field approach
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2022 ◽  
pp. 1-22
François Baccelli ◽  
Michel Davydov ◽  
Thibaud Taillefumier

Abstract Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called ‘Poisson hypothesis’. However, in most applications this hypothesis is only conjectured. In this paper we establish the Poisson hypothesis for a general class of discrete-time, point-process-based dynamics that we propose to call fragmentation-interaction-aggregation processes, and which are introduced here. These processes feature a network of nodes, each endowed with a state governing their random activation. Each activation triggers the fragmentation of the activated node state and the transmission of interaction signals to downstream nodes. In turn, the signals received by nodes are aggregated to their state. Our main contribution is a proof of the Poisson hypothesis for the replica-mean-field version of any network in this class. The proof is obtained by establishing the propagation of asymptotic independence for state variables in the limit of an infinite number of replicas. Discrete-time Galves–Löcherbach neural networks are used as a basic instance and illustration of our analysis.

S N Nedelko ◽  
Aleksei Nikolskii ◽  
Vladimir Voronin

Abstract An impact of nonperturbatively treated soft gluon modes on the value of anomalous magnetic moment of muon a_µ is studied within the mean-field approach to QCD vacuum and hadronization. It is shown that radial excitations of vector mesons strongly enhance contribution of hadronic vacuum polarization to a_µ, doubling the contribution of one-meson processes compared to the result for ground state mesons. The mean field also strongly influences the hadronic light-by-light scattering contribution due to the Wilson line in quark propagators.

Tuba Tekin ◽  
Isabel Blum ◽  
Bjoern Delfs ◽  
Ann-Britt Schönfeld ◽  
Bjoern Poppe ◽  

Abstract Objective This study investigates the perturbation correction factors of air-filled ionization chambers regarding their depth and magnetic field dependence. Focus has been placed on the displacement or gradient correction factor Pgr. Besides, the shift of the effective point of measurement Peff that can be applied to account for the gradient effect has been compared between the cases with and without magnetic field. Approach The perturbation correction factors have been simulated by stepwise modifications of the models of three ionization chambers (Farmer 30013, Semiflex 3D 31021 and PinPoint 3D 31022, all from PTW Freiburg). A 10 cm x 10 cm 6 MV photon beam perpendicular to the chamber’s axis was used. A 1.5 T magnetic field was aligned parallel to the chamber’s axis. The correction factors were determined between 0.4 and 20 cm depth. The shift of Peff from the chamber's reference point Pref, ∆z, was determined by minimizing the variation of the ratio between dose-to-water Dw(zref+∆z) and the dose-to-air Dair(zref) along the depth. Main Results The perturbation correction factors with and without magnetic field are depth dependent in the build-up region but can be considered as constant beyond the depth of dose maximum. Additionally, the correction factors are modified by the magnetic field. Pgr at the reference depth is found to be larger in 1.5 T magnetic field than in the magnetic field free case, where an increase of up to 1% is obserbed for the largest chamber (Farmer 30013). The magnitude of ∆z for all chambers decreases by 40% in a 1.5 T magnetic field with the sign of ∆z remains negative. Significance In reference dosimetry, the change of Pgr in a magnetic field can be corrected by applying the magnetic field correction factor kB Qmsr when the chamber is positioned with its Pref at the depth of measurement. However, due to the depth dependence of the perturbation factors, it is more convenient to apply the ∆z-shift during chamber positioning in relative dosimetry.

2022 ◽  
Vol 130 (1) ◽  
pp. 33
Kieran M. Smith ◽  
Michael F. Reid ◽  
Jon-Paul R. Wells

We report Zeeman infra-red spectroscopy of electronic-nuclear levels of 5I8 →5I7 transitions of Ho3+ in the C4v(F−) centre in CaF2 with the magnetic field along the ⟨111⟩ direction of the crystal. Transitions to the lowest 5I7 state, an isolated electronic doublet, and the next group of states, a pseudo-quadruplet consisting of a doublet and two nearby singlets, exhibit strongly non-linear Zeeman splittings and intensity variations. Simulated spectra based upon a crystal-field analysis give an excellent approximation to the data, illustrating the strong predictive ability of the parametrised crystal-field approach. Anti-crossings in the hyperfine splittings, the basis of quantum information storage in rare-earth doped insulating dielectrics, are also predicted.

2021 ◽  
Vol 130 (24) ◽  
pp. 244302
Yuri Yu. Tarasevich ◽  
Andrei V. Eserkepov ◽  
Irina V. Vodolazskaya

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