A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for physics-informed neural networks (PINNs) methodology is that it becomes possible to represent the loss function in the form of a single term associated with differential equations, thus eliminating the need to tune the scaling coefficients for the terms related to boundary and initial conditions. The weighted loss functions respecting causality were modified and new weighted loss functions based on generalized functions are derived. Numerical experiments have been carried out for a number of problems, demonstrating the accuracy of the proposed methods.

Jarzynski equality and related fluctuation theorems can be formulated for various setups. Such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations, i.e., for completely positive, trace-preserving maps, which preserve the maximally mixed state. We analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the Jarzynski equality. It contains a correction term due to nonunitality of the quantum map. Bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite-dimensional Hilbert space.

We report on optical transmission spectroscopy of the Cr-based frustrated triangular antiferromagnets CuCrO2 and alpha-CaCr2O4, and the spinels CdCr2O4 and ZnCr2O4 in the near-infrared to visible-light frequency range. We explore the possibility to search for spin correlations far above the magnetic ordering temperature and for anomalies in the magnon lifetime in the magnetically ordered state by probing exciton-magnon sidebands of the spin-forbidden crystal-field transitions of the Cr3+ ions (spin S = 3/2). In CuCrO2 and alpha-CaCr2O4 the appearance of fine structures below T_N is assigned to magnon sidebands by comparison with neutron scattering results. The temperature dependence of the line width of the most intense sidebands in both compounds can be described by an Arrhenius law. For CuCrO2 the sideband associated with the 4A2 -> 2T2 transition can be observed even above T_N. Its line width does not show a kink at the magnetic ordering temperature and can alternatively be described by a Z2 vortex scenario proposed previously for similar materials. The exciton-magnon features in alpha-CaCr2O4 are more complex due to the orthorhombic distortion. While for CdCr2O4 magnon sidebands are identified below T_N and one sideband excitation is found to persist across the magnetic ordering transition, only a weak fine structure related to magnetic ordering has been observed in ZnCr2O4.

In this work, we study magnetoelastic interactions by means of ultrasound experiments in $\alpha$-RuCl$_3$ -- a prototypical material for the Kitaev spin model on the honeycomb lattice, with a possible spin-liquid state featuring Majorana fermions and $\mathbb{Z}_{2}$-flux excitations. We present results of the temperature and in-plane magnetic-field dependence of the sound velocity and sound attenuation for several longitudinal and transverse phonon modes propagating along high-symmetry crystallographic directions. A comprehensive data analysis above the ordered state provides strong evidence of phonon scattering by Majorana fermions. This scattering depends sensitively on the value of the phonon velocities relative to the characteristic velocity of the low-energy fermionic excitations describing the spin dynamics of the underlying Kitaev magnet. Moreover, our data displays a distinct reduction of anisotropy of the sound attenuation, consistent with randomization, generated by thermally excited $\mathbb{Z}_2$ visons. We demonstrate the potential of phonon dynamics as a promising probe for uncovering fractionalized excitations in $\alpha$-RuCl$_3$ and provide new insights into the $H$-$T$ phase diagram of this material.

We discuss the following inverse problem: given the run-up data of a tsunami wave, can we recover its initial shape? We study this problem within the framework of the non-linear shallow water equations, a model widely used to study tsunami propagation and inundation. Previously, it has been demonstrated that in the case of infinite sloping bathymetry, it is possible to recover the initial water displacement and velocity from shoreline readings \cite{Rybkin23,Rybkin24,Rybkin25}. We consider a finite sloping bathymerty. We show that it is possible to recover boundary conditions (water displacement and velocity) on a virtual buoy from the shoreline data. Further, we discuss stitching together the shallow water equations and the Boussinesq equation in a more complex piece-wise sloping bathymetry in order to recover the initial conditions, while incorporating the dispersion to our model.

The main purpose of the Baikal-GVD Data Quality Monitoring (DQM) system is to monitor the status of the detector and collected data. The system estimates quality of the recorded signals and performs the data validation. The DQM system is integrated with the Baikal-GVD's unified software framework ("BARS") and operates in quasi-online manner. This allows us to react promptly and effectively to the changes in the telescope conditions.

