arXiv subjects

I. D. Feranchuk

Publications and source records attributed to I. D. Feranchuk.

At least 19 recordsLinked to original sources

arXiv2026

X-ray resonance therapy with parametric X-ray radiation (PXR) for sulfur-containing tumor tissues

We investigate the possibility of usage of the parametric X-ray radiation (PXR) for the selective therapy of superficial sulfur-containing tumor tissues. In these tissues, the concentration of sulfur atoms is significantly higher than in healthy ones. Accordingly, the destruction of cancer cells is caused by the ionization of sulfur atoms. The selective nature of the therapy is determined by the narrow spectral-angular distribution of the PXR photon beam and the resonant absorption of radiation by sulfur atoms. This leads to a significant decrease in the total dose required to achieve the desired effects compared to irradiation with conventional X-ray tubes or electron accelerators.

physics.bio-ph↗

arXiv2025

Approximating Hamiltonian for Hartree-Fock solutions for nonrelativistic atoms

In our work we construct a Hamiltonian, whose eigenstates approximate the solutions of the self-consistent Hartree-Fock equations for nonrelativistic atoms and ions. Its eigenvalues are given by completely algebraic expressions and the eigenfunctions are defined by Coulomb wave-functions orbitals. Within this approximation we compute the binding energy, ionization potentials, electron density distribution, electron density at the nucleus, and atomic scattering factors of nonrelativistic atoms and ions. The accuracy of our results is comparable with those obtained via the usage of the Hartree-Fock method but does not require solving integro-differential equations or numerically computing integrals with complex functions. This approach can serve as a good initial approximation for performing more accurate calculations and for the quantitative evaluation of physical parameters that depend on the electron density of atoms. The proposed approach is of interest for various fields of condensed matter physics, plasma physics and quantum chemistry.

quant-ph↗

arXiv2024

Ground state of the gauge invariant Dicke model: condensation of the photons in non-classical states

We investigate the ground state of two physically motivated modifications of the Dicke model. The first modification corresponds to particles whose phase space contains only two states, for example, particles with spin 1/2 or artificially created qubits. The second modification describes two-level systems that arise as a result of truncating the full Hilbert space of atoms to two levels that are in resonance with the electromagnetic field and are described by the gauge-invariant Dicke model. We demonstrate that the behavior of these systems is qualitatively distinct in both cases. In particular, in the first scenario, a phase transition into the state with a non-zero amplitude of the classical field is possible, while in the second case, the so-called order parameter $η= \braket{\hat{a}}$ of the field's phase transition into a coherent state with photon condensation is zero. At the same time, the average number of photons $\bar{n} = \braket{\hat{a}^\dagger \hat{a}} \neq 0$, and the collective excitation in the system manifests a non-classical "squeezed" state of the field. We analyze the observable characteristics of both systems in a wide range of variation of their parameters.

quant-ph↗

arXiv2023

All-coupling solution for the continuous polaron problem in the Schrödinger representation

The solution for the large-radius Fröhlich polaron in the Schrödinger representation of the quantum theory is constructed in the entire range of variation of the coupling constant. The energy and the effective mass of the polaron are calculated by simple algebraic transformations and are analogous to the results found by Feynman on the basis of the variational principle for the path-integrals of this system. It allows us to solve the long-lived problem of the inequalities of the functional and operator approaches for the polaron problem. The developed method is important for other models of particle-field interaction including those ones for which the standard perturbation theory is divergent.

quant-ph↗

arXiv2022

Superradiant parametric X-ray emission

We compute a spectrum of parametric X-ray radiation (PXR) inside a crystal from a bunch of electrons, which is periodically modulated in density. We consider that the bunch of electrons is exiting from a XFEL channel. We demonstrate that in the case of a resonance between the frequency of parametric X-ray radiation and a frequency of modulation of an electron bunch the sequence of strong quasi-monochromatic X-ray pulses is formed -- superradiant parametric X-ray emission (SPXE) with frequencies multiples of the modulation frequency. The number of photons in the impulse of SPXE in the case of an extremely asymmetric diffraction is comparable with the photon number in the impulse of a XFEL. Moreover the SPXE is directed under the large angle to the electron velocity and every harmonic in the spectrum is emitted under its own angle.

physics.acc-ph↗

arXiv2022

Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model

In the present paper we show that the Hamiltonian describing the resonant interaction of $N$ two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a simple basis set of states. This allows one to find an analytical approximation for the eigenvectors and eigenvalues of the system, which interpolates the numerical solution in a broad range of the coupling constant values. In addition, the introduced basis states provide a regular way of calculating the corrections and estimating the convergence to the exact numerical solution. The obtained results are valid for both quantum Rabi model ($N = 1$) and the Dicke model for $N \geq 2$ atoms.

