One prominent phenomenon in relativistic nucleus-nucleus collisions is jet quenching due to medium-induced partonic energy loss. The observable most directly associated with jet quenching is the suppression of the yield of hadrons with a high transverse momentum p_T, which is quantified by the nuclear modification factor, R_AA (p_T, η). It is defined as the ratio of the inclusive single-hadron yield per unit pseudorapidity η in AA collisions to the corresponding yield in pp collisions, scaled by the average number of binary nucleon-nucleon collisions. In this paper, we investigate the double nuclear modification factor, which was introduced in [1], to simultaneously probe initial and final state effects. We consider a more general case where both hard particles experience energy loss. The hypothesis of the factorization of this factor

R_AA (p_T1, η₁; p_T2, η₂) = F∙R_AA (p_T1,η₁)∙R_AA (p_T2,η₂)

is tested for different types of final-state hadrons within the framework of the HYDJET++ model.

Fig.1 The dependence of the ratio F of the double and the product of single nuclear modification factors on the minimum value of the hadron transverse momentum p_T .

The deviation F from factorization of the production pions in association with kaons and (anti-)protons as well as the production of kaons in association with (anti-)protons was calculated for central PbPb collisions at center-of-mass energy 5.02 TeV per nucleon pair (Fig. 1). Results indicate that the hypothesis of factorization holds reasonably well at moderately high p_T, provided that the effects of double parton scattering can be small or neglected. However factorization violation starts to show at very high p_T. This supports the conclusion that measurements of the double nuclear modification factors offer significant potential for further investigations.

[1] S.P. Baranov, A.V. Lipatov, M.A. Malyshev, and A.M. Snigirev, JETP Letters 119, 823 (2024)

A. S.Chernyshov, I.P. Lokhtin, A.M. Snigirev
JETP Letters 122, issue 5 (2025)

At present, the generally a epted and widely used prop erty of multiparti le amplitudes is the absen e of simultaneous dis ontinuities of amplitudes in energy invariants of overlapping hannels. To justify this prop erty, the Steinmann relations are used. The pap er shows the presen e of su h dis ontinuities and the illegitima y of using the  teinmann relations to prove their absen e. In the ase of infrared singular parts of the amplitudes, the existen e of the simultaneous dis ontinuities is ompletely natural. But it is not limited to su h parts, and is not limited to the existen e of infrared singularities at all, but o urs also in their absen e. The pap er demonstrates the existen e of simultaneous dis ontinuities in the $s_{12}$ and $s_{23}$ hannels for the amplitude with three parti les in the nal state shown in the gure.

The existen e of simultaneous dis ontinuities means that the urrently a epted form of multi-Regge amplitudes is in orre t and should b e taken into a ount when deriving the BFKL (Balitsky-Fadin-Kuraev-Lipatov) equation in the higher approximations.

V. Fadin
JETP Letters 122, issue 4  (2025)

Contrary to their name, black holes in fact glow. According to Stephen Hawking’s famous result, black holes radiate energy and have a temperature. But where does this temperature come from?

In our research, we show that this strange heat of spacetime has a surprisingly topological origin. That is, it depends not just on the local properties of gravity, but on the global shape of spacetime itself. The Big Idea: Curvature Meets Topology.Every object-whether a donut or a sphere-has a property called the Euler characteristic. It's a number that tells you something deep about the object's shape. For example: A sphere has Euler characteristic 2, A donut (torus) has Euler characteristic 0. Our breakthrough is this: the temperature of spacetime horizons (like those around black holes or inside an expanding universe) is related to their Euler characteristic. We prove this using a powerful mathematical tool: the Chern-Gauss-Bonnet theorem, which links curvature and topology. But to apply it to spacetimes, we have to use a clever trick called Wick rotation--a way of turning time imaginary to smooth out the geometry. 


Black holes are examples of phenomena known as causal horizons - which are boundaries in spacetime across which events cannot influence each other due to the finite speed of light. These occur across many various spacetimes, and comprise an interesting intersection between gravity, quantum field theory, and thermodynamics. In the case of the Schwarzschild and de Sitter spacetimes, we find this connection can be characterised by the well-known Wick rotation (also known as analytic continuation) where $t \to i\tau$ and the resulting periodicity becomes $\tau \sim \tau + 2\pi \beta$. This periodicity in the Euclidean time $\tau$ is an indication of a non-trivial thermal state present within the spacetime - with temperature $T_H = 1/\beta$ - indicating a uniform radiation flux from the horizon. 

