Reconstructing a time-dependent quantum Hamiltonian using neural differential equations
Reconstructing a time-dependent quantum Hamiltonian using neural differential equations
A. S. Naumov, V. Yu. Popov
The problem of reconstructing an unknown time-dependent Hamiltonian of a two-level quantum system from its observed dynamics is considered. A method based on a neural network in the Neural ODE framework is proposed, where the continuous evolution of the quantum state is modeled by integrating the Schr¨odinger equation with a parametric Hamiltonian model implemented by the network. The input data consist of measured time series of the expectation values of Pauli operators for a qubit. The network is trained by minimizing the difference between the experimentally observed and simulated trajectories of quantum observables. Using the example of spin dynamics in a time-varying magnetic field, it is shown that the proposed approach allows accurate reconstruction of the parameters of the time-dependent Hamiltonian without interrupting the quantum evolution. The results demonstrate that the Neural ODE model provides continuous handling of the time parameter and robust reconstruction of system dynamics under conditions of limited data and noise.
Show AbstractComparison of long-wave and potential models of tsunami generation by a landslide body using analytical solutions
Comparison of long-wave and potential models of tsunami generation by a landslide body using analytical solutions
M. V. Lebkov$^1$, M. A. Nosov$^{1,2}$
Based on analytical solutions to the problem of the generation of gravity surface waves when moving along the bottom of a rectangular body, a comparative analysis of wave disturbances calculated within the framework of linear long-wave and potential theories was performed. It is shown that for conditions typical of real underwater landslides, the long-wave theory significantly (up to several orders of magnitude) overestimates the wave energy if the horizontal dimensions of the landslide body are comparable to the depth or less than the depth. In this regard, the application of the equations of the long wave theory to describe landslide tsunamis should be limited to cases of extremely extended landslide bodies.
Show AbstractInverse problem of image recovery in multichannel optical system
Inverse problem of image recovery in multichannel optical system
E. I. Kiselyov$^1$, A. V. Razgulin$^1$, N. G. Iroshnikov$^2$
This paper considers the inverse problem of reconstructing a multichannel image distorted by defocusing and associated chromatic aberration. This problem arises in applied ophthalmology problems related to in vivo diagnostics of living human eye structures using optical methods. A mathematical model describing the formation of a multichannel image is proposed, based on a system of integral equations of the convolution type. To solve the ill-posed inverse problem of multichannel image reconstruction, an algorithm is developed based on a modified iterative implicit Tikhonov regularization method in combination with a frequency-localized regularization parameter selection rule and a stopping criterion. The results of the software implementation of the proposed method allow us to evaluate its effectiveness in the inverse problem of multichannel image reconstruction, including for high-resolution images typical for medical applications.
Show AbstractMethod for optimizing acceleration structures for applied purposes using genetic algorithms
Method for optimizing acceleration structures for applied purposes using genetic algorithms
M. A. Borisov$^{1,2}$, V. I. Shvedunov$^{1,2}$
The article provide a description of the method of optimizing the structures of linear electron accelerators operating in the standing wave mode based on the genetic method, using the example of optimizing a medical accelerator.
Show AbstractFe$_{100-х}$Zr$_x$ films ($x = 6-13$ at. %): relationship between phase-structural state and magnetic parameters
Fe$_{100-х}$Zr$_x$ films ($x = 6-13$ at. %): relationship between phase-structural state and magnetic parameters
D. M. Gridin$^{1,2,3}$, E. V. Harin$^4$, V. A. Tejetov$^4$, G. S. Usmanova$^4$, E. N. Sheftel$^4$, A. B. Granovsky$^{1,5,6}$
The results of measurements of hysteresis loops of Fe$_{100-х}$Zr$_x$ films ($x = 6-13$) are presented both in the initial state after their preparation by ion beam deposition and after annealing in vacuum for 1 hour at 300 and 500 ° C. The measurements were performed on a vibrating magnetometer Lake Shore 7407 in magnetic fields up to 16 kOe at room temperature. An analysis of the data obtained by correlation magnetometry using the model of random magnetic anisotropy has shown that the magnetic properties of films are determined by the coexistence of amorphous and nanocrystalline structures, the volume fractions of which depend on the Zr content and the annealing temperature. For all films, even when the ferromagnetic fraction is several percent, a long-range magnetic order is observed, which is explained by the exchange interaction between neighboring ferromagnetic grains grouped into stochastic domains that are isolated from each other by a paramagnetic amorphous phase. The main magnetic parameters of the microstructure of the films are determined.