quant-ph↗

arXiv2020

Radiation induced interaction potential of two qubits strongly coupled with a quantized electromagnetic field

We investigate the interaction of two two-level qubits with a single mode quantum field in a cavity without rotating wave approximation and considering that qubits can be located at an arbitrary distance from each other. We demonstrate that there exists a radiation induced interaction potential between atoms. We studied the properties of the system numerically and in addition constructed a simple analytical approximation. It is shown that the observable characteristics are substantially dependent on the distance between the qubits in the strong coupling regime. This allows one to perform the quantum control of the qubits, which can be exploited for the recording and transmission of quantum information.

quant-ph↗

arXiv2020

Relativistic effective charge model of a multi-electron atom

A relativistic version of the effective charge model for computation of observable characteristics of multi-electron atoms and ions is developed. A complete and orthogonal Dirac hydrogen basis set, depending on one parameter -- effective nuclear charge $Z^{*}$ -- identical for all single-electron wave functions of a given atom or ion, is employed for the construction of the secondary-quantized representation. The effective charge is uniquely determined by the charge of the nucleus and a set of electron occupation numbers for a given state. We thoroughly study the accuracy of the leading-order approximation for the total binding energy and demonstrate that it is independent of the number of electrons of a multi-electron atom. In addition, it is shown that the fully analytical leading-order approximation is especially suited for the description of highly charged ions since our wave functions are almost coincident with the Dirac-Hartree-Fock ones for the complete spectrum. Finally, we evaluate various atomic characteristics, such as scattering factors and photoionization cross-sections, and thus envisage that the effective charge model can replace other models of comparable complexity, such as the Thomas-Fermi-Dirac model for all applications where it is still utilized.

physics.atom-ph↗

arXiv2020

Exact solution for the quantum Rabi model with the $\boldsymbol{\mathsf{A}}^{2}$ term

Quantum Rabi model (QRM) is widely used for the analysis of the radiation-matter interaction at the fundamental level in cavity quantum electrodynamics. Typically the QRM Hamiltonian includes only $\boldsymbol{\mathsf{p}} \cdot \boldsymbol{\mathsf{A}}$ term, however, the complete nonrelativistic Hamiltonian of quantum electrodynamics includes $\boldsymbol{\mathsf{A}}^{2}$ term as well. Here we find an exact solution and demonstrate with the help of the exact canonical transformations that the QRM Hamiltonian with the $\boldsymbol{\mathsf{A}}^{2}$ term (QRMA) is reduced to the standard QRM model Hamiltonian with the renormalized frequency and the coupling constant and the eigenstates are expressed through the squeezed states of the field. As a result, the $\boldsymbol{\mathsf{A}}^{2}$ term qualitatively changes the behavior of the QRM with purely electromagnetic interaction in the strong coupling regime: the value of the ground state energy of an atom inside the cavity is higher than in vacuum and the number of crossing of energy levels with different quantum numbers decreases.

quant-ph↗

arXiv2019

Parametric Mössbauer radiation source

Numerous applications of Mössbauer spectroscopy are related to a unique resolution of absorption spectra of resonant radiation in crystals, when the nucleus absorbs a photon without a recoil. However, the narrow nuclear linewidth renders efficient driving of the nuclei challenging, restricting precision spectroscopy, nuclear inelastic scattering and nuclear quantum optics. Moreover, the need for dedicated X-ray optics restricts access to only few isotopes, impeding precision spectroscopy of a wider class of systems. Here, we put forward a novel Mössbauer source, which offers a high resonant photon flux for a large variety of Mössbauer isotopes, based on relativistic electrons moving through a crystal and emitting parametric Mössbauer radiation essentially unattenuated by electronic absorption. As a result, a collimated beam of resonant photons is formed, without the need for additional monochromatization. We envision the extension of high-precision Mössbauer spectroscopy to a wide range of isotopes at accelerator facilities using dumped electron beams.

physics.acc-ph↗

arXiv2018

Parametric X-ray radiation in the Smith-Purcell geometry for non-destructive beam diagnostics