By applying the Wick rotation to these two well-studied phenomena:

1. 1. Schwarzschild Black Hole: A simple, non-rotating black hole. Its Euclidean version looks like a disc (D²) crossed with a sphere (S²). Its Euler characteristic is 2, and we show that the Hawking temperature is directly related to this number. 
2.  2. de Sitter Universe: A model of a universe filled with dark energy. Here too, Wick rotation gives us a compact space, and again the Euler characteristic determines the temperature-in this case, the Gibbons-Hawking temperature. 

This argument from Wick rotation places primary emphasis on the thermal properties of fields within spacetime. However, the analytic continuation $t \to i\tau$  and resulting angular compactification in $\tau$ is a non-trivial geometric operation that enforces global constraints on the topology of the manifold. For instance, in the case of de Sitter, this procedure maps the non-compact hyperbolic spacetime to the compact 4-sphere. The consequences of this from the geometric perspective are considerable: various integrals over scalars formed from the Riemann curvature are now guaranteed to converge (while before Wick rotation they automatically diverged in time $t$) to topological integers.

Fig.1 Under Wick rotation de Sitter space is transformed into an $S^4$ sphere  while  Black hole - into the product of disk and 2D sphere: $D^2\times S^2$. Both have Euler characteristic $\chi=2$}

Here we demonstrate that these considerations lead to a natural topological origin for horizon thermodynamics. For both Schwarzschild and de Sitter spacetimes, the temperature of the spacetime horizon is shown to be inversely proportional to the Euler characteristic $\chi$ (a topological integer) of the manifold after the Wick rotation and Euclidean time periodicity are performed. In addition, for de Sitter this framework explains topologically the origin of the discrepancy between the two physical temperatures discussed extensively by G. Volovik, A. Polyakov and others. Therefore, while the thermal field theory perspective is computationally powerful in quantifying horizon dynamics, the latter is in fact the consequence of a duality between the causal structure of a spacetime and the global topology of its analytical continuation. 

So why does it matter? This topological approach gives us: 

•  A unified framework to understand horizon temperatures.
•   A new geometrical insight into why time becomes periodic near a horizon.
•   A profound link between heat and shape-suggesting that spacetime itself may know its temperature because of its topology. 

In short, we show that temperature is not just about energy-it's about the shape of space itself.

Hughes J.C.M. and Kusmartsev F.V. 
JETP Letters 122, issue 4 (2025)

 

This work presents the results of direct numerical simulation of gravity water wave turbulence within a fully nonlinear plane-symmetric model. We show that in 1D geometry, the spectrum of weak turbulence of plane gravity waves generated by five-wave resonant interactions (suggested in [1]) is not realized. Instead of that, the main contribution to turbulence is due to wave breaking, which produces a power-law spectrum in both the frequency range and the wavenumber space with the same exponent equal to −4, see Fig.1. To our knowledge, our results represent the first direct numerical confirmation of the strong turbulence spectra predicted in [2]. In strongly nonlinear regime, the calculated probability density function (PDF) for the surface gradient has power-law tails with exponents close to −7/2, which indicates intermittency in turbulence.

Fig.1. The calculated frequency and spatial spectra of surface perturbations compared to the power-law dependencies ω^-4 and k^-4.

1. A.I. Dyachenko, Y.V. Lvov, V.E. Zakharov, Physica D 87(1-4), 233(1995)

2. E.A.Kuznetsov, JETP Lett. 80(2) ,83 (2004)

E.  Kochurin and E. Kuznetsov
JETP Letters 122, issue 4 (2025)

The work proposes an analytical theory of nonlinear generation of large-scale magnetic turbulence in collisionless plasma with an anisotropic velocity distribution of particle in the presence of an external magnetic field. Based on the results of the dispersion analysis of the Weibel-type instability in magnetoactive collisional plasma, and with use of the quasilinear approach, a system of equations describing the evolution of the mean-square magnetic-field energy density of small- and large-scale components of the turbulent field is obtained.

