The current theoretical estimations lead to cross-sections for $AA \to \gamma \gamma AA$ which are somewhat smaller than the measured ones by the ATLAS and CMS Collaborations, In our recent paper, we estimated the contribution of inelastic channels to the Light-by-Light (LbL) scattering in ultraperipheral collisions (UPC) of heavy ions, in which one or both of the incident nuclei dissociate ($A A \to \gamma \gamma X Y$ where $X, Y = A, A'$) due to the photon emission. These new mechanisms are related to extra emissions that are difficult to identify and may be misinterpreted as enhanced $\gamma \gamma \to \gamma \gamma$ scattering. We include processes of coupling of photons to individual nucleons in addition to coherent coupling to the whole nuclei. Both elastic (nucleon in the ground state) and inelastic (nucleon in an excited state) are taken into account. The inelastic nucleon fluxes are calculated using CTEQ18QED photon distribution in nucleon. The inelastic photon fluxes are shown and compared to standard photon fluxes in the nucleus. We present the ratio of the inelastic corrections to the standard contribution to the nuclear cross section. We find that for the ATLAS kinematics the inelastic corrections grow with $M_{\gamma \gamma}$ and rapidity difference. Our results indicate that the inelastic contributions can be of the order of 20-40 \% of the traditional (no nuclear excitation) predictions. We discuss also uncertainties due to the choice of factorization scale.

An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA) into 2D. It is tested on synthetic structures to ensure its effectiveness, with results indicating consistency. The interdisciplinary potential of this method in describing real surfaces and images is demonstrated, revealing previously unknown directional multifractality in data sets from the Martian surface and the Crab Nebula. The multifractal characteristics of Jackson Pollock's paintings are also analyzed. The results point to their evolution over the time of creation of these works.

Since the pioneering work Lohani et. al., Phys. Rev. X 9, 041063 (2019), it became clear that quantum skyrmions have highly unusual properties as compared to the classical skyrmions and, due to their quantumness, cannot be described by continuous magnetic textures akin to the classical skyrmions. Competing nearest-neighbor and next-nearest-neighbor ferromagnetic and antiferromagnetic interactions in triangular spin-frustrated magnets lead to the formation of quantum skyrmion states. In frustrated magnets, skyrmions are characterized by the helical degree of freedom, which can store quantum information. In the limit of a weak electric field, the system can be described as a two-level system, i.e., a skyrmion qubit. Here, we propose a more general formulation of the problem and obtain general analytic solution of the model previously introduced in Psaroudaki et. al., Phys. Rev. Lett. 127, 067201 (2021). Our solution is valid not only for small barrier but for the arbitrary electric field. In the case of a significant barrier, we prove that the system's state is not a Skyrmion qubit as it was thought before, but a Skyrmion qudit. We constructed the density matrix of the Skyrmion qudit and studied its evolution in time. The obtained results suggest that the proposed model can be exploited further to meet the needs of quantum information theory and quantum skyrmionics. We showed that the $l_1$ norm of coherence of the skyrmion quantum qudit is a thousand times larger than the coherence of the skyrmion quantum qubit. The obtained result opens new perspectives for quantum skyrmion-based resource theory.

We discuss inclusive electromagnetic dissociation processes in proton--proton ($pp$) and proton--nucleus ($pA$) scattering at the LHC where one or both of the protons dissociate. These processes which involve the exchange of a virtual photon in the $t$--channel are calculable in terms of deep inelastic structure functions (virtual photoabsorption cross sections). For the $pA \to XA$ reaction there emerges the possibility of measuring the total photoabsorption cross section on the proton at very high energies.

