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)

Fundamental physical constants are naturally included in all laws of physics. Their numerical values should reflect the properties of the world around us, but their origin remains unexplained to this day. It has been suggested since Dirac's work of 1937, 1938 that in a dynamically evolving Universe the physical constants may also be dynamical variables corresponding to the local age of the world. However, numerous laboratory experiments with various atomic and, more recently, nuclear clocks have failed to detect changes in physical constants with time at an ever deeper level, which corresponds at present to an upper limit on the relative change in, for example, the fine structure constant α, 10^(-19)/year. Astronomical spectral measurements allow such tests to go beyond laboratory experiments and study spatial and temporal constraints on variations of physical constants. It turned out that in this case the most sensitive parameter is the dimensionless quantity - the electron-to-proton mass ratio
(μ = m_e/m_p), since it determines the structure of molecular levels in a wide spectral range. The most accurate cosmological constraints, corresponding to look-back time greater than 10 billion years, give an estimate of Δμ/µ < 5*10^(-8), which is based on the analysis of methanol (CH3OH) transitions. The same order of magnitude upper limit was obtained from observations of the methanol lines in the disk of our Galaxy at relatively large galactocentric distances, R ~ 8-12 kpc.  In our work we estimated
Δμ/µ near a massive black hole, the Galactic center, at a distance R ~ 100 pc, which showed a possible decrease of μ at the level Δμ/µ = (-3.7±0.5)*10^(-7). The detected signal requires further independent study.

J.Vorotyntseva, S.Levshakov
JETP Letters 121, issue 8 (2025)
 

We consider a new concept of the evolving Universe, based on the idea of many fields in the vacuum state, where their initial expectation values are zero, but the total energy density is larger than zero. We call this state the polarized vacuum in GR. The exit from this state and "rolling down'' successively in directions determined by different fields is responsible for the evolution of the Universe and can be tested through investigation of the power spectra of cosmological perturbations.

We present a model of the early Universe, which is inspired by the observational data in the spatial wavenumbers $k\in(2\cdot10^{-4}, 10)$ Mpc$^{-1}$ and does not require a solution of the Friedman equations. Based on the observations we build a solution of General Relativity in the form of vacuum attractor, which provides an additional power at $k>10\,$Mpc$^{-1}$. Extending the power spectrum to the scale of kiloparsecs and less can solve the problems of the observed cosmology --- the appearance of the early star formation and supermassive black holes at $z>10$, the birth of primordial black holes, $\Lambda$CDM model, and others.

The trajectories of the dominant field in the model of the early Universe on the phase plane ($\phi$, $\dot\phi$). Bold lines correspond to the vacuum attractor, thin lines to the general solution, and arrows indicate the time direction.

V.N. Lukash, E.V. Mikheeva
JETP Letters 121, issue 6 (2025)

The problem of the nature of anomalous Hall effect was debated since its discovery. In magnetic topological insulators, the quantum anomalous Hall effect has been predicted and experimentally confirmed. However, in other materials with strong spin-orbit coupling, such as semiconductors with Rashba splitting, the transverse conductivity phenomenon is poorly studied.

In this letter, we theoretically investigate how electron scattering on domain walls modifies the intrinsic anomalous Hall response on the surface of a magnetic semiconductor with strong Rashba effect. The band structure of such a semiconductor, characterized by a nontrivial Berry curvature, determines the appearance of a one-dimensional resonant state on the magnetic domain wall in a local exchange gap. Under relatively weak exchange splitting, the resonant state has linear dispersion with small spectral broadening (see the figure). Moreover, it is chiral and localized near the domain wall. It is shown that the presence of a pair of parallel domain walls on the surface can have a measurable physical consequence: an additional almost half-quantized contribution to the anomalous Hall effect. The surface of the BiTeI polar semiconductor doped with transition metal atoms is a suitable material platform for experimental detection of such a contribution.

Spectral behavior, (a) and (b), and spatial profile (c) of electronic resonant states on the surface of the magnetic semiconductor with two parallel domain walls under varying magnetization magnitude in domains.

