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Theory of Casimir Forces: A Unified Approach Using Finite-Temperature Field Theory
Journal of Mathematical Physics. 2025. Vol. 66. No. 12. Article 123301.
We present a quantum theory of Casimir forces between perfect electrical conductors, based on quantum electrodynamics and quantum statistical physics. This theory utilizes Kapusta’s finite-temperature field theory, combined with the Faddeev–Popov ghost formalism. This approach allows us to calculate Casimir forces at finite temperatures, providing both previously known and new physical insights from a unified perspective. Furthermore, our method enables us to compute the stress tensor associated with Casimir forces, in accordance with the Helmholtz free energy of an equilibrium quantum electromagnetic field. Using this method, we calculate the tangential pressure in a slit-like pore due to the Casimir effect.
Kulev Y., Maksaev A., Promyslov V., Linear Algebra and its Applications 2026 Vol. 730 P. 51–72
The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This ...
Added: August 7, 2026
Kanunnikov A., Promyslov V., Vassilieva E., Electronic Journal of Combinatorics 2024 Vol. 31 No. 3 Article P3.6
Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the b-conjecture) are two major open questions relating Jack symmetric functions, the representation theory of the symmetric groups and combinatorial maps. They show that the coefficients in the power sum expansion of some Cauchy sum for ...
Added: August 7, 2026
Ponomarev A., Aleksandrov N., Journal of Physics D: Applied Physics 2026 Vol. 59 Article 315205
Electron attachment and detachment in H2O:O2 and H2O:air mixtures are theoretically studied at moderate (40–100 Td) reduced electric fields. It is shown that there are two synergistic mechanisms of ultra-rapid electron detachment from negative ions in these mixtures, whereas these detachment channels are absent in pure gases. Effective attachment coefficient calculated with consideration for fast ion–molecule ...
Added: August 6, 2026
Khrapai V., Tikhonov E., Nature Physics 2026 P. 1–2
Feng et al.1 presented transport measurements of three-terminal normal–superconductor–normal devices based on topological insulator nanowires. They measured the full differential conductance matrix, defined as Gij = ∂Ii /∂Vj , beyond the linear response regime as a function of various control parameters. Here i, j∈ [1, 2] denote normal terminals biased by the voltages V1 and ...
Added: August 5, 2026
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
G. G. Bondarenko, Kristya V. I., Savichkin D. O. et al., Journal of Surface Investigation: X-Ray, Synchrotron and Neutron Techniques 2026 Vol. 20 No. 2 P. 417–423
A model of a glow gas discharge in a mixture of argon and mercury vapor is formulated in the presence
of a thin insulating film on the cathode surface. Dependences of the discharge characteristics on the
mixture temperature are calculated in the range of its variation, in which a noticeable contribution to ionization
of the working gas is ...
Added: August 1, 2026
Касимов Р. Х., Аржанов А. И., Седых К. О. et al., Оптический журнал 2026 Т. 93 № 1 С. 80–86
Предмет исследования. Использование метода капельного нанесения для изготовления источника одиночных фотонов. Цель работы. Разработка технологического процесса изготовления источника одиночных фотонов на коллоидных квантовых точках для использования их в фотон- ных интегральных схемах. Метод. На первом этапе в программе ANSYS Lumerical рассчитыва- ются период и фактор заполнения фокусирующих элементов связи на длинах волн 545 и 600 ...
Added: July 31, 2026
Nevzorov A., Golikov A., Gneushev D. et al., JETP Letters 2026 Vol. 147–151 No. 3 P. 147–151
This paper demonstrates a special stochastic operation mode of a photonic element with a thin GeTe film deposited at a silicon nitride waveguide. As opposed to traditional deterministic switching between stable states, it has been shown that identical pump laser pulses cause a stochastic change in the transmission coefficient. The discovered effect opens up new ...
Added: July 31, 2026
A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Dual-mode infrared detection via photovoltaic and barrier pyroelectric effects in PbTe p–n junctions
Jarashneli A., Кобцев Д. М., Upcher A. et al., Journal of Applied Physics 2026 Vol. 140 No. 2 Article 024501
In the work, two effects appeared in PbTe p–n junctions under mid-wavelength infrared (2 − 5 μm) and long-wavelength infrared irradiation (≈10.6 μm). The first effect was created by the optical absorption of lR-photons in PbTe and caused by its photovoltage effect. The second novel effect is related to the heating process and the formation ...
Added: July 31, 2026
Nikolaev G. A., Orlov O. V., Andreeva S. et al., Physical Review Applied 2026 Vol. 26 Article 014099
We report the electrical detection of the spin resonance with temporal resolution in a two-dimensional electron system. Spin resonance was excited by pulses of subterahertz radiation characterized by relatively short rise and fall times on the order of 10 ns and was observed as a resonant peak in the high-frequency conductivity of the two-dimensional channel. The ...
Added: July 31, 2026
S. A. Andreeva, Orlov O. V., A. V. Shchepetilnikov et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 6 Article 065420
We investigate the temperature dependence of the pseudospin phase transition at filling factor 𝜈=2 in the quantum Hall regime. Experiments were performed on a high-quality, wide AlAs quantum well, where the pseudospin degree of freedom arises naturally from the near degeneracy and equivalence of the two conduction-band valleys. The anisotropic 𝑔-factor inherent to AlAs enabled independent measurement of ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing
interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications.
Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and
reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Nikolai N. Kalikin, Petr E. Brandyshev, Yury A. Budkov, Journal of Chemical Physics 2026 Vol. 164 No. 15 Article 154904
This study presents a mean-field theory for zwitterionic polymer solutions confined within attractive slit-like nanopores. Building upon our prior model for self-coacervation [Budkov et al., Soft Matter 19, 3281–3289 (2023)], we demonstrate that strong electrostatic dipole–dipole correlations between monomeric units, coupled with attraction to pore walls, can induce capillary-driven liquid–liquid phase separation inside the pore—a ...
Added: April 18, 2026
Ekaterina G. Odintsova, Darya L. Gurina, Yury A. Budkov, Colloids and Surfaces A: Physicochemical and Engineering Aspects 2026 Vol. 736 Article 139693
The behavior of water under nanoscale confinement is crucial for numerous technologies; yet predicting its
properties remains challenging due to the complex interplay of pore geometry and surface chemistry. While the
influence of general hydrophilicity is recognized, the specific role of the flexibility of surface functional groups - a
key molecular-scale feature - has remained underexplored. To address ...
Added: January 24, 2026
Dmitry Vasilyev, Journal of Physics: Conference Series 2021 Vol. 1942 Article 012017
In this work, structural, elastic and thermal properties of the Laves phase Fe2Mo (λ-) with the C14-type structure existing in the Fe – Mo system have been investigated using the quantum mechanical calculations within the frame of the density functional theory (DFT). The equilibrium lattice parameters, atoms position coordinates and average magnetic moment of atoms ...
Added: July 26, 2025
Vasilyev Dmitry, Physica B: Condensed Matter 2021 Vol. 621 No. 15 Article 413307
In this work, a new method of searching a most energetically favorable free energy calculated along different thermal expansion paths of a compound is proposed. This makes it possible to reduce the problem to a one-dimensional case and to consider free energy as having one variable - volume. The method was applied to study the ...
Added: July 25, 2025