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The analysis of the rotation rate of individual sunspots and pores was performed according to the data of the processing of observations by the \textit{Solar Dynamics Observatory/Helioseismic and Magnetic Imager} (SDO/HMI) in the period 2010\,--\,2024. Sunspots stood out in the images in the continuum. To accurately track the spots, we processed 5 images for each day. To determine the polarity of the magnetic field, we superimposed the contours of sunspots on observations of magnetic fields at the same time. This made it possible to track the movement of more than 210 thousand individual sunspots and pores. It is found that the rotation rate is influenced by the rotation rate of the solar atmosphere and the systematic proper motions of the spots. Sunspots and pores of the leading polarity have a rate of meridional movement $\approx 2.4\%$ faster than spots of the trailing polarity. We also found that regular sunspots, which have umbra and penumbra, rotate $\approx 1.5\%$ faster than solar pores, in which penumbra is absent. The dependence of the rotation rate on these area is found. For sunspots with an area of $S> 10$ $\mu$hm, the rotation rate is practically independent of these area. Small sunspots, with an area of lower than $S< 10$ $\mu$hm, rotate $\approx 1.7\%$ slower., Comment: 10 pages, 9 figures

Some time ago, Kobayashi et al. experimentally studied the so-called Lee-Naughton-Lebed's (LNL) angular effect in strong electric fields [K. Kobayashi, M. Saito, E. Omichi, and T. Osada, Phys. Rev. Lett. \textbf{96}, 126601 (2006)]. They found that strong electric fields split the LNL conductivity maxima in $\alpha$-(ET)$_2$-based organic conductor and hypothetically introduced the corresponding equation for conductivity. In this Letter, for the first time we suggest quantum mechanical theory of the LNL angular oscillations in moderately strong electric fields. In particular, we demonstrate that the obtained by us approximate theoretical formula coincides with the hypothetical one and well describes the above mentioned experiments., Comment: 1 figure

In framework of some extension of the quasi-classical Boltzmann kinetic equation, we show that a moderately strong electric field splits the so-called Lee-Naughton-Lebed's magnetoconductivity maxima in a layered quasi-one-dimensional conductor, if we use some reasonable approximation to the equation. By means of the above mentioned approximation, we obtain analytical formula for conductivity in high magnetic and moderately high electric fields and show that it coincides with the hypothetical formula as well as adequately describes the pioneering experimental data by Kobayashi et al. [K. Kobayashi, M. Saito, E. Omichi, and T. Osada, Phys. Rev. Lett. \textbf{96}, 126601 (2006)]., Comment: 1 figure

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular non-local correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model., Comment: 16 pages, 6 figures; v3: fig. 6 added

Herein we present a comparative study among different mesoporous electron transporter layers (ETLs), namely nanometric m-TiO2, m-SnO2 and m-SnO2 quantum dots (QDs), deposited by spray coating method. The experimental data correlated with the photovoltaic parameters indicate that the SnO2 mesoporous layer obtained from the spray deposition of the in-house prepared QDs solution is the best candidate between the three used mesoporous ETLs. The use of the in-house prepared SnO2 QDs solution presents smaller agglomerates composed of 3 nm NPs resulting in the formation of a thinner, more uniform, and compact mesoporous ETL, compared with the other two ETL solutions. The formamidinium-methylamonium-potassium (FAMA@10K) perovskite deposited on this m-SnO2 QDs ETL presents a lower RMS, more uniformity and, a higher amount of PbI2. Interestingly, this higher concentration for PbI2 seems to enhance the performance of the perovskite solar cells (PSC), compared to the other two mesoporous ETLs. Our work reveals that SnO2 QDs solution can be easily produced in the laboratory and it is more suited for the deposition of the mesoporous ETL when choosing a FAMA@10K configuration perovskite solar cell with power conversion efficiency (PCE) higher than 10%., Comment: 20 pages, 14 figures, 6 sections

We study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the Boltzmann weights are equal, the known multiple integral representation (MIR) for the EFP can be given as a finite-size matrix determinant of Fredholm type. Our conjecture is based on the explicit evaluation of the MIR for particular values of geometric parameters and on two kinds of identities for the boundary correlation function. The obtained representation can be further written as the Fredholm determinant of some linear integral operator. We show that as the geometric parameters of the EFP are tuned to the vicinity of the arctic curve arising in the scaling limit, the conjectured determinant turns into the GUE Tracy--Widom distribution., Comment: 27 pages, 5 figures

