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Phase-locking in dynamical systems and quantum mechanics
Journal of High Energy Physics. 2026. Vol. 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.
Budkov Y., Kalikin N., Journal of Chemical Physics 2026 Vol. 165 No. 16 Article 164108
We derive the local pressure tensor generated by the original Rosenfeld fundamental measure theory (FMT) for hard-sphere fluids from an arbitrary infinitesimal deformation. The variation of a finite-distance FMT kernel is written via the line integrals of the local deformation gradient along the straight segment connecting its end points. The resulting symmetric pressure tensor consists ...
Added: October 22, 2026
Ивченко В. С., Иевлева В. А., Matienko D. et al., Журнал технической физики 2026 № 9 С. 1738–1749
Задача о возбуждении бегущих фонон-поляритонных волн на поверхности полярного кристалла падающей извне световой волной (с частотой, близкой к частоте решеточных колебаний) решена теоретически только для бесконечной открытой поверхности кристалла. В случаях, когда часть поверхности покрыта металлической маской, препятствующей проникновению возбуждающего излучения к атомам среды, и эта маска имеет произвольную форму, общепризнанного решения неоднородной задачи нет. ...
Added: October 20, 2026
Logvenkov S. A., Известия РАН. Механика жидкости и газа 2026 № 3 С. 59–75
The problem of the evolution of cell volume fraction in a spherical aggregate composed of cells,
extracellular matrix, and fluid is considered. The aggregate is surrounded by extracellular matrix. The
problem formulation employs a multiphase model of a biological continuum, previously developed by the
author, consisting of two actively interacting solid phases and a fluid. The propagation of ...
Added: October 20, 2026
Lavrukhina E. A., Krasavin D. P., Krishtopenko S. S. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 22 Article 225414
We study coherent electric manipulation of magnetic field induced localized states at a double kink of a helical edge in a HgTe/CdHgTe quantum well. An in-plane magnetic field opens a gap in the one-dimensional (1D) edge spectrum, while changes in the edge orientation generate localized in-gap states at the kinks. We show that, for suitable ...
Added: October 19, 2026
Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
Added: October 19, 2026
Vorontsova T., М.: Академия, 2025.
The textbook has been prepared in accordance with the requirements of the federal state educational standards for secondary vocational education and is intended for studying the professional modules “Information Security in Information and Telecommunication Systems and Networks Using Software and Hardware‑Software Tools, Including Cryptographic Protection Tools” and “Information Security in Automated Systems Using Software and ...
Added: October 19, 2026
Смерчанский П. С., Koledov V. V., Kamantsev A. P. et al., Physics of Metals and Metallography 2026 Vol. 127 No. 6-7 P. 689–693
Heusler alloys of the Ni2MnX family, where X = Ga, In, Sn, …, which have been shown to exhibit
giant magnetocaloric effect (MCE) and magnetically controlled shape memory effect due to thermoelastic
magnetostructural phase transition (MSPT), continue to attract attention. However, these functional properties are fully manifested in strong magnetic fields of at least several T. Currently, ...
Added: October 19, 2026
Naumov A., Рубцов А. С., Samsonov S. et al., Успехи математических наук 2026 Т. 81 № 4 (490) С. 161–162
Краткое сообщение рассматривает Моментные оценки для стохастической аппроксимации ...
Added: October 17, 2026
Roman Avdeev, Yulia Zaitseva, Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
Added: October 17, 2026
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Тукачев Н. В., Bataev V., Abramenkov A. et al., Computational and Theoretical Chemistry 2016 No. 1080 P. 23–32
Electronic state calculations, such as equilibrium geometry parameters, harmonic vibrational frequencies and potential barriers to conformational transitions (as well as conformer energy differences in excited states), using ab initio methods, such as MP2, CCSD(T), CASSCF, CASPT2 and MRCI, were carried out on the formamide molecule in the ground (S0) and the lowest excited singlet (S1) ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2016 Vol. 177 P. 291–300
For conformers of the N-methylformamide (HCONHCH3) molecule, calculations of equilibrium geometry parameters, harmonic vibration frequencies, energy differences and potential barriers to conformational transitions were performed in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states. In the S0 state, the molecule exists in trans and cis stable conformations (having Cs symmetry). ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2017 Vol. 192 P. 30–41
For acetamide molecule (CH3CONH2) in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states calculations of equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions (also conformer energy differences in excited states) using following ab initio methods: MP2, CCSD(T), CASSCF, CASPT2 and MRCI were performed. One-, two- and three-dimensional ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. A., Godunov I. A., Computational and Theoretical Chemistry 2017 Vol. 1113 P. 82–93
Equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions and conformer energy differences for N-methylacetamide (CH3CONHCH3) molecule in S0, S1 and T1 electronic states were calculated in MP2 (S0) and CASPT2 (S1, T1) levels of theory. It is known that there are two planar (or effectively planar) conformers of N-methylacetamide in the ground ...
Added: October 14, 2026
Тукачев Н. В., Maslennikov D., Sosorev A. et al., The Journal of Physical Chemistry Letters 2019 Vol. 10 No. 12 P. 3232–3239
Conformational space of polyphenylenevinylene oligomers is systematically investigated computationally at energies relevant for room temperature dynamics in a solvent and in a solid state. Our calculations show that optimal oligomer structures are essentially planar. However, lack of a deep minimum at the planar geometry allows for large molecular deformations even at very low temperatures. At ...
Added: October 14, 2026
Тукачев Н. В., Akkuratov A., Kuznetsov I. et al., Synthetic Metals 2020 Vol. 259 Article 116231
Four new conjugated polymers based on benzodithiophene, thiophene and 2,1,3-benzothiadiazole or 5,6-difluoro-2,1,3-benzothiadiazole were synthesized and investigated as absorber materials for organic photovoltaics. The effect of (bi)thiophene π-spacers and fluorine substitution on the physicochemical and optoelectronic properties of the polymers was revealed and correlations were drawn with their electrical characteristics in organic solar cells. In particular, ...
Added: October 14, 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