abstract

A hypothetic Hidden Sector of the Universe, consisting of sterile fermions (“sterinos”) and sterile mediating bosons (“sterons”) of mass dimension 1 (not 2!) — the last described by an antisymmetric tensor field — requires to exist also a scalar isovector and scalar isoscalar in order to be able to construct electroweak invariant coupling (before spontaneously breaking its symmetry). The introduced scalar isoscalar might be a resonant source for the diphoton excess of 750 GeV, suggested recently by experiment.

abstract

We study the decay law for a moving unstable particle. The usual time-dilatation formula states that the decay width for an unstable state moving with a momentum \(p\) and mass \(M\) is \(\tilde {\mit \Gamma }_{p}={\mit \Gamma } M/\sqrt {p^{2}+M^{2}}\) with \({\mit \Gamma }\) being the decay width in the rest frame. In agreement with previous studies, we show that in the context of QM as well as QFT, this equation is not correct provided that the quantum measurement is performed in a reference frame in which the unstable particle has momentum \(p\) (note, a momentum eigenstate is not a velocity eigenstate in QM). We then give, to our knowledge for the first time, an analytic expression of an improved formula and we show that the deviation from \(\tilde {\mit \Gamma }_{p}\) has a maximum for \(p/M=\sqrt {2/3},\) but is typically very small. Then, the result can be easily generalized to a momentum wave packet and also to an arbitrary initial state. Here, we give a very general expression of the non-decay probability. As a next step, we show that care is needed when one makes a boost of an unstable state with zero momentum/velocity: namely, the resulting state has zero overlap with the elements of the basis of unstable states (it is already decayed!). However, when considering a spread in velocity, one finds again that \(\tilde {\mit \Gamma }_{p}\) is typically a very good approximation. The study of a velocity wave packet represents an interesting subject which constitutes one of the main outcomes of the present manuscript. In the end, it should be stressed that there is no whatsoever breaking of special relativity, but as usual in QM, one should specify which kind of measurement on which kind of state is performed.

abstract

In the present work, we report a comprehensive analysis of shell-model results for high-spin states of \(^{87}\)Sr and \(^{87}\)Zr for recently available experimental data within the full \(f_{5/2}pg_{9/2}\) model space using JUN45 and jj44b effective interactions developed for this model space. In this work, we have compared the energy levels, electromagnetic transition probabilities, quadrupole and magnetic moments with available experimental data. We have confirmed the structure of high-spin states of these two nuclei which were tentatively assigned in the recent experimental work. In the case of \(^{87}\)Sr, for positive-parity states up to \(\sim 7.5\) MeV, both interactions predict very good agreement with experimental data, while negative-parity states are slightly suppressed in jj44b calculation. For the \(^{87}\)Zr nucleus, the jj44b interaction predicts higher energies for the negative-parity states beyond \(J \geq 27/2^{-}\). The configuration, which have one hole in \(\nu g_{9/2}\) orbital, is responsible for generating the states in \(^{87}\)Sr. In the case of \(^{87}\)Zr, low-lying positive-parity states come with the configuration having three holes in the \(\nu g_{9/2}\), while the odd-parity states have configuration \(\nu (f_{5/2}^{-1}g_{9/2}^{-2})\).

abstract

We present in this paper how the single-photon wave function for transversal photons (with the direct sum of ordinary unitary representations of helicity 1 and \(-1\) acting on it) is subsumed within the formalism of Gupta–Bleuler for the quantized free electromagnetic field. The rigorous Gupta–Bleuler quantization of the free electromagnetic field is based on our generalization (published formerly) of the Mackey theory of induced representations which includes representations preserving the indefinite Krein-inner-product given by the Gupta–Bleuler operator. In particular, it follows that the results of Białynicki-Birula on the single-photon wave function may be reconciled with the causal perturbative approach to QED.

abstract

We revisit the concept of chiral disorder in QCD in the presence of a QED magnetic field \(|eH|\). Weak magnetism corresponds to \(|eH|\le 1/\rho ^2\) with \(\rho \approx 1/3\) fm the vacuum instanton size, while strong magnetism the reverse. Asymptotics (ultra-strong magnetism) is in the realm of perturbative QCD. We analyze weak magnetism using the concept of the quark return probability in the diffusive regime of chiral disorder. The result is in agreement with expectations from chiral perturbation theory. We analyze strong and ultra-strong magnetism in the ergodic regime using random matrix theory including the effects of finite temperature. The strong magnetism results are in agreement with the currently reported lattice data in the presence of a small shift of the Polyakov line. The ultra-strong magnetism results are consistent with expectations from the perturbative QCD. We suggest a chiral random matrix effective action with matter and magnetism to analyze the QCD phase diagram near the critical points under the influence of magnetism.

abstract

We study a class of percolation models in complex networks in which nodes are characterized by changed hidden variables reflecting the variational properties of nodes, and the occupied probability of each link is determined by the hidden variables of the end nodes at each time. By the mean field theory, we find analytical expressions for the phase of percolation transition. It is determined by the distribution of the hidden variables for the nodes and the occupied probability between pairs of them. Moreover, the analytical expressions obtained are checked by means of numerical simulations on a particular model. Besides, the general model can be applied to describe and control practical diffusion models, such as disease diffusion model, scientists cooperation networks, and so on.

abstract

In this paper, we employ the multiscale multifractal analysis (MMA) method to investigate the fractal properties of wind speed records depending on their magnitude of the fluctuations and the timescale. The MMA results show that the high-frequency wind speed records appear to be far more complex and contain abundant information, which cannot be detected by the popular scaling analysis method, i.e. , multifractal detrended fluctuation analysis (MF-DFA). Comparing the Hurst surfaces of nine groups of wind speed data, we find that for the negative \(q\)s, all the surfaces exhibit intensive fluctuations and significant differences. In addition, the distribution histograms of Hurst surfaces for the positive \(q\)s reveal that the large fluctuations of all wind speed data depend on the spatial positions, which is further illustrated by the wind roses. Subsequent analysis of shuffled and surrogate series reveals that the multifractality of wind speed time series is mainly stemming from the long-range correlation, while has less to do with broad probability density function. Finally, the effect of sampling period is discussed. The results suggest that a sampling period of 20 min is sufficient to characterize multiscale multifractal properties of high-frequency wind speed data.

abstract

This work attempts to investigate the influence of a minimal length scale on the statistical aspects of the paramagnetic system. The angular momentum operator and the magnetostatic field in 3-dimensional space described by the Kempf algebra is studied in the special case of \(\alpha '=2\alpha \) up to the first order over the deformation parameter \(\alpha \). The modified thermodynamical characteristics of the paramagnetic system such as mean energy, entropy, magnetization are obtained. It is shown that the relative magnetization approximately depends on the deformation parameter and orbital angular momentum. The upper limit of the deformation parameter is estimated.