While cosmic reionization has been broadly constrained by global observables, the interplay between internal sources (Milky Way, M31, and their satellites) and external ionization fronts remains poorly understood in a realistic Local Group (LG) context. To address this issue, we perform radiative transfer post-processing on the original HESTIA LG constrained simulation. We calibrate our source models using a uniform 1024^3 particle, dark-matter only, HESTIA simulation coupled with a subgrid collapse-fraction model to match the global reionization observables. These source models are then applied to the HESTIA zoom-in simulations, which consist of a 4096^3 particle effective resolution in the zoom region centered on the Milky Way (MW) and M31 haloes, which resolves haloes down to 10^8 solar masses. We find that in all scenarios, reionization within the LG proceeds in an inside-out manner with the progenitors of the MW and M31 having 50 percent of their material ionized by z ~ 9-8.6, significantly earlier than the global midpoint at z ~ 7-7.7, noting that external fronts from large-scale structure play a negligible role, even under the most permissive feedback model. We further show that present-day satellite galaxies exhibit only a weak correlation between their reionization redshift and their present-day radial distance from their host halo, with somewhat tighter trends around M31 than the MW. Finally, we find that satellites which assembled before reionization are systematically more massive today, suggesting that the oldest stellar populations preferentially reside in the most massive subhaloes.

In the framework of light-cone formulation of relativistic dynamics, arbitrary spin massless fields propagating in the four-dimensional AdS space are studied. For such fields, the complete list of light-cone gauge cubic interaction vertices is obtained. Realization of relativistic symmetries on space of light-cone gauge massless AdS fields is also obtained. The light-cone gauge vertices for massless AdS fields take simple form similar to the one for massless fields in the flat space.

We developed the full magnetohydrodynamical analytical jet model that allows accurate reproducing of a transversal and longitudinal structure for a highly collimated relativistic jets. This model can be used as a setup for convenient solution of radiative transfer equations and modelling the total intensity and polarization maps. We show that the analytical fits are in excellent agreement with the numerical solutions of full magnetohydrodynamical equations. Our approach allows setting easily different models for an emitting plasma number density. For example, we show that the equipartition number density ranges from several to tens of percent of a total number density. We show that the Doppler-corrected emissivity distribution behave in such a way that we may expect a limb brightened intensity pattern on a sub-parsec scale and a spine-brightened structure downstream. We reproduce the broken power-law dependence of a jet pressure at its boundary from the jet radius. The corresponding power exponents are in agreement with the parabola-to-cone transition observed directly in nearby sources.

In the framework of Lorentz covariant on-shell approach, interacting continuous-spin fields and integer-spin fields in flat space are investigated. Continuous-spin fields are considered by using a Lorentz vector superspace formulation, while integer-spin fields are considered by using oscillator formulation. All parity-even cubic vertices for self-interacting continuous-spin fields realized as functions on the Lorentz vector superspace are obtained. Cross-interactions of continuous-spin fields and integer-spin fields are also derived. Several representatives of cubic vertices realized as distributions are obtained. We show that manifestly Lorentz invariant formal cubic action involving at least one continuous-spin field turns out to be divergent. We find the modification of such action which maintains Lorentz invariance and leads to finite cubic action. One-to-one correspondence of Lorentz covariant cubic vertices and light-cone gauge cubic vertices is demonstrated explicitly.

The scheme of photon-number tomography is discussed in the framework of star-product quantization. The connection of dual quantization scheme and observables is reviewed. The quantizer and dequantizer operators and kernels of star product of tomograms in photon-number tomography scheme and its dual one are presented in explicit form. The fidelity and state purity are discussed in photon{number tomographic scheme, and the expressions for fidelity and purity are obtained in the form of integral of the product of two photon-number tomograms with integral kernel which is presented in explicit form. The properties of quantumness are discussed in terms of inequalities on state photon{number tomograms.

For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central. In [OP1] we described three generating sets of the characteristic subalgebras of the symplectic and orthogonal quantum matrix algebras. One of these -- the set of the elementary sums -- is finite. In the symplectic case the elementary sums are in general algebraically independent. On the contrary, in the orthogonal case the elementary sums turn out to be dependent. We obtain a set of quadratic reciprocal relations for these generators. Next, we resolve the reciprocal relations for the quantum orthogonal matrix algebra extended by the inverse of the quantum matrix. As an auxiliary result, we derive the commutation relations between the q-determinant of the quantum orthogonal matrix and the generators of the quantum matrix algebra, that is, the components of the quantum matrix.