It is shown that, even in the absence of interparticle collisions, anomalous collisions of particles due to scattering on small-scale magnetic fluctuations lead to instability of long-wave harmonics, which are stable in the linear approximation. The non-linear growth of such harmonics at a given anisotropy of the particle velocity distribution, consistent with the dynamics of short-wave perturbations at the saturation stage and possible anisotropic particle injection, occurs in the superexponential regime and corresponds to an explosive-type instability (Fig. 1).

The growth law of the large-scale magnetic field is found analytically and the critical time of explosive instability is estimated. This type of fundamental plasma process is expected in a number of transient phenomena in laboratory and astrophysics, e.g., in accretion disks and jets, in stellar winds and coronal flares, in collisionless shock waves and laser ablation processes.

Fig.1 Time dependence of the mean-square magnetic-field energy density $w$. The dotted and dash-dotted lines are numerical solutions for small- and large-scale components of the turbulent field, and the blue and red solid lines are analytical solutions, respectively. A formal explosion takes place at a normalized time $\tau_c$.

N.Emel’yanov and V.V.Kocharovskii
JETP Letters 122, issue 2 (2025)

This work presents a theoretical method to estimate the transparency of grain boundaries in granular superconducting films. The study is motivated by the need to better understand how grains boundary influence
the superconducting properties and vortex physics in such materials. Scanning tunneling microscopy (STM) allows high-resolution measurement of the local density of states (LDOS) in superconductors, revealing variations related
to Abrikosov vortices and grain boundaries.
Physical Picture. Vortices in thin superconducting films are strongly affected by the transparency of grain boundaries. Vortex cores can be pinned at the boundaries or inside the grains. The spatial variation of the
superconducting order parameter and LDOS around vortex cores reflects these pinning scenarios.
Theoretical Model. The film is modeled as a network of cylindrical grains with boundaries of finite transparency, characterized by a boundary resistance parameter 𝑅𝐵 . The first scenario is considered when the
vortex is located in the grain center. The Usadel equations for dirty superconductors are solved in the circular cell approximation, with appropriate boundary conditions accounting for interface transparency. Numerical Results. Calculations show that the order parameter and shielding current density exhibit sharp
jumps at grain boundaries, the magnitude of which depends on the interface transparency and the grain size. The LDOS also changes abruptly at the boundary, with the difference between LDOS values on both sides of the
interface serving as a direct measure of boundary transparency.
Experimental relevance. The approach provides a practical route to extract an information about intergranular transparency from STM measurements of the LDOS near vortices in granular films. It is shown that boundaries located several coherence lengths from the vortex center provide the most sensitive data for this estimation. The developed method offers a way to diagnose the electronic quality of grain boundaries in superconducting films, which is crucial for optimizing performance of superconducting electronics and devices. The figure shows Abrikosov vortex in a cylindrical grain (left) and the dependencies of the magnitude of the
screening current density J on the distance r from the vortex core for various grain sizes.

Khapaev M.M., Kupriyanov M.Yu., Golubov A.A., Stolyarov V.S.
JETP Letters 122, issue 2 (2025)

The magnetic bubble domains in iron garnet films, the time-honored objects of micromagnetism, have recently come into focus due to their similarity to skyrmions. It has been known for decades that the bubble domains can be induced by an external magnetic field. However, this method cannot control the number of nucleated domains and their position. Furthermore, magnetic field control relying on bulky inductive elements does not match the requirements of modern microelectronics.

In this paper the local technique for magnetic domains generation is proposed: the site of bubble domain “blowing” is determined by the contact point with the sharp tip where the strain gradient is maximum, while the size of the domain can be tuned by voltage application between the tip and sample substrate. The possibility of the combined electro-mechanical control of noncollinear spin textures is interesting in the context of straintronics and spintronics.

From the fundamental point of view this result serves as an illustration of a profound analogy between the symmetry of chiral spin structures and flexural deformation in crystals. 

A.P.Pyatakov et al.,
JETP Letters 122, issue 3 (2025)

The paper reports a derived kinetic equation describing the dynamics of an atomic localized ensemble in a broadband squeezed light field taking into account second-order effects in the constant of interaction of atoms with the field (Stark interaction). Traditionally in deriving  the kinetic equation for an open system, effects of this kind are usually ignored, but due to the established specific properties  they are considered as being "built in" and tend to renormalize  the terms of the kinetic equation determined by first-order effects.