We investigate parametric X-ray radiation (PXR) under condition of the extremely asymmetric diffraction, when the ultra-relativistic electron bunch is moving in \textit{vacuum} parallel to the crystal-vacuum interface, close to the crystal surface. This type of geometry coincides with the well known mechanism of generation of radiation, when the self-field of the particle beam interacts with the reflecting metal grating, namely the Smith-Purcell effect. We demonstrate that in this geometry the main contribution is given via a tail region of the beam distribution, which penetrates the crystal and X-rays are radiated along the normal to the crystal surface. We determine the electron beam characteristics, when this phenomenon can be observed. It is essential that in this geometry the majority of electrons does not undergo multiple scattering and consequently the characteristics of the particle beam are not changed, thus allowing the usage of the emitted X-rays for the purpose of non-destructive beam diagnostics, which can complement the traditional knife-edge method.

physics.acc-ph↗

arXiv2017

Analytic model of a multi-electron atom

A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis completeness allows us to employ the secondary-quantized representation for the construction of regular perturbation theory, which includes in a natural way correlation effects, converges fast and enables an effective calculation of the subsequent corrections. The hydrogen-like basis set provides a possibility to perform all summations over intermediate states in closed form, including both the discrete and continuous spectra. This is achieved with the help of the decomposition of the multi-particle Green function in a convolution of single-electronic Coulomb Green functions. We demonstrate that our fully analytical zeroth-order approximation describes the whole spectrum of the system, provides accuracy, which is independent of the number of electrons and is important for applications where the Thomas-Fermi model is still utilized. In addition already in second-order perturbation theory our results become comparable with those via a multi-configuration Hartree-Fock approach.

quant-ph↗

arXiv2017

Analytic approximation for eigenvalues of a class of $\mathcal{PT}$ symmetric Hamiltonians

An analytical approximation for the eigenvalues of $\mathcal{PT}$ symmetric Hamiltonian $\mathsf{H} = -d^{2}/dx^{2} - (\mathrm{i}x)^{ε+2}$, $ε> -1$ is developed via simple basis sets of harmonic-oscillator wave functions with variable frequencies and equilibrium positions. We demonstrate that our approximation provides high accuracy for any given energy level for all values of $ε> -1$.

quant-ph↗

arXiv2017

Radical increase of the parametric X-ray intensity under condition of extremely asymmetric diffraction

Parametric X-ray radiation (PXR) from relativistic electrons moving in a crystal along the crystal-vacuum interface is considered. In this geometry the emission of photons is happening in the regime of extremely asymmetric diffraction (EAD). In the EAD case the whole crystal length contributes to the formation of X-ray radiation opposed to Laue and Bragg geometries, where the emission intensity is defined by the X-ray absorption length. We demonstrate that this phenomenon should be described within the dynamical theory of diffraction and predict a radical increase of the PXR intensity. In particular, under realistic electron-beam parameters, an increase of two orders of magnitude in PXR-EAD intensity can be obtained in comparison with conventional experimental geometries of PXR. In addition we discuss in details the experimental feasibility of the detection of PXR-EAD.

physics.acc-ph↗

arXiv2017

Soliton-like solution in quantum electrodynamics

A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density operator of the electron-positron field. Then, by modeling the state vector in analogy with the theory of superconductivity, we minimize the functional for the energy of the system. This results in the equations of the self-consistent field, where the solutions are associated with the collective excitation of the electron-positron field---the soliton-like solution. In addition, the canonical transformation of the variables allowed us to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.

hep-th↗

arXiv2016

Spontaneous emission in a quantum system driven by the resonant field beyond the rotating wave approximation

Quasi-stationary states of the quantum system in the driving resonant field are considered without rotating wave approximation. Conditions under which the spontaneous emission could be suppressed in this system are investigated in the special case when the frequency of the driving field is essentially less than the frequency of spontaneous emission. It is shown that the characteristic parameters of the effect are substantially changed in comparison with the results corresponding to RWA. The real physical system for which the considered effects could be observed is described.

quant-ph↗

arXiv2016

Physical background for parameters of the quantum Rabi model

We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode, while the second one describes the interaction with field fluctuations. The first part is usually associated with the resonant cavity mode. This division enables us to determine the applicability condition of the single-mode approximation. In addition we identify simple approximate relations for the description of the eigenstates, eigenfunctions and the time evolution of the quantum Rabi model beyond the rotating wave approximation.

quant-ph↗

arXiv2016

Regularization of ultraviolet divergence for a particle interacting with a scalar quantum field

When a nonrelativistic particle interacts with a scalar quantum field, the standard perturbation theory leads to a dependence of the energy of its ground state on an undefined parameter---"momentum cutoff"---due to the ultraviolet divergence. We show that the use of nonasymptotic states of the system results in a calculation scheme in which all observable quantities remain finite and continuously depend on the coupling constant without any additional parameters. It is furthermore demonstrated that the divergence of traditional perturbation series is caused by the energy being a function with a logarithmic singularity for small values of the coupling constant.

quant-ph↗