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Phase-locking in dynamical systems and quantum mechanics
Journal of High Energy Physics. 2026. Article 101.
In this study, we discuss the Prüfer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schr¨odinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the band-gap structure of the Hill equation. For the parametric oscillator, we provide the relation between the non-adiabatic Hannay angle and the Poincar´e rotation number of the corresponding dynamical system. In terms of quantum mechanics, the integer rotation number is connected to the quantization number via the Milne quantization approach and exact WKB. Using recent results concerning the exact WKB approach in quantum mechanics, we discuss the possible non-perturbative effects in the dynamical systems on the torus and for parametric oscillator. The semiclassical WKB is interpreted in the framework of a slow-fast dynamical system. The link between the classification of the coadjoint Virasoro orbits and the Hill equation yields a classification of the phase-locking domains in the parameter space in terms of the classification of Virasoro orbits. Our picture is supported by numerical simulations for the model of the Josephson junction and Mathieu equation.
Боровицкая И. В., Пименов В. Н., Коршунов С. Н. et al., Перспективные материалы 2026 № 10 С. 37–54
Проведено сравнение, обобщение и систематизация механизмов эрозии и разрушения
поверхности малоактивируемых материалов, перспективных для использования в
качестве материалов вакуумной камеры термоядерных реакторов: ванадия, его сплава
V – 10 Ti – 6 Cr – 0,05 Zr – 0,1 Si и вольфрама при последовательном воздействии на
них ионных и тепловых потоков. Тепловые потоки имитировали с помощью мощного
импульсного лазерного излучения (ЛИ), создаваемого ...
Added: September 22, 2026
Iontsev M.A., Mukhin S. I., Fistul M. V., Physical Review B: Condensed Matter and Materials Physics 2019 Vol. 100 No. 2
We report a theoretical study of the ac response of superconducting quantum metamaterials (SQMs), i.e., an array of qubits (two-level systems) embedded in a low-dissipative resonator. By making use of a particular example of a SQM, namely the array of charge qubits capacitively coupled to the resonator, we obtain a second-order phase transition between an ...
Added: September 22, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., Муллабаева А. У., Уфимский математический журнал 2010 Т. 2 № 1 С. 52–58
В данной статье введены обобщённые пространства Фока и рассмотрены основные свойства этих пространств. Найдена операция, сопряженная к операции умножения на переменную в обобщенном пространстве Фока. Также определены собственные функции сопряженного оператора. Изучены обобщенное преобразование Лапласа и задача построения базиса для введенных пространств. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 855–862
Tasks related to the automation of medical data processing are becoming more urgent. Particular attention is paid to systems for monitoring and analyzing human physiological parameters. Such systems often use specialized sensors to capture biomedical images, such as infrared cameras. This article describes our study of the problem of segmenting the eye pupil and iris ...
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 844–854
Improving image quality is becoming an increasingly popular task, especially when working with mobile devices. One common approach to image enhancement is the use of convolutional neural networks. However, to achieve good results, such networks must be large enough, otherwise there is a risk of unwanted artifacts. In addition, large convolutional neural networks require significant ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Optical Memory and Neural Networks (Information Optics) 2024 Vol. 33 P. 424–434
This study explores the development of classifiers for microbial images, specifically focusing on streptococci captured via microscopy of live samples. Our approach uses AutoML-based techniques and automates the creation and analysis of feature spaces to produce optimal descriptors for classifying these microscopic images. This technique leverages interpretable taxonomic features based on the external geometric attributes ...
Added: September 21, 2026
Aleksei Samarin, Aleksei Toropov, Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1053–1060
This paper presents a novel approach to classification in biomedical imaging, specifically targeting polyp recognition in video endoscopy snapshots. Our method leverages specialized image descriptors to enhance the accuracy and robustness of polyp recognition. By employing these specialized descriptors, we address the challenges inherent in analyzing biomedical images from open datasets. Our approach not only ...
Added: September 21, 2026
Самарин А. В., Торопов А. Г., Савельев А. Г. et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1044–1052
This paper presents a study aimed at improving the detection quality of small-sized microorganisms under challenging microscopic conditions through the application of a lightweight combined image preprocessing model. We focused on the task of detecting diplococci in images obtained through dynamic sample microscopy. The proposed approach employs predefined filters for image preprocessing, combined with the ...
Added: September 21, 2026
Singapore: Springer Singapore, 2025.
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., / Series arXiv "math". 2025. No. 2511.20141.