The operation of a small-size Cherenkov gamma-ray telescope TAIGA-IACT with camera on SiPMs OnSemi MicroFJ-60035 has been modelled by multiparticle Monte Carlo (MC) methods. The model implies that telescope camera is equipped with two specific types of filters of 290-590 nm (visible+NUV) and 220-320 nm (MUV+UVB)-bands, each covering half of the camera pixels in some uniform order. This allows one to measure the fraction of UV-radiation in total amount of Cherenkov radiation of an extensive air shower (EAS), that can be used for efficient gamma-hadron separation. The corresponding quality factor takes values up to 5.07 in the 10-100 TeV range depending on the distance to EAS axis and camera orientation.

We review the status of the Lake Baikal Neutrino Experiment. The Neutrino Telescope NT200 has been operating since 1998 and has been upgraded to the 10 Mton detector NT200+ in 2005. We present selected astroparticle physics results from long-term operation of NT200. Also discussed are activities towards acoustic detection of UHE-energy neutrinos, and results of associated science activities. Preparation towards a km3-scale (Gigaton volume) detector in Lake Baikal is currently a central activity. As an important milestone, a km3-prototype string, based on completely new technology, has been installed and is operating together with NT200+ since April, 2008.

The cross section for different processes induced by $e^+e^-$ annihilation, in the kinematical limit $\beta_{\mu}\approx\beta_{\pi}=(1-m_{\pi}^2/\epsilon^2)^{1/2}\sim 1$, is calculated taking into account first order corrections to the amplitudes and the corrections due to soft emitted photons, with energy $\omega\le\Delta E\le \epsilon$in the center of mass of the$e^+e^-$ colliding beams. The results are given separately for charge--odd and charge--even terms in the final channels $\pi^+\pi^-(\gamma)$ and $\mu^+\mu^-(\gamma)$. In case of pions, form factors are taken into account. The differential cross sections for the processes: $e^++e^-\to e^++e^-(+\gamma)$, $\to \pi^++\pi^-(\gamma)$, $\to \mu^++\mu^-(\gamma),\to \gamma\gamma(\gamma)$ have been calculated and the corresponding formula are given in the ultrarelativistic limit $\sqrt{s}/2= \epsilon \gg m_{\mu}\sim m_{\pi}$ . For a quantitative evaluation of the contribution of higher order of the perturbation theory, the production of $\pi^+\pi^-$, including radiative corrections, is calculated in the approach of the lepton structure functions. This allows to estimate the precision of the obtained results as better than 0.5% outside the energy region corresponding to narrow resonances. A method to integrate the cross section, avoiding the difficulties which arise from singularities is also described.

The current study formulates a convective model of the Lorenz type near the temperature of maximum density. The existence of this temperature actualizes water dynamics in temperate lakes. There is a conceptual interest what this feature induces in Lorenz-type models. The consideration starts with the zero coefficient of thermal expansion. Other steps are like famous Tritton's approach to derive the Lorenz model. This allows us to reduce difficulties with a selection of Galerkin functions. The analysis focuses on changes induced by zeroing the coefficient of thermal expansion. It results in a five-dimensional Lorenz-type model, whose equations are all nonlinear. The new model reiterates many features of the standard Lorenz model. The nontrivial critical points appear, when the zero critical point becomes unstable. The nontrivial critical points correspond to two possible directions of fluid flow. Phase trajectories of the new model were studied numerically. The results are similar to the known five-dimensional extensions of the Lorenz model.

The pentaquark $P_c^+(4450)$ recently discovered by LHCb has been interpreted as a bound state of $\Psi(2S)$ and nucleon. The charmonium-nucleon interaction which provides the binding mechanism is given, in the heavy quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor (EMT). In this work we show in model-independent way, by exploring general properties of the effective interaction, that $\Psi(2S)$ can form bound states with nucleon and $\Delta$. Using the Skyrme model to evaluate the effective interaction in the large-$N_c$ limit and estimate $1/N_c$ corrections, we confirm the results from prior work which were based on a different effective model (chiral quark soliton model). This shows that the interpretation of $P_c^+(4450)$ is remarkably robust and weakly dependent on the details of the effective theories for the nucleon EMT. We explore the formalism further and present robust predictions of isospin $\frac32$ bound states of $\Psi(2S)$ and $\Delta$ with masses around $4.5\,{\rm GeV}$and widths around$70\,{\rm MeV}$. The approach also predicts broader resonances in the $\Psi(2S)$-$\Delta$ channel at $4.9\,{\rm GeV}$ with widths of the order of $150\,{\rm MeV}$. We discuss in which reactions these new isospin $\frac 32$ pentaquarks with hidden charm can be observed.

