Section 1. Topics on theoretical electrodynamics

HUBBARD MODEL SURPRISE: COMPETITION OF MULTIPLE LOW LYING ORDERED STATES

Rozhkov A. V., Sboychakov A. O.

Abstract 

In this paper, we discuss the competition of low-lying ordered states in the spectrum of Hubbard model. Available numerical and analytical calculations performed in various regimes show unambiguously that for the Hubbard and similar Hamiltonians, there is a whole set of dissimilar non-superconducting low-lying states with extremely close eigenenergies. These states compete with each other for the opportunity to become the ground state of the system. We argue here that the parameters of this competition are such that the value of finding the single state with the lowest eigenenergy is very limited. Currently available results suggest the need for the re-evaluation of the role played by the Hubbard model (and other related simplified models) in theoretical studies of many-electron correlated systems. We also show that the weak interaction Hubbard model can be used as a convenient theoretical playground for studying such competition.

Keywords: Hubbard model, ground state, doping, spin-density wave, phase separation, domain walls

EFFICIENT SUPPRESSION OF PHASE NOISE BY A DRIVING FORCE IN A LINEAR OSCILLATOR

Nefedkin N. E., Andrianov E. S., Pukhov A. A., Vinogradov A. P.

Abstract 

In this work, it is considered forced oscillations of a linear oscillator interacting with a reservoir responsible for dissipation and noise impact. It is known that in the case of a linear oscillator, noise does not affect the frequency of forced oscillations, and the damping of the autocorrelation function of the amplitude does not depend on either the properties of the oscillator or the parameters of the external action, but is determined only by noise. It is shown that, unlike the amplitude of the oscillator, there are certain values of the amplitude and frequency of the external field, as well as the rate of dissipation of the oscillator, which separate two different regimes of the oscillator phase dynamics. In the first regime, the phase noise of the oscillator and the phase diffusion coefficient do not depend on the properties of the external force and are determined by the interaction of the oscillator with the reservoir. As a consequence, the autocorrelation function of the phase cosine decays at large times. In the second regime, the phase diffusion coefficient becomes dependent not only on the interaction with the reservoir, but also on the parameters of the external force. This dependence manifests itself in the fact that in this regime the diffusion coefficient decreases by two orders of magnitude. As a consequence, the autocorrelation function of the phase cosine does not decay at large times; the system "remembers" the initial value of the phase. Using the formalism of the Adler equation for the phase, it is shown that the transition from the first regime to the second one occurs when the effective potential for the phase becomes a nonmonotonic function.

Keywords: stochastic resonance, phase noise, phase diffusion, phase correlation time, influence of noises and dissipation on behavior of phase of linear oscillator

Section 2. Topics on experimental electrodynamics

EVALUATION OF THE INFLUENCE OF IMPERFECTION OF THE MARK-12 COLLIMATOR REFLECTOR SURFACE ON THE FIELD DISTRIBUTION IN THE QUIET ZONE

Balabukha N. P., Bulychev E. V., Zubov A. S., Menshikh N. L., Solosin V. S., Fedorov S. A.

Abstract 

The paper presents an analysis of the influence of the imperfection of the collimator reflector surface on the uneven distribution of the field in the quiet zone. The imperfection of the collimator reflector surface is called the deviation of the reflecting surface from the theoretical one. Based on the detailed studies of the structure of the reflector surface of the MARK-12 collimator located at ITAE RAS, a computer model of this reflector has been developed. Calculations of the uneven of the field distribution in the quiet zone of the collimator for the existing and theoretical reflector surfaces were carried out using the method of physical optics. The contributions of the taper (influence of the radiation pattern of the irradiator) and ripple components to the uneven distribution of the field in the quiet zone are determined.

Keywords: compact range, reflector, quiet zone, field distribution, root mean square

Section 3. Topics on interaction of an electromagnetic field with materials

COMPUTER SIMULATION OF RAMAN RADIATION OF MOLECULES IN SPHERICAL METAL SHELLl

Ivanov A. V., Sarychev A. K., Bakholdin N. V., Bykov I. V., Ryzhikov I. A.

Abstract 

Computer simulation of the radiation of molecules placed in a metal shell is performed. The model qualitatively describes amplification of the radiation from protein globules covered with a thin silver shell. The variation of surface-enhanced Raman scattering (SERS) signal is calculated as function of the thickness of the metal nanolayer deposited over a protein globule. The radiating molecular dipole interacts with the metal shell and excites surface plasmons. The plasmon oscillation reaches its maximum when the frequency of molecular dipole is close to the plasmon resonance of the metal shell, and the dipole itself is located near the plasmon shell. There is thickness of the silver shell hemispheres, which make it possible to excite dipole, quadrupole, octupole, and other plasmon resonances. At the resonant thickness, the electric field modes propagate both along the inner and outer boundaries of the silver shell, which results in the enhancement the SERS effect. It is shown that for submicron-sized globules, the resonant amplification of radiation falls on the silver coating thickness of tens of nanometers, which corresponds to the thickness of continuous films. The developed simple model qualitatively reproduces the enhancement of SERS from the SARS-CoV-2 receptor-binding domain (RBD) spike protein coated with a thin silver film.

Keywords: plasmon resonance, metal shell, radiation amplification, giant Raman scattering, receptor binding domain, coronavirus SARS-CoV-2

OPTICAL SENSORS BASED ON SILICON DISKS RESONATORS

Ivanov A. V., Bykov I. V., Barbillon G., Sarychev A. K.

Abstract 

A periodic system of disk resonators is researched and developed. The system is made of crystalline silicon with a surface nanolayer of silver. The measured angular dependences of the reflectance of the disk resonators demonstrate deep dips in a wide range of the visible and infrared spectral ranges. The spectrum of the reflectance weakly depends on the angle of incidence. The measured reflectance spectra indicate the excitation of collective plasmon oscillations in the periodic system of disk resonators, including standing waves that amplify the local electromagnetic field. Work has been carried out to measure the Raman signal in a system of silicon disk resonators. The Raman scattering signal in the system of disks at the excitation frequency of the silicon optical phonon is amplified by more than 102 times with respect to the signal on the smooth region of the sample. The results of mapping the Raman signal indirectly demonstrate the distribution of amplified local fields over the entire surface of the system of disk resonators. The advantage of the proposed system of disk resonators is ability to obtain a reproducible stable Raman signal at given frequencies, which can be varied by changing the period and the diameter of the disks.

Keywords: plasmon resonance, disk resonators, silicon, SERS

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