General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.
The existence of standing high frequency electromagnetic (EM) solitons in a fully degenerate overdense electron plasma is studied applying relativistic hydrodynamics and Maxwell equations. The stable soliton solutions are found in both relativistic and nonrelativistic degenerate plasmas.A significant amount of recent publications describe electromagnetic (EM) waves in relativistic plasmas and majority of them discuss possible roles of these waves in different astrophysical phenomena. Highly relativistic plasmas are observed in the cores of white dwarfs [2], in magnetosphere of pulsars [1], in the MeV epoch of the early Universe [4] and additionally, they probably show up in the bipolar jets in Active Galactic Nuclei (AGN) [3]. Plasma can be relativistic in two following cases: either bulk velocities of fluid cells should be close to the speed of light, or the kinetic energy of particles should be greater then their rest energy. In compact objects, such as white dwarfs and magnetars, the number densities of electrons is believed to be roughly between 10 26 cm −3 and 10 34 cm −3 [5], [6]. High density plasma can be produced in the laboratory as well, indeed contemporary petawatt laser systems have the focal intensities I = 2 × 10 22 W/cm 2 [7]. Moreover, pulses with higher than I = 10 26 W/cm 2 intensities are expected to be achieved soon [8]. Superdense plasmas might be formed with densities in the range of 10 23 cm −3 and 10 28 cm −3 [9], during the interaction of such EM pulses with solid or gaseous targets. Such plasma will be opaque for conventional laser systems operate at wavelengths λ ∼ 1µm. The Linac Coherent Light Source (LCLS) is an X-ray free-electron laser produce femtosecond powerful pulses of coherent soft and hard X-rays with wavelengths from 2.2nm to 0.06nm [10]. Exploiting the possibility to focus X-ray laser beams on a spot with down to laser wavelength, the focal intensities I ≃ 7 × 10 25 W/cm 2 are expected to be reached [11]. Successful operation of X-ray free-electron lasers in different centers world wide [12] opens up new perspectives to study the EM pulse penetration and its subsequent dynamics in super dense plasma in laboratory conditions.Highly compressed plasma with an average interparticle distance smaller than their thermal de Broglie wavelength, can be considered as a degenerate Fermi gas. When plasma density increases, the more ideal it becomes and the interactions of its particles can be neglected [13].EM solitons in classical relativistic plasma is being studied intensively [14], but existence and stability of solitary solutions in degenerate quantum relativistic plasma are investigated mostly for low frequencies (see [15] and references therein). The publication goal is to consider existence of a standing, high frequency EM soliton in the relativistic degenerate electron plasma. Importance of the standing soliton solutions for overall dynamics of EM pulses is established theoretically [16] -[19] as well as experimentally for classical relativistic plasma [20]. These publicatio...
Cascading failures abound in complex systems and the Bak–Tang–Weisenfeld (BTW) sandpile model provides a theoretical underpinning for their analysis. Yet, it does not account for the possibility of nodes having oscillatory dynamics, such as in power grids and brain networks. Here, we consider a network of Kuramoto oscillators upon which the BTW model is unfolding, enabling us to study how the feedback between the oscillatory and cascading dynamics can lead to new emergent behaviors. We assume that the more out-of-sync a node is with its neighbors, the more vulnerable it is and lower its load-carrying capacity accordingly. Also, when a node topples and sheds load, its oscillatory phase is reset at random. This leads to novel cyclic behavior at an emergent, long timescale. The system spends the bulk of its time in a synchronized state where load builds up with minimal cascades. Yet, eventually, the system reaches a tipping point where a large cascade triggers a “cascade of larger cascades,” which can be classified as a dragon king event. The system then undergoes a short transient back to the synchronous, buildup phase. The coupling between capacity and synchronization gives rise to endogenous cascade seeds in addition to the standard exogenous ones, and we show their respective roles. We establish the phenomena from numerical studies and develop the accompanying mean-field theory to locate the tipping point, calculate the load in the system, determine the frequency of the long-time oscillations, and find the distribution of cascade sizes during the buildup phase.
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