This paper presents a novel approach to neural network compression that addresses redundancy at both the filter and architectural levels through a unified framework grounded in information flow analysis. Building on the concept of tensor flow divergence, which quantifies how information is transformed across network layers, we develop a two-stage optimization process. The first stage ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2009 Т. 424 № 5 С. 591–593
В данной статье вводится определенный класс дифференциальных уравнений с переменными коэффициентами, который тесно связан с операцией умножения Адамара и операторами Данкла имеющими применение в математической физике. Показано, что уравнения этого класса могут быть сведены к уранвениям в обобщенных производных с постоянными коэффициентами. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 169–178
This study explores the incorporation of specialized self-attention mechanisms into deep learning architectures, with a particular emphasis on segmenting human iris and pupil regions in infrared images. In this work, we present some modified versions of nonlocal blocks designed to enhance self-attentive properties while addressing the distinct characteristics of infrared imaging data. By applying these customized ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 10 Article 359
Timely identification and accurate delineation of ultra-early ischemic stroke lesions in non-contrast computed tomography (CT) scans of the human brain are of paramount importance for prompt medical intervention and improved patient outcomes. In this study, we propose a deep learning-driven methodology specifically designed for segmenting ultra-early ischemic regions, with a particular emphasis on both the ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2012 Т. 443 № 3 С. 293–295
В данной работе введены обобщенные частные производные, изучены дифференциальные уравнения в обобщенных частных производных с постоянными коэффициентами и доказан фундаментальный принцип Эйлера для таких уравнений. Устанавливлена связь с классом уравнений в обычных частных производных с переменными коэффициентами. ...
Added: September 21, 2026
Springer, Cham, 2025.
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 6 P. 1–20
This study presents a unified low-parameter approach to multi-class classification of microorganisms (micrococci, diplococci, streptococci, and bacilli) based on automated machine learning. The method is designed to produce interpretable taxonomic descriptors through analysis of the external geometric characteristics of microorganisms, including cell shape, colony organization, and dynamic behavior in unfixed microscopic scenes. A key advantage ...
Added: September 21, 2026
Shilov A. L., Elesin L., Kravtsov M. et al., Nature Communications 2026 Vol. 17 No. 1 Article 9734
Identifying the microscopic processes limiting conductivity is essential for understanding correlated quantum materials. In twisted bilayer graphene, metallic resistivity follows ρ ~ Tα with widely varying α, fueling competing interpretations from phonon-limited transport and umklapp scattering to strange metallicity and heavy-fermion renormalization. Here, we use terahertz excitation to selectively heat electrons while keeping the lattice cold, separating ...
Added: September 20, 2026
Tsarev P., Yakov V. Fominov, SCIPOST PHYSICS 2025 Vol. 19 No. 6 Article 148
Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resistively Shunted Junction (RSJ) model, an important example of a nonlinear dynamical system. The ...
Added: December 20, 2025
Glutsyuk A., Александров А. А., Горский А. С., / Series arXiv "math". 2025.
In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the ...
Added: June 23, 2025
Piasotski K., Lesser O., Reich A. et al., Physical Review B: Condensed Matter and Materials Physics 2025 Vol. 111 No. 17 Article 174527
Recent experiments on planar superconductor-topological insulator-superconductor (S-TI-S) junctions, e.g., in the Corbino geometry, have reported low-temperature nonzero Josephson currents in states with integer fluxoid (flux) induced in the junction by a perpendicular magnetic field. This effect was discussed in connection with Majorana zero modes localized in Josephson vortices of such junctions. Here, we provide an ...
Added: May 27, 2025
Li Z., Fattah A., Timashev P. et al., 2022 Vol. 22 No. 15 Article 5907
The development of synthetic biology has enabled massive progress in biotechnology and in approaching research questions from a brand-new perspective. In particular, the design and study of gene regulatory networks in vitro, in vivo, and in silico have played an increasingly indispensable role in understanding and controlling biological phenomena. Among them, it is of great ...
Added: March 12, 2024
Artem V. Polkin, Pavel A. Ioselevich, SCIPOST PHYSICS 2023 Vol. 15 Article 100
We study Multiple Andreev Reflections in long diffusive superconductor(S)-normal metal(N)-superconductor junctions with low-transparency interfaces. Assuming strong thermalization in the weak link, we calculate the current-voltage dependence I(V). At intermediate temperatures, εTh≪T≪Δ, the current is dominated by noncoherent multiple Andreev reflections and is obtained analytically. The results are generalized to a ferromagnetic junction. We find that the exchange ...
Added: November 13, 2023
Ladjal B., , in: 13th International Conference on Power, Energy and Electrical Engineering (CPEEE), February 25-27, 2023. Tokyo, Japan.: IEEE, 2023. P. 188–192.
In some situations, it is possible to synthesize control actions for nonlinear systems using the theoretical underpinnings of solving linear-quadratic issues. A technique based on the application of the Riccati equation, the parameters of which depend on the state of the object, is one of the promising and quickly emerging approaches for creating nonlinear regulators. ...
Added: September 18, 2023
Marychev P., Водолазов Д. Ю., Beilstein Journal of Nanotechnology 2020 Vol. 11 P. 858–865
We calculate the current–phase relation (CPR) of a SN-S-SN Josephson junction based on a SN bilayer of variable thickness composed of a highly disordered superconductor (S) and a low-resistivity normal metal (N) with proximity-induced superconductivity. In such a junction, the N layer provides both a large concentration of phase in the weak link and good ...
Added: January 12, 2023