Nuclear reactions in flares

Rieger, E.

doi:10.1007/3-540-55246-4_93

Cited by 3 publications

(4 citation statements)

References 46 publications

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“…The flare of 1983 May 7, whose time history is shown in Figure 3, exhibits a burst on the rising part of the emission (Rieger 1989). It is again most apparent in the energy band 10-25 MeV and lacks a significant counterpart at X-ray energies.…”

Section: Observationsmentioning

confidence: 97%

Gamma-Ray Precursors of Solar Flares

Rieger

1994

International Astronomical Union Colloquium

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Bursts have been observed by the gamma-ray spectrometer on SMM at medium-and high-energy gamma-rays that precede the flare maximum. The negligible contribution of nuclear lines in the spectra of these events and their impulsive appearance suggests that they are hard-electron-dominated events superposed on the flares. Spatial resolution at gamma-ray energies will be necessary to decide whether this kind of bursts is cospatial with the flares or whether they occur in the flares' vicinity.

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Section: Observationsmentioning

confidence: 97%

Gamma-Ray Precursors of Solar Flares

Rieger

1994

International Astronomical Union Colloquium

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“…(B13) the local static susceptibility diverges only at the transition. 52 Although they may not play a role in the SK model, Griffiths singularities are likely to appear in other SMF Hamiltonians associated with disordered dynamical systems (e.g., systems where J ij is short ranged). 53 In such cases, it will be interesting to understand whether the Griffiths singularities actually correspond to observable features in the original classical system, possibly relating to the presence of separate characteristic temperatures, as is the case for the dynamical, the thermodynamic one-step replica-symmetry-breaking and the full replica-symmetry-breaking transitions in the p ≥ 3 Ising spin glass model.…”

Section: Griffiths Singularitiesmentioning

confidence: 99%

Quantum mechanical and information theoretic view on classical glass transitions

2010

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Using the mapping of the Fokker-Planck description of classical stochastic dynamics onto a quantum Hamiltonian, we argue that a dynamical glass transition in the former must have a precise definition in terms of a quantum phase transition in the latter. At the dynamical level, the transition corresponds to a collapse of the excitation spectrum at a critical point. At the static level, the transition affects the ground-state wave function: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be nonlocal and impossible to be determined with any local probe. Here we instead propose to use concepts from quantum information theory that are not centered around local order parameters, such as fidelity and entanglement measures. We show that for systems derived from the mapping of classical stochastic dynamics, singularities in the fidelity susceptibility translate directly into singularities in the heat capacity of the classical system. In classical glassy systems with an extensive number of metastable states, we find that the prefactor of the area law term in the entanglement entropy jumps across the transition. We also discuss how entanglement measures can be used to detect a growing correlation length that diverges at the transition. Finally, we illustrate how static order can be hidden in systems with a macroscopically large number of degenerate equilibrium states by constructing a three-dimensional lattice gauge model with only short-range interactions but with a finite temperature continuous phase transition into a massively degenerate phase.

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“…The sequential associative memory model is a neural network, in which the sequence of patterns is embedded as an attractor through the Hebbian (correlation) learning [12,13,14,15]. When the number of the patterns, p, is on the order O(N ), where N is the number of the processing units, the model has frustrated interactions [16]. Previously, the properties at stationary states had been exactly analyzed by the path-integral method [13,14] because the theoretical treatment of transient dynamics was difficult.…”

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confidence: 99%

“…Moreover, there is a chaotic attractor around the repellor P . The Lyapunov exponent of the chaotic attractor, which can be easily calculated from the equations (13)- (16), is positive i.e. 0.038.…”

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confidence: 99%

Low-dimensional chaos induced by frustration in a non-monotonic system

2003

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PACS. 05.45.Ac -Low-dimensional chaos. PACS. 02.70.Rr -General statistical methods. PACS. 05.45.-a -Nonlinear dynamics and nonlinear dynamical systems.Abstract. -We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a nonmonotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this large-degree-of-freedom system. Two-parameter bifurcation diagrams are obtained from the order-parameter equations. Then we analytically show that the chaos is low-dimensional at the macroscopic level when the system has some degree of frustration, but that the chaos definitely does not occur without the frustration.c EDP Sciences

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Nuclear reactions in flares

Cited by 3 publications

References 46 publications

Gamma-Ray Precursors of Solar Flares

Gamma-Ray Precursors of Solar Flares

Quantum mechanical and information theoretic view on classical glass transitions

Low-dimensional chaos induced by frustration in a non-monotonic system

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