V. N. Men’shov, I. P. Rusinov, E. V. Chulkov
JETP Letters 121, issue 5 (2025)

A relatively simple method for implementing the conditions of the built-in Coulomb blockade in a quantum dot directly during the epitaxial growth of a heterostructure is proposed. This is achieved by adjusting the Fermi energy to the energy of the electron level in the quantum dot by forming a p-n-p doping profile by introducing a thin GaAs layer with n-type conductivity into the structure at a certain distance from the quantum dot layer. In this case, a neutral or charged state of an exciton in a QD can be realized without applying an external electric field, but only by varying the doping level in the n-GaAs layer and its distance to the quantum dot in accordance with the developed analytical model. Experimental studies of the spin dynamics and statistics of single-photon emission made it possible to obtain comprehensive information on the charge state of single quantum dots, the emission of which is coupled with the fundamental mode of a microcolumn microresonator. A significant increase in the probability of obtaining the required charge state for quantum dots formed using the Stranski–Krastanov growth mechanism is shown. For neutral and multiply charged quantum dots, this probability is in the range of 90-96%, and for singly charged quantum dots in the range of 70-95%. This approach represents a significant step towards complete control of optical processes in individual quantum dots for their potential application in quantum photonics.

A.I.Galimov, Yu.M.Serov, M.V.Rakhlin et al.,
JETP Letters 121, issue 5 (2025)

Currently, development of compact coherent soft X-ray sources is of particular interest, as they open up a number of important technological and scientific applications. High-harmonic generation in noble gases represents the only way for routinely producing such radiation by compact tabletop lasers in the laboratories worldwide. Coherent ultrashort-pulse X-ray sources based on high-harmonic generation are used to examine layered samples (including microelectronic components) with ultrahigh resolution, follow light-induced chemical reactions via time-resolved X-ray absorption spectroscopy and produce attosecond pulses. The latter are of high demand for problems of extreme laser fields (up to Schwinger limit) and nuclear photonics with the potential to refine existing theoretical models of quantum electrodynamics and develop new approaches.

In this paper we present high-harmonic generation based on a compact source of coherent X-ray radiation developed at Lomonosov Moscow State University. It is utilizing Cr:Forsterite laser technology, which is favored for high-harmonic generation due to the square scaling of the cutoff frequency versus laser wavelength. Soft X-ray pulses in the range of 45-83 eV (27.6–14.9 nm, Fig.1) with a total photon flux of 1.1·10⁹ photons/s were obtained, using an argon gas jet. Optimization of the harmonic flux along with the soft X-ray beam divergence was performed by introducing a frequency chirp into the pump pulse. We believe that the developed compact bright X-ray source represent the first experimental step towards generation of attosecond laser pulses in Russian Federation and can be integrated into rapidly developing domestic free-electron lasers and synchrotron sources in order to increase their temporal coherence.

Fig.1.Generated harmonic spectrum.

Rumiantsev B, Migal’ E., Lobushkin E., Pushkin A., Potemkin F.

JETP Letters 121, issue 5 (2025)

The coexistence of electric and magnetic orders in multiferroics imposes certain restrictions on the symmetry of the magnetic and crystalline structures of substances. However, many of them, having a non-centrosymmetric crystal structure, can exhibit magnetoelectric properties even in the paramagnetic state when a magnetic field is applied. Here we report the detection of electric polarization induced by the magnetic field H in single crystals of a trigonal non-centrosymmetric paramagnetic Nd₃Ga₅SiO₁₄ with a langasite structure. In small fields, the polarization is quadratic in H and for components in the basic ab plane it is described by two magnetoelectric susceptibilities (α₁ and α₂), while along the trigonal axis c it appears only starting from the fourth-order terms, ~H⁴. In strong magnetic fields at low temperatures, when the Nd³⁺ magnetic moments are saturated, the dependence of polarization on the field changes qualitatively and approaches to quasi-linear one for all crystallographic directions, and its magnitude increases greatly (up to 250 µC/m² along the c axis at 5 T, see Figure). A quantitative description of the effects observed in Nd₃Ga₅SiO₁₄ based on the spin-Hamiltonian of the Nd³⁺ ion in local low-symmetric (C₂) positions is presented, taking into account the symmetry-allowed magnetoelectric interactions. Nonlinear magnetoelectric invariants based on the local susceptibilities of Nd³⁺ ions are constructed, taking into account the nonequivalence of their magnetization and allowing us to describe the observed field, temperature and orientation dependences of polarization using few magnetoelectric parameters.

Figure. (a) The angular dependence of the electric polarization P_c along c axis, measured at 4.2 K at H =1.3 T when the magnetic field rotates in the ac plane. (b) The dependences of P_c  on a magnetic field applied in ac plane at an angle of 60^o from c axis at different temperatures (the inserts in (a) and (b) explain the geometry of the experiment). (c) The dependence of the dP_c/dH⁴ derivative on 1/T³, which characterizes the temperature dependence of the fourth order magnetoelectric susceptibility α₃. Symbols are an experiment, lines are a theory.