The advancement of liquid phase electron beam induced deposition has enabled an effective direct-write approach for functional nanostructure synthesis with the possibility of three-dimensional control of morphology. For formation of a metallic solid phase, the process employs ambient temperature, beam-guided, electrochemical reduction of precursor cations resulting in rapid formation of structures, but with challenges for retention of resolution achievable via slower electron beam approaches. The possibility of spatial control of redox pathways via the use of water-ammonia solvents has opened new avenues for improved nanostructure resolution without sacrificing the growth rate. We find that ammonia concentration locally modulates reaction kinetics, altering the balance between reducing and oxidizing species, leading to distinct deposition outcomes. The key effect is an 'electrochemical lensing', achieved at an optimum ammonia concentration, in which a tightly confined and highly reducing environment is created locally to enable high resolution, rapid beam-directed nanostructure growth. We demonstrate this unique approach to high resolution synthesis through a combination of analysis and experiment.

We consider the homogeneous five-vertex model on a rectangle domain of the square lattice with so-called scalar-product boundary conditions. Peculiarity of these boundary conditions is that the configurations of the model are in an one-to-one correspondence with the 3D Young diagrams limited by a box of a given size. We address the thermodynamics of the model using a connection of the partition function with the $\tau$-function of the sixth Painlev\'e equation. We compute an expansion of the logarithm of the partition function to the order of a constant in the size of the system. We find that the geometry of the domain is crucial for phase transition phenomena. Two cases need to be considered separately: one is where the region has an asymptotically square shape and the second one is where it is of an arbitrary rectangle, but not square, shape. In the first case there are three regimes, which can be attributed to dominance in the configurations of a ferroelectric order, disorder, and anti-ferroelectric order. In the second case the third regime is absent., Comment: 52 pages, 7 figures; v2: Sections 1, 4, and 5 extended, references added

The plasmonic tip of a scanning tunnelling microscope (STM) is functionalized with a single fluorescent molecule and is scanned on a plasmonic substrate. The tunneling current flowing through the tip-molecule-substrate junction generates a narrow-line emission of light corresponding to the fluorescence of the negatively charged molecule suspended at the apex of the tip, i.e., the emission of the excited molecular anion (trion). The fluorescence of this molecular probe is recorded for tip-substrate nanocavities featuring different plasmonic resonances, for different tip-substrate distances and applied bias voltages, and on different substrates. We demonstrate that the width of the emission peak can be used as a probe of the trion-plasmon coupling strength and that the energy of the emitted photons is governed by the molecule interactions with its electrostatic environment. Additionally, we theoretically elucidate why the direct contact of the suspended molecule with the metallic tip does not totally quench the radiative emission of the molecule., Comment: 9 pages in the main manuscript, including 4 figures, 11 pages in the supporting info, including 5 figures and 1 table

Recently, we have started to investigate behavior of a composite quantum body in an external gravitational field in the framework of General Relativity [see, for a review, A. G. Lebed, Mod. Phys. Lett. A, {\bf 35}, 2030010 (2020)]. As the simplest example, we have considered a hydrogen atom in a weak gravitational field. Our results are the following. The Einstein's Equivalence Principle survives for the most of macroscopic ensembles of the atoms, containing the stationary quantum states. On the other hand, we have demonstrated that this principle is sometimes broken. In particular, it is broken for the so-called Gravitational demons, which are the coherent macroscopic ensembles of two or more stationary quantum states in the hydrogen atoms. In the above cited paper we have considered the Gedanken experiment, where the gravitational field is suddenly switched on in a free from gravitation space. In the current paper we consider the much more realistic from experimental point of view Gedanken experiment and come to the same conclusion about violations of the Einstein's Equivalence Principle for the Gravitational demons., Comment: 4 pages

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second and higher order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes., Comment: 9 pages, 9 figures

Weak interaction of temporal cavity solitons due to gain saturation and recovery in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that in addition to the usual soliton repulsion leading to a harmonic mode-locking regimes a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that this attraction can lead either to a pulse merging or to a pulse bound state formation., Comment: 8 pages, 6 figures

We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and proved using a recursion relation. In later works, another determinant formulas were given by Kostov for the rational case and by Foda and Wheeler for the trigonometric case. Here, we develop an approach in which the recursion relation is replaced by a system of algebraic equations with respect to one set of spectral parameters. We prove that this system has a unique solution. The result can be easily given as a determinant parametrized by an arbitrary basis of polynomials. In particular, the choice of the basis of Lagrange polynomials with respect to the second set of spectral parameters leads to the Izergin-Korepin representation, and the choice of the monomial basis leads to the Kostov and Foda-Wheeler representations., Comment: 18 pages, 2 figures; v2: minor corrections