The improved results on a direct search for a new X(16.7 MeV) boson which could explain the anomalous excess of $e^+e^-$ pairs observed in the excited 8Be nucleus decays ("Berillium anomaly") are reported. Due to its coupling to electrons, the X boson could be produced in the bremsstrahlung reaction e-Z -> e-ZX by a high-energy beam of electrons incident on active target in the NA64 experiment at the CERN SPS and observed through its subsequent decay into $e^+e^-$ pair. No evidence for such decays was found from the combined analysis of the data samples with total statistics corresponding to 8.4\times 10^{10} electrons on target collected in 2017 and 2018. This allows to set the new limits on the $X$--$e^-$ coupling in the range 1.2 \times 10^{-4} < \epsilon_e < 6.8 \times 10^{-4}, excluding part of the parameter space favored by the Berillium anomaly. We also set new bounds on the mixing strength of photons with dark photons (A') from non-observation of the decay $A' \to e^+e^-$ of the bremsstrahlung A' with a mass below 24 MeV.

We demonstrate that thermoelectric signal as well as dc Josephson current may be severely enhanced in multi-terminal superconducting hybrid nanostructures exposed to a temperature gradient. At temperatures $T$ strongly exceeding the Thouless energy of our device both the supercurrent and the thermo-induced voltage are dominated by the contribution from non-equilibrium low energy quasiparticles and are predicted to decay slowly (algebraically rather than exponentially) with increasing $T$. We also predict a non-trivial current-phase relation and a transition to a $\pi$-junction state controlled by both the temperature gradient and the system topology. All these features are simultaneously observable in the same experiment.

We develop further the general light-cone gauge approach in AdS space and apply it for studying continuous-spin field. For such field, we find light-cone gauge Lagrangian and realization of relativistic symmetries. We find a simple realization of spin operators entering our approach. Generalization of our results to the gauge invariant Lagrangian formulation is also described. We conjecture that, in the framework of AdS/CFT, the continuous-spin AdS field is dual to light-ray conformal operator. For some particular cases, our continuous-spin field leads to reducible models. We note two reducible models. The first model consists of massive scalar, massless vector, and partial continuous-spin field involving fields of all spins greater than one, while the second model consists of massive vector, massless spin-2 field, and partial continuous-spin field involving all fields of spins greater than two.

The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially we prove a number of lower and upper bounds for the resolvent of such operators. We consider two applications of these results. First we obtain pointwise estimates for principal eigenfunction of jump generators perturbed by a compactly supported potential (so-called nonlocal Schrödinger operators). Then we consider the Cauchy problem for the corresponding inhomogeneous evolution equations and study the behaviour of its solutions.

We study, both theoretically and experimentally, the features on the current-voltage characteristic of a highly transparent Josephson junction caused by transition of the superconducting leads to the normal state. These features appear due to the suppression of the Andreev excess current. We show that by tracing the dependence of the voltage, at which the transition occurs, on the bath temperature and by analyzing the suppression of the excess current by the bias voltage one can recover the temperature dependence of the heat flow out of the junction. We verify theory predictions by fabricating two highly transparent superconductor-graphene-superconductor (SGS) Josephson junctions with suspended and non-suspended graphene as a non-superconducting section between Al leads. Applying the above mentioned technique we show that the cooling power of the suspended junction depends on the bath temperature as $\propto T_{\rm bath}^{3.1}$ close to the superconducting critical temperature.

Compact formulas (1), (28) presented in this paper permit to formulate the Kallen-Lehmann harmonic decompositions of the products of two spinor and of spinor and scalar harmonic functions on AdS and Wightman functions on dS spaces; the correct flat space limits of the corresponding Kallen-Lehmann densities is demonstrated, the connection between poles of the Kallen-Lehmann density and the late-time divergence of the spinor-scalar loop is traced in the Yukawa model with light scalar field. Also in Sec. 4 the relatively simple, suitable for calculations Kallen-Lehmann representations of the real parts of spinor and scalar one-loop self-energies on dS space-time are proposed, and corresponding spectral equations for conformal dimensions in the chain approximation are written down.

Currently, the superconducting diode effect (SDE) is actively discussed due to large application potential in superconducting electronics. In particular, the superconducting hybrid structures based on three-dimensional (3D) topological insulators are among the best candidates due to the strongest spin-orbit coupling (SOC). Most of the theoretical studies of the SDE focus either on full numerical calculation, which is often rather complicated or on the phenomenological approach. In the present paper we perform a comparison of the linearized and nonlinear microscopic approaches in the superconductor/ ferromagnet/ 3D topological insulator (S/F/TI) hybrid structure. Employing the quasiclassical Green's function formalism we solve the problem self-consistently. We show that the results obtained by the linearized approximation are not qualitatively different from the nonlinear solution. Main distinction in the results between the two methods is quantitative, i. e. they yield different supercurrent amplitudes. However, when calculating the so-called diode quality factor the quantitative difference is eliminated and both approaches can result in a good agreement.

