Abstract. Electron-positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for e + e − annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process e + e − → γ + γ * and the emission of two real hard photons: e + e − → γ + γ + γ * . A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DAΦNE, CLEO-C and B-meson factories.
It is shown that a sufficiently pure mesoscopic metallic ring will exhibit a magnetic phase transition to a low-temperature state with a persistent orbital current in zero external field (to a flux-phase state). The transition temperature and the spontaneous persistent current depend strongly on the geometry of the ring and of the Fermi surface.PACS numbers: 72.10.BgThe conductance across mesoscopic cylinders and rings made of normal metals such as Mg, Cu, or Au was found to be a periodic function of the magnetic flux enclosed by the ring, with periods h/2e and/or h/e. {~4 This implies the existence of persistent currents around rings made of nonsuperconducting metals. 2,5 "" 9 Such currents were detected recently in the magnetization of a collection of isolated mesoscopic rings. ,0The flux O, which drives the persistent current /, is the sum of the externally applied flux <£> e and of the flux 0/ from the persistent current itself, 0=0^4-0/. Most theoretical discussions neglect the second term, 2,6 which is justified for the experimental structures realized so far. However, at a sufficiently low level of elastic defect scattering, at sufficiently low temperature, and at small 0 e , 0/ can become of order <& e or even larger. This raises the possibility of orbital magnetic phase transitions. In this paper we show that in the so-called ballistic regime, a mesoscopic ring will make a transition from a hightemperature state with zero current to a low-temperature state with a persistent current already in the absence of an external field. ] l The magnitude of this spontaneous current and of the transition temperature T c depends strongly on the external geometry and on that of the Fermi surface. By model calculations for a thick torus with R « 400 A, with the Fermi velocity of Cu and with a flat Fermi surface, we find 0 < T c < 70 K. For a spherical Fermi surface with otherwise the same parameters we estimate 7Vs of a few tens of mK. We discuss the reductions of T c by inelastic and by elastic scattering.We consider a metallic torus with radius R and with circular cross section nidi I) 1 , where R and d are on a mesoscopic length scale (10 2 -10 4 lattice constants). Some elastic scattering by surface roughness and by defects within the material is admitted; 2,12 however, we assume l e > 2KR for the elastic mean free path ("ballistic" regime). A magnetic field lies parallel to the axis of symmetry, small enough to leave the radius of the Landau orbit at the Fermi energy very large compared to d [£<200 T (Ref. 8)]. It will then mainly affect the phase of the azimuthal orbitals, by shifting it according to the semiclassical boundary condition dr< p p n (r)p tpn =
A semiphenomenological model is proposed to study magnetic fluxes and currents in mesoscopic rings at nonzero temperature. The model is based on a Langevin equation for a flux subject to thermal equilibrium Nyquist noise. Quenched randomness, which mimics disorder, is included via the fluctuating parameter method. It is shown that self-sustaining and persistent currents survive in the presence of Nyquist noise and quenched disorder but the stability threshold can be shifted by noise.Quantum phenomena manifested at the mesoscopic level have attracted much experimental and theoretical attention. Phase coherence and persistent currents can be mentioned as examples. It is known that a small metallic ring threaded by a magnetic flux displays a persistent current, 1 signifying quantum coherence of electrons called coherent electrons. Moreover, it has been theoretically shown that in such a system self-sustaining currents can run even if the external flux is switched off. 2 At temperature Tϭ0, the system is in the ground state and only coherent electrons exist. 3 Then the persistent current flows without dissipation. At temperature TϾ0 the amplitude of the persistent current run by coherent electrons decreases and some electrons become ''normal'' ͑i.e., noncoherent͒. The motion of normal electrons is random and their flow is dissipative. Under some conditions, coherent conduction and normal conduction coexist, resulting in dissipation of a total current. It was confirmed experimentally 4 in that mesoscopic rings connected to a current source presented a nonzero ohmic resistance.Thermal motion of charge carriers in any conductor is a source of random fluctuations of current which is called Nyquist noise. 5 This thermal equilibrium noise is universal and exists in any conductor, irrespective of the type of conduction. Moreover, this noise increases with temperature. Therefore at relatively high temperatures and relatively large rings, universal conductance fluctuations and shot noise can be neglected, 6,7 and only Nyquist noise can play an important role. Nyquist noise generates the flux fluctuations which indirectly influence persistent currents run by coherent electrons. In the paper we analyze the steady states of magnetic fluxes and currents in a mesoscopic system subject to dissipation and fluctuations. Our main goal is to answer the question of whether persistent and self-sustaining currents survive in the presence of dissipation and fluctuations. We introduce a semiphenomenological model formulated as a Langevin equation with a noise term and with terms of a quantum origin. Our model is minimal in the sense that in the limiting cases it reduces to the well-established models of the quantum persistent current of coherent electrons and the classical Nyquist current of normal electrons. The approach used could be justified in a more elegant way applying the methods of thermofield dynamics. 8 Now, let us formulate our model: The system is a collection of rings ͑individual current channels͒ stacked along a certain axis ...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.