In ultraperipheral heavy-ion collisions (UPCs) at the Large Hadron Collider (LHC) Pb nuclei are excited through interactions induced by strong electromagnetic fields. The expected excitation energy could reach hundreds MeV, which leads to the subsequent emission of various particles, including neutrons, protons, and alpha particles. To accurately describe deexcitation of nuclei, we have developed two novel approaches. The first method utilizes the Heavy Ion Phase Space Exploration (HIPSE) model to simulate pre-equilibrium emissions and to estimate the excitation energy of the remaining nucleus. Our second approach introduces a new technique for modeling the excitation energy of the nucleus. This method consists of a two-component function to represent the excitation energy distribution more precisely, accounting for the energy loss due to the interaction between photons and quasi-deuteron. Both of these modeling techniques are integrated with the results produced by the GEMINI++ generator, which implements the Hauser-Feshbach formalism to simulate the statistical decay of excited nuclei. The alternative calculations are done with EMPIRE platform. Using these approaches, we obtained the cross sections for the emission of neutrons, protons, and alpha particles resulting from UPC at the LHC. Our results were compared with the experimental data of the ALICE group on neutron and proton multiplicities.

We discuss the production of $D$ mesons and $J/\psi$ quarkonia in proton-nucleus collisions in the fixed-target LHCb experiment. We consider gluon-gluon fusion within $k_t$-factorization, processes initiated by intrinsic charm in the nucleon and perturbative recombination mechanism. All the mechanisms seem to be necessary to describe the LHCb experimental data. We get an upper limit for the probability of the large-$x$ $c \bar c$ Fock component in the nucleon, which is slightly less than 1 \%. The recombination mechanism allows the description of $D^0$ and $\bar D^0$ asymmetry observed by the LHCb collaboration.\\ We also discuss the production of $J/\psi$ quarkonia, including color singlet mechanisms. We include $g^* g^* \to J/\psi g$ and $g^* g^* \to \chi_c(1^+,2^+)(\to J/\psi \gamma)$within$k_t$-factorization approach. Different unintegrated gluon distributions from the literature are used. A reasonable agreement is achieved with some distributions from the literature.

Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity, which often manifests itself in a fractal or even multifractal structure. As a generalisation of fractal analysis, multifractal analysis of complex networks is a useful tool for the identification and quantitative description of the spatial hierarchy of both theoretical and numerical fractal patterns. Nowadays, there are many methods of multifractal analysis. However, all these methods take into account only the fact of connection between nodes (and eventually the weight of edges) and do not take into account the real positions (coordinates) of nodes in space. However, intuition suggests that the geometry of network nodes' position should have a significant impact on its true fractal structure. Many networks identified in nature (e.g. air connection networks, energy networks, social networks, mountain ridge networks, networks of neurones in the brain, street networks) have their own often unique and characteristic geometry, which is not taken into account in the identification process of multifractality in commonly used methods. In this paper, we propose a multifractal network analysis method that takes into account both connections between nodes and the location coordinates of nodes (network geometry). We show the results for different geometrical variants of the same network and reveal that this method, contrary to the commonly used method, is sensitive to changes in network geometry. We carry out tests for synthetic as well as for real-world networks.

We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 min to 10 min. Our study is based on empirical data from the American stock market consisting of tick-by-tick recordings of 31 stocks listed in Dow Jones Industrial Average during the years 2008-2011. Since all the considered quantities except the returns show strong daily patterns related to the variable trading activity in different parts of a day, which are the best evident in the autocorrelation function, we remove these patterns by detrending before we proceed further with our study. We apply the multifractal detrended cross-correlation analysis with sign preserving (MFCCA) and show that the strongest power-law cross-correlations exist between trading activity and volume traded, while the weakest ones exist (or even do not exist) between the returns and the remaining quantities. We also show that the strongest cross-correlations are carried by those parts of the signals that are characterized by large and medium variance. Our observation that the most convincing power-law cross-correlations occur between trading activity and volume traded reveals the existence of strong fractal-like coupling between these quantities.

