# Andrey V. SoldatovRussian Academy of Sciences | RAS · Steklov Mathematical Institute

Andrey V. Soldatov

PhD

## About

63

Publications

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214

Citations

## Publications

Publications (63)

It was shown by a study of the incoherent part of the low-frequency resonance fluorescence spectrum of the polar quantum emitter driven by semiclassical external laser field and damped by non-squeezed vacuum reservoir that the emitted fluorescence field is squeezed to some degree nevertheless. As was also found, a higher degree of squeezing could,...

A two-level quantum emitter with broken inversion symmetry driven by external semiclassical monochromatic high-frequency electromagnetic (e.g., laser) field and damped by squeezed vacuum reservoir with finite bandwidth is presented. The squeezed vacuum source is assumed to be either degenerate parametric oscillator (DPO) or a non-degenerate paramet...

It is shown that a two-level quantum system with broken inversion symmetry possessing dipole moment operator with permanent non-equal diagonal matrix elements, driven by external semiclassical monochromatic high-frequency electromagnetic (laser) field and damped by broadband squeezed vacuum reservoir can amplify or absorb weak probe electromagnetic...

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level open quantum system with finite number \(N\) of quantum eigenstates interacting with arbitrary external deterministic fields and dissipative environment simultaneously. Unlike conventional master equations deri...

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the s...

The model of a single multilevel one-electron atom with violated symmetry such that its transition dipole-moment operator has constant diagonal matrix elements, among which not all are pairwise equal to each other, has been studied. It has been shown that the expression for the far electromagnetic field of such an atom does not contain any apprecia...

Using the projection operator method, we obtain approximate time-local and time-nonlocal master equations for the reduced statistical operator of a multilevel quantum system with a finite number N of quantum eigenstates coupled simultaneously to arbitrary classical fields and a dissipative environment. We show that the structure of the obtained equ...

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can...

It is shown that a two-level quantum system possessing dipole moment operator with permanent non-equal diagonal matrix elements and driven by external semiclassical monochromatic high-frequency electromagnetic (EM) (laser) field can amplify EM radiation waves of much lower frequency.

Conditions are found under which a simple two-level quantum system possessing dipole moment operator with permanent non-equal diagonal matrix elements and driven by external semiclassical monochromatic high-frequency EM (laser) field can radiate continuously at much lower frequency. Possible ways to experimental observation and practical implementa...

We show that a sequence of improving upper bounds to the ground state energy of the quantized Fröhlich polaron model can be obtained in a regular way by means of combining a variational method originated from the theory of coherent states with a generalized variational approach in quantum mechanics. Due to their variational nature, these bounds hol...

Non-equilibrium properties of a model system comprised of a subsystem of magnetic moments strongly coupled to a selected Bose field mode and weakly coupled to a heat bath made of a plurality of Bose field modes was studied on the basis of non-equilibrium master equation approach combined with the approximating Hamiltonian method. A variational mast...

A variational approach is proposed that allows one to obtain in a regular way a sequence of improvable upper bounds for the ground-state energy of various polaron models confined in an external electrostatic potential. The proposed approach can be used for an arbitrary electron–phonon interaction constant and allows generalization to the case of po...

A method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, is applied to investigation of the energy spectrum and eigenstates of a two-electron two-dimensional quantum dot (QD) formed by a parabolic confining potential in the presence of ex...

A method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, is applied to investigation of the energy spectrum and eigenstates of a two-electron two-dimensional quantum dot (QD) formed by a parabolic confining potential in the presence of ex...

It was shown that an infinite sequence of improving non-increasing upper
bounds to the ground state energy (GSE) of a slow-moving piezoeletric polaron
can be devised.

By using the plane-wave expansion for the electromagnetic-field vector
potential, transition matrix elements between the relativistic bound and
unbound states of hydrogenic atoms were expressed explicitly in terms of finite
series made of hypergeometric functions. This representation for the above
mentioned matrix elements proved very convenient fo...