The kinetic equation is derived by applying algebraic resonance perturbation theory, which defines the creating, annihilating, and counting process for a quantum stochastic differential equation. For this purpose, the Stark interaction operator of a system with a broadband quantized electromagnetic field with a nonzero photon density is represented as a quantum counting process at the stage of formation of the electromagnetic field concerned. The equation differs from the known ones, but appears to agree with them in particular and limiting cases.

Stark interaction manifests itself in a change in the shape of the superradiance pulse of an atomic ensemble in the Dicke state and additional shifts in the energy levels of the atom. The figure shows graphs of superradiance pulses for ensembles in the Dicke state with the same value of the number of atoms under conditions of Stark interaction with squeezed light (red graph), neglect of Stark interaction with squeezed light (blue graph), and ensemble radiation into vacuum (green graph).

Trubilko A.I. and Basharov A.M.
JETP Letters 122, issue 1 (2025)

It is well known that there is a close connection between gravity and thermodynamics. This is especially true for the physics of black holes, whose thermodynamics is more or less generally accepted. It is determined by the temperature of the Hawking radiation from the horizon of the black hole, and the corresponding entropy is proportional to the area of the horizon, $S_{\rm BH}=A/4G$. However, in the case of the thermodynamics of the cosmological horizon in an expanding de Sitter Universe, the situation is not so clear. There are several different approaches to de Sitter thermodynamics with different assumptions about its temperature and entropy. The reason is that, unlike a black hole, the de Sitter state is not a localized object. It cannot be considered as a region bounded by the cosmological horizon. The de Sitter state is an unbounded symmetric state with constant scalar curvature.

It is usually assumed that the corresponding temperature of the de Sitter state is related to the temperature of the Hawking radiation from the cosmological horizon, the Gibbons-Hawking temperature $T_{\rm GH}=H/2\pi$, where $H$ is the Hubble parameter. However, if we consider the behavior of any object, for example an atom, placed in a de Sitter medium, it turns out that this object perceives the de Sitter vacuum as a heat bath with twice the Gibbons-Hawking temperature, $T=2T_{\rm GH}=H/\pi$. Since all points in de Sitter space are equivalent both inside and outside the horizon, this temperature is uniform, being the same for all local observers. Thus, a factor of two provides the difference between two physical temperatures: the local temperature $T$ and the temperature $T_{\rm GH}$ of the Hawking radiation from the cosmological horizon. This is one of the contradictions present in the construction of the thermodynamics of the de Sitter state.

Here we discuss the connections between these two thermodynamics, local thermodynamics and the thermodynamics of the Hubble volume, the volume of the region inside the cosmological horizon. (i) The local temperature is exactly twice the Gibbons-Hawking temperature. This connection has a simple explanation, following from de Sitter symmetry. (ii) There is a holographic connection between these thermodynamics. The entropy density integrated over the Hubble volume coincides with the entropy of the horizon, $S_{\rm Hubble}=S_{\rm horizon}=A/4G$, where $A$ is the area of the cosmological horizon. (iii) There is also a connection between the first law of local thermodynamics and the first law of global thermodynamics. Due to de Sitter symmetry, the first law is valid for an arbitrary volume $V$, which can be smaller or larger than the Hubble volume. This first law can also be applied to Hubble volume. In this case, the first law is expressed in terms of the entropy of the horizon. It is important that in both cases the thermodynamics is determined by the temperature $T=H/\pi$.

This consideration was also applied to the contracting de Sitter, for which $S_{\rm Hubble}=S_{\rm horizon}=-A/4G$. The entropy of the contracting de Sitter is negative, since its horizon is similar to the horizon of a white hole.

G.E.Volovik
JETP Letters 121, Issue 10 (2025)

Carrier localization in a random band potential is known to determine luminescence and lasing properties of visible-range InGaN-based light emitters. In this work, we study related effects in indium-rich InGaN ternary alloys with the near-infrared range spectral response. The investigated samples feature strong n-type residual doping inherent to InN, and we exploit this fact to perform all-optical characterization of the valence band tail states. Non-thermal hole distribution emerging at low temperatures is revealed, using time-resolved photoluminescence. A consistent model is proposed, which explains the observed strong red shift of the stimulated emission wavelength with respect to the spontaneous emission and luminescence quenching behavior at the increasing temperature.

K.Kudryavtsev, B.Andreev, D.Lobanov, M.Kalinnikov, A.Novikov, Z.Krasilnik
JETP Letters 121, issue 8 (2025)