We discuss the role of intrinsic charm (IC) in the nucleon for forward production of $c$-quark (or $\bar c$-antiquark) in proton-proton collisions for low and high energies. The calculations are performed in collinear-factorization approach with on-shell partons, $k_T$-factorization approach with off-shell partons as well as in a hybrid approach using collinear charm distributions and unintegrated (transverse momentum dependent) gluon distributions. For the collinear-factorization approach we use matrix elements for both massless and massive charm quarks/antiquarks. The distributions in rapidity and transverse momentum of charm quark/antiquark are shown for a few different models of IC. Forward charm production is dominated by $gc$-fusion processes. The IC contribution dominates over the standard pQCD (extrinsic) $gg$-fusion mechanism of $c\bar c$-pair production at large rapidities or Feynman-$x_F$. We perform similar calculations within leading-order and next-to-leading order $k_T$-factorization approach. The $k_T$-factorization approach leads to much larger cross sections than the LO collinear approach. At high energies and large rapidities of $c$-quark or $\bar c$-antiquark one tests gluon distributions at extremely small $x$. The IC contribution has important consequences for high-energy neutrino production in the Ice-Cube experiment and can be, to some extent, tested at the LHC by the SHIP and FASER experiments by studies of the $\nu_{\tau}$ neutrino production.

The dissipative dynamics of the spin chain coupled to the non-Markovian magnonic reservoir was studied. The chirality of the chain is formed due to the magnetoelectric coupling. We explored the sign of the trace distance derivative and found the alternating positive/negative periods in system's time evolution. The negative sign is associated with the flow of information from the system to the bath and decrease in states distinguishability, while the positive sign is related to the flow of the information in the opposite direction and increase in distinguishability. We found the distinct effect of the applied electric and magnetic fields. While the Dzyaloshinskii-Moriya interaction and external electric field lead to reshuffling of the periods, the applied magnetic field leads to the swift positive-negative transitions. Thus, in the helical quantum rings coupled to the non-Markovian magnonic baths, it is possible to control the directions of information flow through the external fields.

We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including DGLAP evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of $\sigma(x,r)/\alpha(r)$. At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function $F_L(x,Q^2)$ finding good agreement with HERA data.

We evaluate the cross section for diffractive bremsstrahlung of a single photon in the $pp \to pp \gamma$ reaction at high energies and at forward photon rapidities. Several differential distributions, for instance, in $y$, $k_{\perp}$ and $\omega$, the rapidity, the absolute value of the transverse momentum, and the energy of the photon, respectively, are presented. We compare the results for our standard approach, based on QFT and the tensor-pomeron model, with two versions of soft-photon-approximations, SPA1 and SPA2, where the radiative amplitudes contain only the leading terms proportional to $\omega^{-1}$. The SPA1, which does not have the correct energy-momentum relations, performs surprisingly well in the kinematic range considered. We discuss also azimuthal correlations between outgoing particles. The azimuthal distributions are not isotropic and are different for our standard model and SPAs. We discuss also the possibility of a measurement of two-photon-bremsstrahlung in the $pp \to pp \gamma \gamma$ reaction. In our calculations we impose a cut on the relative energy loss (0.02 < \xi_{i} < 0.1, $i = 1,2$) of the protons where measurements by the ATLAS Forward Proton (AFP) detectors are possible. The AFP requirement for both diffractively scattered protons and one forward photon (measured at LHCf) reduces the cross section for $p p \to p p \gamma$ almost to zero. On the other hand, much less cross-section reduction occurs for $pp \to pp \gamma \gamma$ when photons are emitted in opposite sides of the ATLAS interaction point and can be measured by two different arms of LHCf. For the SPA1 ansatz we find $\sigma(pp \to pp \gamma \gamma) \simeq 0.03$ nb at $\sqrt{s} = 13$ TeV and with the cuts 0.02 < \xi_{i} < 0.1, 8.5 < y_{3} < 9, -9 < y_{4} < -8.5. Our predictions can be verified by ATLAS and LHCf combined experiments.

We show some results related to the classical Banach-Tarski paradox in the setting of finite-dimensional normed spaces over a non-Archimedean valued field $K$. For instance, all balls and spheres in $K^n$, and the whole space $K^n$ (for $n\ge 2$) are paradoxical with respect to certain groups of isometries of $K^n$. If $K$ is locally compact (e.g., $K$ is the field $\mathbb{Q}_p$ of $p$-adic numbers for any prime number $p$), any two bounded subsets of $K^n$ with nonempty interiors are equidecomposable (and paradoxical) with respect to a certain group of isometries of $K^n$ (for $n\ge 2$).