The Andromeda Galaxy recurrent nova M31N 2008-12a had been observed in eruption ten times, including yearly eruptions from 2008-2014. With a measured recurrence period of $P_\mathrm{rec}=351\pm13$ days (we believe the true value to be half of this) and a white dwarf very close to the Chandrasekhar limit, M31N 2008-12a has become the leading pre-explosion supernova type Ia progenitor candidate. Following multi-wavelength follow-up observations of the 2013 and 2014 eruptions, we initiated a campaign to ensure early detection of the predicted 2015 eruption, which triggered ambitious ground and space-based follow-up programs. In this paper we present the 2015 detection; visible to near-infrared photometry and visible spectroscopy; and ultraviolet and X-ray observations from the Swift observatory. The LCOGT 2m (Hawaii) discovered the 2015 eruption, estimated to have commenced at Aug. $28.28\pm0.12$ UT. The 2013-2015 eruptions are remarkably similar at all wavelengths. New early spectroscopic observations reveal short-lived emission from material with velocities $\sim13000$ km s$^{-1}$, possibly collimated outflows. Photometric and spectroscopic observations of the eruption provide strong evidence supporting a red giant donor. An apparently stochastic variability during the early super-soft X-ray phase was comparable in amplitude and duration to past eruptions, but the 2013 and 2015 eruptions show evidence of a brief flux dip during this phase. The multi-eruption Swift/XRT spectra show tentative evidence of high-ionization emission lines above a high-temperature continuum. Following Henze et al. (2015a), the updated recurrence period based on all known eruptions is $P_\mathrm{rec}=174\pm10$ d, and we expect the next eruption of M31N 2008-12a to occur around mid-Sep. 2016.

The probably most fundamental information about a particle is contained in the matrix elements of its energy momentum tensor (EMT) which are accessible from hard-exclusive reactions via generalized parton distribution functions. The spin decomposition of the nucleon and Ji sum rule are one example. Less prominent but equally important information is encoded in the stress tensor, related to the spatial components of the EMT, which shows in detail how the strong forces inside the nucleon balance to form a bound state. This provides not only unique insights on nucleon structure. It also leads to fascinating new applications to hadron spectroscopy which allow us to formulate new interpretations of the charmonium-nucleon pentaquarks discovered by LHCb. Recent progress is reviewed in this short overview article.

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence and the relative entropy of coherence are considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification processes.

We present results of optical polarization observations performed with the MASTER robotic net for three types of objects: gamma-ray bursts, supernovae, and blazars. For the Swift gamma-ray bursts GRB100906A, GRB110422A, GRB121011A, polarization observations were obtained during very early stages of optical emission. For GRB100906A it was the first prompt optical polarization observation in the world. Photometry in polarizers is presented for Type Ia Supernova 2012bh during 20 days, starting on March 27, 2012. We find that the linear polarization of SN 2012bh at the early stage of the envelope expansion was less than 3%. Polarization measurements for the blazars OC 457, 3C 454.3, QSO B1215+303, 87GB 165943.2+395846 at single nights are presented. We infer the degree of the linear polarization and polarization angle. The blazars OC 457 and 3C 454.3 were observed during their periods of activity. The results show that MASTER is able to measure substantially polarized light; at the same time it is not suitable for determining weak polarization (less than 5%) of dim objects (fainter than 16$^m$). Polarimetric observations of the optical emission from gamma-ray bursts and supernovae are necessary to investigate the nature of these transient objects.