It was shown that an infinite convergent sequence of improving non-increasing
upper bounds to the ground state energy of a slow-moving acoustical polaron can
be obtained by means of generalized variational method. The proposed approach
is especially well-suited for massive analytical and numerical computations of
experimentally measurable propertie...

An approach is proposed which allows one to investigate dynamical and thermodynamical properties of models with four-fermion interaction of general type. The approach combines ideas of the standard Bogolubov's approximating Hamiltonian method for the models with separable interaction with the method of Hartree–Fock approximation based on the ideas...

An approach to calculate both the Fourier transforms of singular spinor components of relativistic eigenfunctions of hydrogen-like atoms and those of their multiple products is developed. The method simplifies calculations of the momentum representation for the eigenfunctions belonging to the discrete spectrum. Besides, it reduces the procedure of...

A single-mode colored loss-noise dye-laser model is treated by means of a new version of approximate effective Markovian equation for all values of noise intensity and correlation time. The steady-state probability density is derived and various scenarios of possible noise-induced nonequilibrium phase transitions are considered. The proposed method...

The problem of precise estimation of the low-lying discrete energy spectrum of quantum dots was addressed rigorously by means of the methods of upper and lower bounds for eigenvalues of linear Hermitian operators in Hilbert space. It was shown that the method of intermediate problems for eigenvalues and the classical Rayleigh–Ritz method may be fus...

A reported experimental evidence for gravitational quantum bound states of neutrons in the Earth's gravitational field1 is discussed regarding possible employment of these states to prove the existence of gravitational field quanta through their interaction with a beam of ultracold neutrons.

For the first time to our knowledge, a general, explicit formula for exact transition matrix elements in relativistic hydrogenic atoms is derived, by using the plane-wave expansion for the electromagnetic-field vector potential. By applying the obtained formula, discrete-discrete and discrete-continuous matrix elements are evaluated analytically an...

The relaxation dynamics in the case of a discretized atom-field interaction model, being of great importance in quantum optics, is investigated numerically by an algorithm based on Seke's self-consistent projection operator method. The transition from reversible to irreversible dynamics in the continuous limit is simulated numerically. The dependen...

A closed analytic form for relativistic bound-unbound and unbound-unbound transition matrix elements of hydrogenic atoms by using the plane-wave expansion for the electromagnetic-field vector potential is derived. By applying the obtained formulae, these transition matrix elements can be evaluated analytically and numerically.

The upper bound on the ground-state energy for the Fröhlich polaron is derived by means of a new version of variational principle based on the Wick symbols formalism and the coherent states theory. The bound is continuous in some respect, i.e. it is valid for all values of coupling parameter including the intermediate regions. Asymptotic behavior o...

The dynamics of a discretized atom-field interaction model with a physically relevant form factor is analyzed. It is shown that after some short time interval only a small fraction of eigenvalues and eigenstates (belonging to the close vicinity of the excited atomic state energy E = ω0/2) contributes to the nondecay probability amplitudes in the lo...

The ground-state energy of the Fröhlich polaron model in a magnetic field is investigated by means of the Wick symbols formalism. The upper bound on the ground-state energy is derived which is valid for all values of magnetic field and coupling strength.

A single-mode colored-loss-noise dye-laser model with additive spontaneous emission noise term is treated by a new version of approximate effective Fokker–Planck equation which is proved to be valid below at and above threshold. Particular attention is paid to the dye-laser operation below threshold, where the additive noise term seems to play irre...

A recent paper by Facchi and Pascazio, in which the advantage of numerical evaluations of deviations from exponential decay was pointed out, makes a revisitation of the subject necessary. All the more, since the above-mentioned authors have not estimated the error bounds (being absolutely necessary in any calculation) for their results. On the cont...

Gene selection model with colored noise term is investigated by means of a new version of approximate effective Markovian equation proposed earlier. The steady-state probability density is derived for the whole range of model and noise parameters. It is proved that at least for the so-called symmetric case, the increase of the colored noise correla...

By using the plane-wave expansion for the electromagnetic-field vector potential, relativistic bound–bound, bound–unbound and unbound–unbound transition matrix elements for hydrogenic atoms are expressed universally in terms of hypergeometric functions. By applying the obtained formulas, these transition matrix elements can be evaluated analyticall...