The ultraperipheral collisions are the source of various interesting phenomena based on photon-induced reactions. We calculate cross sections for single and any number of n, p, $\alpha$, $\gamma$-rays in ultraperipheral heavy-ion collision for LHC energies. We analyze the production of a given number of neutrons relevant for a recent ALICE experiment, for $\sqrt{s_{NN}}$ = 5.02~TeV. In our approach, we include both single and multiple photon exchanges as well as the fact that not all photon energies are used in the process of equilibration of the residual nucleus. We propose a simple two-component model in which only part of photon energy $E_\gamma$ is changed into the excitation energy of the nucleus ($E_{exc} \neq E_{\gamma}$) and compare its results with outcomes of HIPSE and EMPIRE codes. The role of high photon energies for small neutron multiplicities is discussed. Emission of a small number of neutrons at high photon energies seems to be crucial to understand the new ALICE data. All effects work in the desired direction, but the description of the cross section of four- and five-neutron emission cross sections from first principles is rather demanding. The estimated emission of charged particles such as protons, deuterons and $\alpha$ is shortly discussed and confronted with very recent ALICE data, obtained with the proton Zero Degree Calorimeter.

During its most recent return, comet 12P/Pons-Brooks experienced 14 well-documented outbursts, observed between June 13, 2023, and April 2024, at heliocentric distances ranging from $4.26\,$au to $0.85\,$au. After perihelion, the comet experienced two additional outbursts between June and August 31, 2024, at heliocentric distances of $1.20\,$au and $2.26\,$au, respectively. Using observational data, we developed a numerical model to estimate the mass ejected during these events, focusing on the sublimation of ice through the porous cometary nucleus. The key factors affecting ejected mass estimates are the outburst amplitude and the active surface area during both quiet sublimation and the outburst phases. Pogson's law was used to express outburst magnitude, incorporating scattering cross-sections of cometary agglomerates. The model iteratively determined the mass ejected in observed outbursts, considering various ice types (H$_{2}$O and CO$_{2}$) controlling sublimation activity. Our results indicate that the mass ejected during these outbursts ranges from 10$^{10}$ to 10$^{13}$ kg. Our findings highlight the significant role of surface morphology and thermodynamic conditions in cometary outbursts, providing insights into the mechanisms driving these phenomena and their implications for cometary evolution and dust trail formation. Based on the analysis of observational data, we propose a six-level classification system for cometary outbursts.

Comets and asteroids have long captured human curiosity, and until recently, all documented examples belonged to our Solar System. That changed with the discovery of the first known interstellar object, 1I/2017 U1 ('Oumuamua), in 2017. Two years later, Gennady Borisov discovered a second interstellar object: 2I/Borisov. From its initial images, the object's diffuse appearance hinted at its cometary nature. To better understand the photometric evolution of comet 2I as it traveled through the inner Solar System, we compiled observations using medium-sized telescopes. This data is crucial for gaining insights into its size and composition, as well as how such objects, after millions of years in interstellar space, behave when exposed to the Sun's radiation. Given that 2I is the first interstellar comet ever observed, constraining its behavior is of great scientific interest. In this paper, we present photometric data gathered from observatories in Crimea and Catalonia, highlighting the importance of systematic photometric studies of interstellar objects using meter-class telescopes. Our observations showed a steady increase in the comet's brightness as it approached perihelion, likely due to the slow sublimation of ices. Over the pre-perihelion observation period, we did not detect any significant changes in magnitude. The analysis of observations reveals a steady increase in comet brightness as it approached perihelion, likely due to the sublimation of ices, with no observable outbursts during the five-month pre-perihelion period. Additionally, we discuss the challenges in ground-based observation of comets posed by light pollution today, particularly in urban areas, where visual observations are severely limited. Using sample surface brightness measurements, we demonstrate the impact of light pollution and outline the importance of systematic photometric studies for interstellar objects.