Baikal-GVD is a next generation, kilometer-scale neutrino telescope currently under construction in Lake Baikal. GVD is formed by multi-megaton sub-arrays (clusters) and is designed for the detection of astrophysical neutrino fluxes at energies from a few TeV up to 100 PeV. The design of the Baikal-GVD allows one to search for astrophysical neutrinos with flux values measured by IceCube already at early phases of the array construction. We present here preliminary results of the search for high-energy neutrinos via the cascade mode with the Baikal-GVD neutrino telescope.

Baikal-GVD has recently published its first measurement of the diffuse astrophysical neutrino flux, performed using high-energy cascade-like events. We further explore the Baikal-GVD cascade dataset collected in 2018-2022, with the aim to identify possible associations between the Baikal-GVD neutrinos and known astrophysical sources. We leverage the relatively high angular resolution of the Baikal-GVD neutrino telescope (2-3 deg.), made possible by the use of liquid water as the detection medium, enabling the study of astrophysical point sources even with cascade events. We estimate the telescope's sensitivity in the cascade channel for high-energy astrophysical sources and refine our analysis prescriptions using Monte-Carlo simulations. We primarily focus on cascades with energies exceeding 100 TeV, which we employ to search for correlation with radio-bright blazars. Although the currently limited neutrino sample size provides no statistically significant effects, our analysis suggests a number of possible associations with both extragalactic and Galactic sources. Specifically, we present an analysis of an observed triplet of neutrino candidate events in the Galactic plane, focusing on its potential connection with certain Galactic sources, and discuss the coincidence of cascades with several bright and flaring blazars.

Fractionalized excitations are of considerable interest in recent condensed-matter physics. Fractionalization of the spin degrees of freedom into localized and itinerant Majorana fermions are predicted for the Kitaev spin liquid, an exactly solvable model with bond-dependent interactions on a two-dimensional honeycomb lattice. As function of temperature, theory predicts a characteristic two-peak structure of the heat capacity as fingerprint of these excitations. Here we report on detailed heat-capacity experiments as function of temperature and magnetic field in high-quality single crystals of {\alpha}-RuCl3 and undertook considerable efforts to determine the exact phonon background. We measured single-crystalline RhCl3 as non-magnetic reference and performed ab-initio calculations of the phonon density of states for both compounds. These ab-initio calculations document that the intrinsic phonon contribution to the heat capacity cannot be obtained by a simple rescaling of the nonmagnetic reference using differences in the atomic masses. Sizable renormalization is required even for non-magnetic RhCl3 with its minute difference from the title compound. In {\alpha}-RuCl3 in zero magnetic field, excess heat capacity exists at temperatures well above the onset of magnetic order. In external magnetic fields far beyond quantum criticality, when long-range magnetic order is fully suppressed, the excess heat capacity exhibits the characteristic two-peak structure. In zero field, the lower peak just appears at temperatures around the onset of magnetic order and seems to be connected with canonical spin degrees of freedom. At higher fields, beyond the critical field, this peak is shifted to 10 K. The high-temperature peak located around 50 K is hardly influenced by external magnetic fields, carries the predicted amount of entropy, R/2 ln2, and may resemble remnants of Kitaev physics.

A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under which the Jarzynski equality and related fluctuation theorems hold. It is essential that the representing quantum channel be unital. Under the mentioned condition, we first derive the corresponding Jarzynski equality. For bistochastic map and its adjoint, we further formulate a theorem of Tasaki-Crooks type. In the context of unital channels, some notes on heat transfer between two quantum systems are given. We also consider the case of a finite system operated by an external agent with a feedback control. When unital channels are applied at the first stage and, for a mutual-information form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations. These are extension of the previously given results to unital quantum operations.

Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications. Until now, skyrmions have been observed in a variety of magnets that exhibit nearly parallel alignment for the neighbouring spins, but theoretically, skyrmions with anti-parallel neighbouring spins are also possible. The latter, antiferromagnetic skyrmions, may allow more flexible control compared to the conventional ferromagnetic skyrmions. Here, by combining neutron scattering and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattice with an incipient meron character is stabilized in MnSc$_2$S$_4$ through anisotropic couplings. Our work demonstrates that the theoretically proposed antiferromagnetic skyrmions can be stabilized in real materials and represents an important step towards implementing the antiferromagnetic-skyrmion based spintronic devices.