We investigate the turn-on process in a laser cavity where the roundtrip time is several orders of magnitude greater than the active medium timescales. In this long delay limit the electromagnetic field build-up can be mapped experimentally roundtrip after roundtrip. We show how coherence settles down starting from a stochastic initial condition. In the early stages of the turn-on, we show that power drop-outs emerge, persist for several round-trips and seed dark solitons. These latter structures exhibit a chaotic dynamics and emit radiation that can lead to an overall turbulent dynamics depending on the cavity dispersion., Comment: 6 pages, 8 figures

We calculate the parallel upper critical magnetic field $H_{\parallel}(0)$ for an in-plane isotropic quasi-two-dimensional (Q2D) chiral triplet superconductor at zero temperature, $T=0$. In particular, the ratio $H_{\parallel}(0)/(|dH^{GL}_{\parallel}/dT|_{T=T_c}T_c) = 0.815$ is defined, where $|dH^{GL}_{\parallel}/dT|_{T=T_c}$ is the so-called Ginzburg-Landau slope of the upper critical magnetic field, $T_c$ is a superconducting transition temperature at $H=0$. We show that the theoretically obtained above mentioned value strongly contradicts to the experimentally measured ones in a candidate for a chiral triplet superconductivity Sr$_2$RuO$_4$, which provides one more argument against the chiral triplet scenario of superconductivity in this compound. Our results may be useful for establishing chiral triplet superconductivity in other Q2D candidates for this phenomenon., Comment: 6 pages

Relativistic electron losses in Earth's radiation belts are usually attributed to electron resonant scattering by electromagnetic waves. One of the most important wave mode for such scattering is the electromagnetic ion cyclotron (EMIC) mode. Within the quasi-linear diffusion framework, the cyclotron resonance of relativistic electrons with EMIC waves results in very fast electron precipitation to the atmosphere. However, wave intensities often exceed the threshold for nonlinear resonant interaction, and such intense EMIC waves have been shown to transport electrons away from the loss cone due to the force bunching effect. In this study we investigate if this transport can block electron precipitation. We combine test particle simulations, low-altitude ELFIN observations of EMIC-driven electron precipitation, and ground-based EMIC observations. Comparing simulations and observations, we show that, despite of the low pitch-angle electrons being transported away from the loss cone, the scattering at higher pitch angles results in the loss cone filling and electron precipitation.

Abstract Interaction equations governing slow time evolution of the coordinates and phases of two interacting temporal cavity solitons in a delay differential equation model of a nonlinear mirror mode-locked laser are derived and analyzed. It is shown that non-local pulse interaction due to gain depletion and recovery can lead either to a development of harmonic mode-locking regime, or to a formation of closely packed incoherent soliton bound state with weakly oscillating intersoliton time separation. Local interaction via electric field tails can result in an anti-phase or in-phase stationary and breathing harmonic mode-locking regimes., Comment: 5 figures

We consider the six-vertex model with the rational weights on an $s\times N$ square lattice, $s\leq N$, with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are imposed. For a finite lattice, it can be computed by the quantum inverse scattering method in terms of determinants. In the large $N$ limit, the result boils down to an explicit terminating series in the parameter of the weights. Using the saddle-point method for an equivalent integral representation, we show that as $s$ next tends to infinity, the one-point function demonstrates a step-wise behavior; at the vicinity of the step it scales as the error function. We also show that the asymptotic expansion of the one-point function can be computed from a second-order ordinary differential equation., Comment: 29 pages, 5 figures

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum inverse scattering method, we derive three different integral representations for these states. By suitably combining such representations, and using certain antisymmetrization relation in two sets of variables, it is possible to derive integral representations for various correlation functions. In particular, focusing on the emptiness formation probability, besides reproducing the known result, obtained by other means elsewhere, we provide a new one. By construction, the two representations differ in the number of integrations and their equivalence is related to a hierarchy of highly nontrivial identities., Comment: 42 pages, 4 figures

Delay differential equation model of a NOLM-NALM mode-locked laser is developed that takes into account finite relaxation rate of the gain medium and asymmetric beam splitting at the entrance of the nonlinear mirror loop. Asymptotic linear stability analysis of the continuous wave solutions performed in the limit of large delay indicates that in a class-B laser flip instability leading to a period doubling cascade and development of square-wave patterns can be suppressed by a short wavelength modulational instability. Numerically it is shown that the model can demonstrate large windows of regular fundamental and harmonic mode-locked regimes with single and multiple pulses per cavity round trip time separated by domains of irregular pulsing., Comment: 8 pages, 10 figures

The interactions between the excited states of a single chromophore with static and dynamic electric fields confined to a plasmonic cavity of picometer dimensions are investigated in a joint experimental and theoretical effort. In this configuration, the spatial extensions of the confined fields are smaller than the one of the molecular exciton, a property that is used to generate fluorescence maps of the chromophores with intra-molecular resolution. Theoretical simulations of the electrostatic and electrodynamic interactions occurring at the chromophore-picocavity junction are able to reproduce and interpret these hyper-resolved fluorescence maps, and reveal the key role played by subtle variations of Purcell, Lamb and Stark effects at the chromophore-picocavity junction.