We formulate AdS_2 higher spin gravity as BF theory with fields taking values in sl(N,R) algebra treated as higher spin algebra. The theory is topological and naturally extends the Jackiw-Teitelboim gravity model so as to include higher spin fields. The BF equations linearized about AdS_2 background are interpreted as describing higher spin partially-massless fields of maximal depth along with dilaton fields. It is shown that there are dual metric-like formulations following from the original linearized BF higher spin theory. The duality establishes a dynamical equivalence of the metric-like field equations that can be given either as massive scalar field equations or as conservation conditions for higher spin currents.

We investigate superconductor-insulator quantum phase transitions in ultrathin capacitively coupled superconducting nanowires with proliferating quantum phase slips. We derive a set of coupled Berezinskii-Kosterlitz-Thouless-like renormalization group equations demonstrating that interaction between quantum phase slips in one of the wires gets modified due to the effect of plasma modes propagating in another wire. As a result, the superconductor-insulator phase transition in each of the wires is controlled not only by its own parameters but also by those of the neighboring wire as well as by mutual capacitance. We argue that superconducting nanowires with properly chosen parameters may turn insulating once they are brought sufficiently close to each other.

A search for sub-GeV dark matter production mediated by a new vector boson $A'$, called dark photon, is performed by the NA64 experiment in missing energy events from 100 GeV electron interactions in an active beam dump at the CERN SPS. From the analysis of the data collected in the years 2016, 2017, and 2018 with $2.84\times10^{11}$ electrons on target no evidence of such a process has been found. The most stringent constraints on the $A'$ mixing strength with photons and the parameter space for the scalar and fermionic dark matter in the mass range $\lesssim 0.2$ GeV are derived, thus demonstrating the power of the active beam dump approach for the dark matter search.

(abridged) We consider a secular orbital evolution of a supermassive binary black hole (SBBH) with unequal masses $M_p$ and M_s &lt; M_p in a central part of a non-spherical nuclear star cluster (NSC). When the mass of NSC inside the orbit is smaller than $M_{s}$ dynamical friction becomes inefficient. The subsequent orbital evolution of SBBH is largely governed by perturbing tidal potential of NSC arising from its non-sphericity. When the perturbing potential is mainly determined by quadrupole harmonics with azimuthal number $|m|=2$ the secular dynamics of the SBBH does not conserve any components of the angular momentum and can lead to the formation of highly eccentric orbits. Such orbits can experience an efficient circularization due to emission of gravitational waves (GW). In this Paper we consider this situation in some detail. We study analytically and numerically the orbital evolution taking into account the important effect of Einstein apsidal precession and estimate the largest possible value of $e$, which can be obtained. We then estimate a possibility of fast orbital circularization through emission of gravitation waves on a highly eccentric orbit, with circularization timescale of the order of the orbital period. We find that our mechanism could result in such events on a time scale of the order of or smaller than a few Gyr. It is stressed that for particular values of the model parameters such events may sometimes be distinguished from the ones expected in more standard scenarios, since in our case the eccentricity may remain substantial all the way down to the final merger. It is also noted that our results can be applied to other astrophysical settings, e.g. to study the orbital evolution of a binary star or a proto planetary system inside a massive deformed gas cloud.

Totally symmetric arbitrary spin fields in AdS space, conformal fields, conformal currents, and shadow fields in flat space are studied. Light-cone formulation for such fields, currents, and shadows is obtained. Use of the Poincare parametrization of AdS space allows us to treat fields in flat and AdS spaces on equal footing. Light-cone gauge realization of relativistic symmetries for fields, currents, and shadows is also obtained. The light-cone formulation for fields is obtained by using the gauge invariant Lagrangian which is presented in terms of the modified de Donder divergence, while the light-cone formulation for currents and shadows is obtained by using gauge invariant approach to currents and shadows. This allows us to demonstrate explicitly how ladder operators entering the gauge invariant formulation of fields, currents, and shadows manifest themselves in the light-cone formulation for fields, currents, and shadows.

We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n spacetime dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed 2-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder-Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein-Yang-Mills theory we consider free higher spin fields, multi-frame gravity, and parameterized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.

We consider the Wilson line networks of the Chern-Simons $3d$ gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus $2d$ CFT. After general discussion that summarizes and further extends results known in the literature we explicitly obtain the one-point torus block and two-point torus blocks through particular matrix elements of toroidal Wilson network operators in irreducible finite-dimensional representations of $sl(2,\mathbb{R})$ algebra. The resulting expressions are given in two alternative forms using different ways to treat multiple tensor products of $sl(2,\mathbb{R})$ representations: (1) $3mj$ Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor products of the fundamental $sl(2,\mathbb{R})$ representation.