A.A. Mukhin , V.Yu. Ivanov, A.M. Kuzmenko, A.Yu. Tikhonovsky, B.V. Mill
 JETP Letters 121, issue 4 (2025)

In the thermodynamics of the conventional macroscopic systems the entropy is the extensive quantity, i.e. it is proportional to the volume of the system. That is why the splitting of the system with volume $V$ in two parts with volumes $V_1+V_2=V$ does not change the total entropy of the system,  $S(V_1+V_2)=S(V_1) +S(V_2)$. This, however, is not applicable to the thermodynamics of the black hole: the entropy of the black hole is not extensive. The splitting of the black hole of mass $M$ to two black holes with the same total mass $M_1+M_2=M$ leads to the decrease of the total entropy,  $S(M_1) +S(M_2) < S(M_1+M_2)$.

The composition rule for the black holes and thus the black hole thermodynamics can be obtained by consideration of the quantum processes -- processes of quantum tunneling. The calculations of the rate of quantum tunneling process of radiation of particles and photons from the black hole hole gives the temperature of the black hole radiation, which coincides with the Hawking temperature. On the other hand, the radiation of small black holes by the larger ones (or in general the splitting of the black hole to the smaller parts) are described by the processes of macroscopic quantum tunneling.

The macroscopic quantum tunneling is the rear event caused by quantum fluctuations, which in the black hole thermodynamics can be considered in the same manner as thermal fluctuations.
According to Landau-Lifshitz book "Statistical Physics", thermal fluctuations in the macroscopic system lead to decrease of the entropy, and thus the processes of the black hole fragmentation are determined by the change of the entropy after the splitting.  Then, the calculations of the rate of the fragmentation using the method of the macroscopic quantum tunneling allow us to obtain the composition rule for the black hole entropy:
\begin{equation}
\sqrt{S(M_1 + M_2)}=\sqrt{S(M_1)}+ \sqrt{S(M_2)}\,,
\label{CompositionN}
\end{equation}
which reproduces the Bekenstein-Hawking entropy. So, the macroscopic quantum tunneling approach is actually another way for the derivation of the black hole entropy.
 
 This composition rule demonstrates that the black holes obey the special type of the generalized statistics -- the Tsallis-Cirto statistics with $\delta=2$. This also suggests that the black hole  can be considered as an ensemble of the elementary black holes with the Planck-scale mass $M_0=1/\sqrt{4\pi G}$. The black hole mass is $M=NM_0$, where $N$  is the number of these micro black holes, which play the role of the black hole "atoms". The  Bekenstein–Hawking entropy of the black hole with $N$ atoms, is $S(N)=N^2$.

G.E. Volovik
JETP Letters 121, issue 4 (2025)

Dear readers and authors!

In April 2025 our journal Pis'ma v ZhETF (JETP Letters), celebrates 60 years of its history. The journal was founded on the initiative of Peotr Kapitza, and established by the Decree of the Presidium of Soviet Academy of sciences. The first issue was published on April, 1, 1965. From its inception to the present day, the journal was aimed at a wide readership of researchers from various fields of physics. Its mission is to provide a rapid publication platform for short communications on new results from research of the highest significance and highest priority in all areas of experimental and theoretical physics. We decided to inform our authors and readers on the 60th anniversary of our Journal with this brief note solely, since a fairly detailed article on the history of the foundation and development of the JETP Letters was published in Physics-Uspekhi [1] to the 50th anniversary of the Journal.

We are proud that among the authors who published their research in our journal are eleven Nobel Prize winners, and a great number of outstanding scientists, including:

Today, as in previous years, Pis'ma v ZhETF (JETP Letters) is the Russia’s premier physics letter journal, authoritative and influential source of verified information for researchers working in various fields of physics. The journal continues to retain its leadership position in Russia, and is noticeable also at the international arena. Full texts of all articles published in Pis'ma v ZhETF, throughout the entire history of the journal, are available on the journal's Internet portal, and on other sites created by order of the Russian Academy of Sciences.

In addition to the Russian edition of the journal, all articles are published in English in the JETP Letters and indexed in international databases, almost simultaneously with the release of the Pis'ma v ZhETF; the full texts of the vast majority of them are also available in open access.

The JETPL editorial board traces new and “hot” topics in physical sciences, and recently included into the journal scope such fields as quantum informatics, biophysics, and medical physics.

Now as well as 60 preceding years, the journal serves scientific community and welcome new original experimental and theoretical research contributions, new ideas, and new authors!

JETP Letters Editorial board