Using an asymptotic technique we develop a generalized version of class-B Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime, but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power., Comment: 14 pages, 5 figures

We derive integral equation for superconducting gap, which takes into account the quantum nature of electron motion in a parallel magnetic field in a quasi-two-dimensional (Q2D) superconductor in the presence of a non-zero perpendicular field component. By comparison of our theoretical results with the recent experimental data obtained on the NbS$_2$, we show that the orbital effect against superconductivity partially destroys superconductivity in the so-called Ginzburg-Landau area of this Q2D conductor, as expected. Nevertheless, at relatively high magnetic fields, $H \simeq 15 \ T$, the orbital effect starts to improve the Fulde-Ferrell-Larkin-Ovchinnikov phase in the NbS$_2$, due to the quantum nature of electron motion in a parallel magnetic field. In our opinion, this is the most clear demonstration that the orbital effect against superconductivity in a parallel magnetic field has a reversible nature., Comment: 6 pages, no figures

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Yet, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential, that dictates the particle number distribution of each protein subunit, from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulate an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multi-component mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of Succinate Dehydrogenase (SDH) with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell., Comment: 8 figures

We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato-Lefever equation with fourth order dispersion. We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourth-order dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the the bound state stability., Comment: 7 pages, 7 figures

We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box of given size). The partition function of an inhomogeneous model is given in terms of a determinant. For the homogeneous model, it can be given in terms of a Hankel determinant. We also show that in the homogeneous case the partition function is a $\tau$-function of the sixth Painlev\'e equation with respect to the rapidity variable of the weights., Comment: 32 pages, 5 figures; v2: misprints corrected

It was theoretically predicted more than 20 years ago [A.G. Lebed and K. Yamaji, {\it Phys. Rev. Lett.} {\bf80}, 2697 (1998)] that a triplet quasi-two-dimensional (Q2D) superconductor could restore its superconducting state in parallel magnetic fields, which are higher than its upper critical magnetic field, $H > H_{c2}(0)$. It is very likely that recently such phenomenon has been experimentally discovered in the Q2D superconductor UTe$_2$ by Nicholas Butch, Sheng Ran and their colleagues and has been confirmed by Japanese-French team. We review our previous theoretical results, using such a general method that it describes the reentrant superconductivity in the above mentioned compound as well as will hopefully describe the similar phenomena, which can be discovered in other Q2D superconductors., Comment: Invited Brief Review for journal Modern Physics Letters B, accepted (2020)

It is well known that a four-fold symmetry of the parallel upper critical magnetic field disappears in the Ginzburg-Landau (GL) region in quasi-two-dimensional (Q2D) $d$-wave superconductors. Therefore, it has been accurately calculated so far as a correction to the GL results, which is valid close to superconducting transition temperature and is expected to be stronger at low temperatures. As to the case $T=0$, some approximated methods have been used, which are good only for closed electron orbits and unappropriate for the open orbits which exist in a parallel magnetic field in Q2D superconductors. For the first time, we accurately calculate the four-fold anisotropy of the parallel upper critical magnetic field in a pure Q2D $d$-wave superconductor at $T=0$, where it has the highest possible value. Our results are applicable to Q2D $d$-wave high-Tc and organic superconductors., Comment: 5 pages, 2 figeres

We review our recent theoretical results about inequivalence between passive gravitational mass and energy for a composite quantum body at a macroscopic level. In particular, we consider macroscopic ensembles of the simplest composite quantum bodies - hydrogen atoms. Our results are as follows. For the most ensembles, the Einstein's Equivalence Principle is valid. On the other hand, we discuss that for some special quantum ensembles - ensembles of the coherent superpositions of the stationary quantum states in the hydrogen atoms (which we call Gravitational demons) - the Equivalence Principle between passive gravitational mass and energy is broken. We show that, for such superpositions, the expectation values of passive gravitational masses are not related to the expectation values of energies by the famous Einstein's equation, i.e, $m_g \neq \frac{E}{c^2}$. Possible experiments at the Earth's laboratories are briefly discussed, in contrast to the numerous attempts and projects to discover the possible breakdown of the Einstein's Equivalence Principle during the space missions., Comment: Brief review