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 $$0<\alpha \leqslant 1$$....     

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 $$\varOmega $$)...     

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}^{ -...     

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).     

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....     

Free Self-decomposability and Unimodality of the Fuss–Catalan Distributions

Journal of Statistical Physics - We study properties of the Fuss–Catalan distributions $$\mu (p,r)$$, $$p\ge 1$$, $$01$$ there exists $$r_{0}(p)$$, with $$p-1     

Experimental and Evaluated Data on the Photodisintegration of $${}^{{197}}$$ Au

Physics of Atomic Nuclei - The cross sections evaluated for the ( $$\gamma,1n$$ ) and ( $$\gamma,2n$$ ) partial photoneutron reactions on $${}^{\textrm{197}}$$ Au by means of objective physical...     

Poisson Statistics for Beta Ensembles on the Real Line at High Temperature

Journal of Statistical Physics - This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $$\beta N \rightarrow const \in (0, \infty )$$, with N...     

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...     

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...     

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- $$\ell \over 2$$ ( $${\ell \in {\mathbb {N}}}$$ )...     

Cosmological Acceleration as a Consequence of Quantum de Sitter Symmetry

Physics of Particles and Nuclei Letters - Physicists usually understand that physics cannot (and should not) derive that $$c \approx 3 \times {{10}^{8}}$$ m/s and $$\hbar \approx 1.054 \times...     

Reliability of Results of Photonuclear Experiments for $${}^{58}$$ Ni

Physics of Atomic Nuclei - The reliability of experimental data on the cross sections ( $$\gamma,1n$$ ) and ( $$\gamma,2n$$ ) partial reaction cross sections measured for $${}^{58}$$ Ni nuclei in...     

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...     

Local Resolvent Estimates for <Emphasis Type="Italic">N</Emphasis>-body Stark Hamiltonians

For an N-body Stark Hamiltonian , the resolvent estimate holds uniformly in with Re and Im , where , and is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by introducing the localization in the configuration space, a refined resolvent estimate holds uniformly in with Re and Im . Dedicated to Professor Hideo Tamura on the occasion of his 60th birthday     

A measurement of the branching ratio∑ +→pγ/∑ +→pπ 0⋆

In an experiment performed in the CERN SPS hyperon beam we have obtained a value for the branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to p\pi }}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to p\pi }}^0 of\left( {2.46_{ - 0.35}^{ + 0.30} } \right) \times 10^{ - 3} ,$$ corresponding to a branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to all}}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to all}}of\left( {1.27_{ - 0.18}^{ + 0.16} } \right) \times 10^{ - 3} .$$ This result is discussed in the context of present understanding of hyperon radiative decays.     

Conformal properties of nonpeeling vacuum space-times

In a previous paper we investigated a class ofnonpeeling asymptotic vacuum solutions which were shown to admit finite expressions for the Winicour-Tamburino energy-momentum and angular momentum integrals. These solutions have the property that $$\psi _0 = O(r^{ - 3 - \in _0 } ), \in _0 \leqslant 2$$ and $$\psi _1 = O(r^{ - 3 - \in _1 } ), \in _1< \in _0 and \in _1< 1$$ withψ ₂,ψ ₃, andψ ₄ having the same asymptotic behavior as they do for peeling solutions. The above investigation was carried out in the physical space-time. In this paper we examine the conformal properties of these solutions, as well as the more general Couch-Torrence solutions, which include them as a subclass. For the Couch-Torrence solutions $$\begin{gathered} \psi _0 = O(r^{ - 2 - \in _0 } ) \hfill \\ \psi _1 = O(r^{ - 2 - \in _1 } ), \in _1< \in _0 {\text{ }}and \in _1 \leqslant 2 \hfill \\ \end{gathered} $$ and , $$\psi _2 = O(r^{ - 2 - \in _2 } ),{\text{ }} \in _2< \in _1 {\text{ }}and \in _2 \leqslant 1$$ withψ ₃ andψ ₄ behaving as they do for peeling solutions. It is our purpose to determine how much of the structure generally associated with peeling space-times is preserved by the nonpeeling solutions. We find that, in general, a three-dimensional null boundary (?⁺) can be defined and that the BMS group remains the asymptotic symmetry group. For the general Couch-Torrence solutions several physically and/or geometrically interesting quantities     

On gravitational Stefan-Boltzmann law and Casimir effect in FRW universe

General Relativity and Gravitation - We perform, in a manifestly $$\mathrm{SO}(n-1,1)$$ [ $$\mathrm{SO}(n)$$ ] covariant fashion, the Hamiltonian analysis of general relativity in n dimensions...     

A global attracting set for the Kuramoto-Sivashinsky equation

New bounds are given for the L²-norm of the solution of the Kuramoto-Sivashinsky equation $$\partial _t U(x,t) = - (\partial _x^2 + \partial _x^4 )U(x,t) - U(x,t)\partial _x U(x,t)$$ , for initial data which are periodic with periodL. There is no requirement on the antisymmetry of the initial data. The result is $$\mathop {\lim \sup }\limits_{t \to \infty } \left\| {U( \cdot ,t)} \right\|_2 \leqslant const. L^{8/5} $$ .     

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