=$$7,308 $ the solution is time periodic. So the critical Reynolds number for the first Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 7,307.75 $ and $ \mathrm{Re} $$=$$ 7,308 $. Time periodical behavior begins smoothly, imperceptibly at the bottom left corner at a tiny tertiary vortex; all other vortices stay still, and then it spreads to the three relevant corners of the square cavity so that all small vortices at all levels move periodically. The primary vortex stays still. At $ \mathrm{Re} $$=$$ 13,393.5 $ the solution is time periodic; the long-term integration carried out past $ t_{\infty} $$=$$ 126,562.5 $ and the fluctuations of the kinetic energy look periodic except slight defects. However, at $ \mathrm{Re} $$=$$ 13,393.75 $ the solution is not time periodic anymore: losing unambiguously, abruptly time periodicity, it becomes chaotic. So the critical Reynolds number for the second Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 13,393.5 $ and $ \mathrm{Re} $$=$$ 13,393.75 $. At high Reynolds numbers $ \mathrm{Re} $$=$$ 20,000 $ until $ \mathrm{Re} $$=$$ 30,000 $ the solution becomes chaotic. The long-term integration is carried out past the long time $ t_{\infty} $$=$$ 150,000 $, expecting the time asymptotic regime of the flow has been reached. The distinctive feature of the flow is then the appearance of drops: tiny portions of fluid produced by splitting of a secondary vortex, becoming loose and then fading away or being absorbed by another secondary vortex promptly. At $ \mathrm{Re} $$=$$ 30,000 $ another phenomenon arises—the abrupt appearance at the bottom left corner of a tiny secondary vortex, not produced by splitting of a secondary vortex.     

Decays of Higgs Bosons Into a Gauge Boson and a Fermion-Antifermion Pair

Russian Physics Journal - Decay channels of the Higgs boson H into a gauge boson and a longitudinally polarized fermion-antifermion pair $$ H\to Z\overline{ff} $$ and $$ H\to...     

A look at multiparticle production via modified combinants

The European Physical Journal A - The transverse momentum ($$p_{T}$$) distribution of strange hadrons ($$K_{S}^{0}$$ and $$\varLambda $$) and multi-strange hadrons( $$\varXi $$ and $$\varOmega $$)...     

On the problem of splitting deformations of super Riemann surfaces

Letters in Mathematical Physics - An odd deformation of a super Riemann surface $$\mathcal {S}$$ is a deformation of $$\mathcal {S}$$ by variables of odd parity. In this article, we study the...     

Higher spin $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ s l 2 R-matrix from equivariant (co)homology

Letters in Mathematical Physics - We compute the rational $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ R-matrix acting in the product of two spin- $$\ell \over 2$$ ( $${\ell \in {\mathbb {N}}}$$ )...     

Peculiarity of the $${}^{{12}}$$ C(0 $${{}^{+}}$$ ) and $${}^{{12}}$$ C(2 $${{}^{+}}$$ ) Energy Spectrum in a 3 $$\alpha$$ Model

Physics of Atomic Nuclei - Lowest energy spectrum of the $${}^{12}$$ C nucleus is analyzed in the 3 $$\alpha$$ -cluster model with a deep $$\alpha\alpha$$ potential of Buck, Friedrich and Wheatley...     

Search for H → WW → $$\ell \nu \ell \nu $$ Decays of a Heavy Higgs Boson Produced in pp Collisions at $$\sqrt s $$ = 13 TeV Using a 139-fb–1 Event Sample Recorded by the ATLAS Experiment

Physics of Atomic Nuclei - Events with final-state electron and muon pairs produced in pp collisions at $$\sqrt s $$ = 13 TeV are analyzed toward detecting H → WW → $$\ell \nu \ell \nu...     

Coherent Photoproduction of Neutral Pseudoscalar Mesons $$\boldsymbol{\pi^{0}\pi^{0}}$$ and $$\boldsymbol{\pi^{0}\eta}$$ on Light Nuclei

Physics of Atomic Nuclei - The coherent photoproduction of $$\pi^{0}\pi^{0}$$ and $$\pi^{0}\eta$$ on nuclei in the mass-number region of $$A\leqslant 7$$ is studied systematically over the range...     

Search for Scalar Resonance in the ωϕ System in the Pion-Nuclear Interaction at Momentum of 29 GeV/c

Physics of Atomic Nuclei - The charge-exchange reaction $${{\pi }^{ - }}p \to n\omega (783)\phi (1020)$$ , $$\omega \to {{\pi }^{ + }}{{\pi }^{ - }}{{\pi }^{0}}$$ , $$\phi \to {{K}^{ + }}{{K}^{ -...     

Frobenius manifolds and a new class of extended affine Weyl groups of A-type

Letters in Mathematical Physics - We present a new class of extended affine Weyl groups $$\widetilde{W}^{(k,k+1)}(A_l)$$ for $$1\le k     

Landau–Khalatnikov–Fradkin Transformation and Even $$\zeta$$ Functions

Physics of Atomic Nuclei - An exact formula that relates standard $$\zeta$$ functions and so-called hatted $$\zeta$$ ( $$\hat{\zeta}$$ ) functions in all orders of perturbation theory is presented....     

Non-ergodic delocalization in the Rosenzweig–Porter model

Letters in Mathematical Physics - We consider the Rosenzweig–Porter model $$H = V + \sqrt{T}\, \varPhi $$ , where V is a $$N \times N$$ diagonal matrix, $$\varPhi $$ is drawn from the $$N...     

Studying the $$\alpha$$ -Decay Half-Lives of Nuclei in the Range $${68\leqslant Z\leqslant 118}$$ by Double-Folding and Cluster Formation Formalisms

Physics of Atomic Nuclei - In this study, we have systematically calculated $$\alpha$$ -decay half-lives for even–even nuclei in the range $$68\leqslant Z\leqslant 118$$ within the...     

Three Classes of Orthomodular Lattices

Let denote the class of all orthomodular lattices and denote the class of those that are commutator-finite. Also, let denote the class of orthomodular lattices that satisfy the block extension property, those that satisfy the weak block extension property, and those that are locally finite. We show that the following strict containments hold: Dedicated to the memory of Günter Bruns.     

Neutron Structure Properties of Titanium in a Supernova

Physics of Atomic Nuclei - We calculated important neutron matter properties of $${}^{44}$$ Ti in the envelope of supernova SN 1987A and its isotopic chain ( $$12\leqslant N\leqslant 82$$ ) using...     

Adsorption of oxygen on low-index surfaces of Ti3Al alloy

Physics of the Solid State - The atomic and electronic structure of the three surfaces of Ti3Al alloy—(0001), ( $$1\bar 100$$ ), and ( $$11\bar 20$$ )—is calculated by the projector...