Show AbstractCombining chiral optical Tamm states into one mode of a hybrid structure
Combining chiral optical Tamm states into one mode of a hybrid structure
N. V. Rudakova$^{1,2}$, S. Y. Vetrov$^{1,2}$, I. V. Timofeev$^{1,2}$
The excitation conditions and effective control possibilities are investigated for two coupled chiral optical Tamm states arising at boundaries of a crystalline liquid crystal coupled with polarization-preserving anisotropic mirrors. Numerical modeling has shown that varying the parameters makes it possible to control the magnitude of transmission coefficient of the structure, the optimization of the spectral characteristics, as well as the profile of the local field intensity. In this case, the polarization of the incident light has a significant effect on the excitation efficiency. It is shown that the hybrid mode of two chiral optical Tamm states smoothly transforms into a single Fabry-Perot mode in the process of increasing coupling between them.
Show AbstractFacility for measurement of sky background variations in the infrared at the Caucasian Mountain Observatory of the SAI MSU
Facility for measurement of sky background variations in the infrared at the Caucasian Mountain Observatory of the SAI MSU
I. A. Komarova$^1$, A. M. Tatarnikov$^2$, S. G. Zheltoukhov$^3$
The description of the device constructed at the SAI MSU based on a commercial infrared light-sensitive module for the study of the sky background brightness (SBB) distribution in the infrared is presented. The procedure of observations with the instrument and the algorithm for accounting for the contribution of the instrumental background to the total signal are described. The results of measurements of the SBB at the Caucasus Mountain Observatory at wavelengths of 3.7~$\mu$m and 4.7~$\mu$m carried out in December 2024 are presented. An estimate of the SBB at zenith corresponding to the star $7.3^{\rm m}$ at 1 arcsec$^2$ of the sky is obtained.
Show AbstractMorphological methods for estimating the relative time shift of infrasound signals
Morphological methods for estimating the relative time shift of infrasound signals
A. F. Idrisov, A. I. Chulichkov
The present work is devoted to solving the problem of estimating the relative time delay of infrasound signals propagating from a pulse source along different trajectories in a layered homogeneous atmosphere. To solve the problem, morphological methods of signal analysis are used, developed at the Department of Mathematical Modeling and Computer Science, Faculty of Physics, Lomonosov Moscow State University. The methods are applied to the infrasound signals data recorded by barographs located at different points on the Earth’s surface. The time delay of the signals from different barographs allows us to estimate the direction of arrival of the sound wave, which allows us to further determine the position of the signal source and study the structure of the atmosphere.
Show AbstractAnalysis of hystersis behavior of the lock-in range in a Zeeman ring laser
Analysis of hystersis behavior of the lock-in range in a Zeeman ring laser
M. E. Grushin$^2$, E. G. Lariontsev$^1$, I. I. Savel'ev$^2$, E. V. Soukhov$^2$
Broad hystersis area of the lock-in range in a Zeeman ring laser till now were not described theoretically. In this paper we propose a new model accounting an additional coupling of the counterpropagating waves due to their diffraction on the gratings induced in the cavity mirrors. Hysteresis area of the lock-in range have been studied experimentally.
Show AbstractSoftware implementation of orbit construction methods in the CR3BP
Software implementation of orbit construction methods in the CR3BP
T. A. Syachina, A. G. Rudnitskiy
This paper presents a software implementation of methods for accurate calculation of orbital parameters for near-Earth space, as well as for the vicinity of the Lagrange points. The program is based on modern mathematical models and algorithms providing high accuracy and efficiency of calculations. Various perturbing factors are taken into account and the possibility to model spacecraft motion in complex gravitational conditions is implemented. The results of the program are compared with known software solutions for ballistic and navigation calculations.
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