We investigate translation length functions for two-generated groups acting by isometries on $\Lambda$-trees, where $\Lambda$ is a totally ordered Abelian group. In this context, we provide an explicit formula for the translation length of any element of the group, under some assumptions on the translation lengths of its generators and their products. Our approach is combinatorial and relies solely on the defining axioms of pseudo-lengths, which are precisely the translation length functions for actions on $\Lambda$-trees. Furthermore, we show that, under some natural conditions on four elements $\alpha, \beta, \gamma, \delta \in \Lambda$, there exists a unique pseudo-length on the free group $F(a,b)$ assigning these values to $a$, $b$, $ab$, $ab^{-1}$, respectively. Applications include results on properly discontinuous actions, discrete and free groups of isometries, and a description of the translation length functions arising from free actions on $\Lambda$-trees, where $\Lambda$ is Archimedean. This description is related to the Culler--Vogtmann outer space.

We present a study of the central exclusive production (CEP) of $\eta$ and $\eta'(958)$ mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and $f_{2 \mathbb{R}}$ reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy $\sqrt{s} = 13$ TeV. Both, total cross sections and several differential distributions are presented. For $pp \to pp \eta$, we find an upper limit for the total cross section of 2.5 $\mu$b for pseudorapidity of the $\eta$ meson |\eta_{M}| < 1 and 5.6 $\mu$b for 2 < \eta_{M} < 5. For $pp \to pp \eta'$, we predict the cross section to be in the range of $0.3-0.7 \,\mu$b for pseudorapidity of the $\eta'$ meson |\eta_{M}| < 1 and $0.9-2.1 \,\mu$b for 2 < \eta_{M} < 5. This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We also consider CEP of the pseudoscalars $\eta$ and $\eta'(958)$ and the pseudovector meson $f_{1}(1285)$ in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.

Quantumness imposes a fundamental limit on measurement accuracy. The paradigmatic cases are Heisenberg's uncertainty relation in the original formulation, Robertson's formulation, and improved uncertainty relations. However, the more universal measures are given in terms of quantum entropies. Uncertainties of measurements done on one quantum system correlated with another quantum system constitute a more intriguing question. Quantum correlations can influence the lower bound of uncertainties, and the reason for this is the quantum memory. In this article, we study uncertainties of measurements performed on one quantum dot correlated with the second one through the superconductor, hosting the Majorana boundary modes. We prove that the Majorana quasiparticles allow the uncertainties to reach the minimal possible lower bound. By rigorous theoretical considerations, we obtain the result of experimental relevance expressed in terms of only two parameters: the overlap between Majorana modes and their coupling strength with the quantum dots. We show that the overlap between Majorana modes reduces quantum uncertainties, which is a general result of fundamental importance. We also propose the protocol to measure spins in both quantum dots, consecutively, and demonstrate that the result of the second measurement would depend on the presence of Majorana quasiparticles. This could serve as an indirect tool for their empirical observation, which is of importance for the ongoing discussions concerning unambiguous detection of the Majorana quasiparticles in nanoscopic hybrid structures.

We calculate cross sections for the production of different neutron classes $0n 0n$, $0nXn+Xn0n$ and $Xn Xn$, possible to measure in Zero Degree Calorimeters (ZDCs), associated with photon-photon scattering in UPC of lead on lead. The calculations are performed for the ATLAS kinematics. Our calculations for neutron classes are tested against existing data for $\rho^0$ production in UPC. We get a good agreement for absolute cross section as well as very good results for fractional cross section which gives confidence to the analogous calculation for diphoton production, corresponding to $\gamma \gamma \to \gamma \gamma$ scattering. We present both absolute as well as fractional cross sections for the different neutron classes. We also show different distributions in impact parameter, photon rapidity, transverse momentum, diphoton invariant mass and photon rapidity difference. The shapes of the photon distributions depend on the neutron classes which we quantify in this paper. It would be valuable to test our predictions using the ATLAS main detector and the ATLAS ZDCs.