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In t...

Upper bound estimates for the ground state energy of quantized Fröhlich's model of the free and impurity bound Landau-Pekar polaron were derived by means of a variational method based on the Wick symbol formalism and the theory of coherent states. The bounds so obtained are valid at arbitrary electron-phonon coupling strength. The proposed approach...

Method of intermediate problems was applied to investigation of the energy spectrum of the Fröhlich polaron model. It was
shown that various infinite sequences of non-decreasing improvable lower bound estimates for the low-lying branch of the slow-moving
polaron excitation energy spectral curve adjacent to the ground state energy can be derived for...

An infinite convergent sequence of improving non-increasing upper bounds to the low-lying branch of the slowmoving "physical" Fr̈ohlich polaron ground-state energy spectral curve, adjacent to the ground state energy of the polaron at rest, was obtained by means of generalized variational method. The proposed approach isespecially well-suited for ma...

By using the plane-wave expansion for the electromagnetic-field vector potential, relativistic bound-bound, bound-unbound and unbound-unbound transition matrix elements for hydrogenic atoms are expressed universally in terms of hypergeometric functions. By applying the obtained formulas, these transition matrix elements can be evaluated analyticall...

ohlich polaron model. It was shown that various innite sequences of non-decreasing improvable lower bound estimates for the polaron ground state energy can be derived for arbitrary values of the electron-phonon interaction constant. The proposed approach allows for explicit numerical evaluation of the thus obtained lower bound estimates at all orde...

Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic field is discussed. Being smooth at the QD boundaries and of finite depth and range, this potential can only confine a finite numbe...

It is shown that the method of intermediate problems, which provides improvable convergent lower bounds for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be linked in a natural way to the stochastic variational method, thus resulting in an effective tool for analytical and numerical investigation of the energy spectrum...

We study the absorption and dispersion properties of a weak probe field monitoring a two-level atom driven by a trichromatic field. We calculate the steady-state linear susceptibility and find that the system can produce a number of multilevel coherence effects predicted for atoms composed of three and more energy levels. Although the atom has only...

We investigate the absorption and dispersion properties of a two-level atom driven by a polychromatic field. The driving field
is composed of a strong resonant (carrier) frequency component and a large number of symmetrically detuned sideband fields
(modulators). A rapid increase in the absorption at the central frequency and the collapse of the re...

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving held is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuni...

The response of a two-level atom in a strong polychromatic field composed of a large number of equidistant frequency components is investigated. We calculate numerically, as well as analytically,:the stationary population inversion and show that the saturation of the atomic transition strongly depends on whether or not there is a central (resonant)...

We analyze the steady-state population inversion in a two-level atom driven by three laser fields of unequal frequencies. The dependence of the population inversion on initial relative phases between the driving lasers and cancellation of subharmonic resonances are predicted and explained in terms of quantum interference between dressed states of t...

An alternative way of reconstructing a function from its Laplace transform using the Widder inversion method was shown to be useful in treating some problems of nonequilibrium statistical mechanics. As an example of a suc-cessful application of the method, a decay was investigated of the excited atomic state in a simple, but nonetheless physically...

A recent paper by Facchi and Pascazio, in which the advantage of numerical evaluations of deviations from exponential decay was pointed out, makes a revisitation of the subject necessary. All the more, since the above-mentioned authors have not estimated the error bounds (being absolutely necessary in any calculation) for their results. On the cont...

A new technique, based on the self-consistent projection-operator method due to Seke, is used for the derivation of a sequence of diagonalized effective Hamiltonians. As demonstrated in an example, the new technique is a powerful method for the calculation of quantum-mechanical eigenvalues and eigenstates. Unlike other methods, not only the problem...

Originally, the Seke self-consistent projection-operator method has been developed for treating non-Markovian time evolution of probability amplitudes of a relevant set of state vectors. In the so-called Born approximation the method leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamilt...

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In t...

An approach is proposed which allows one to investigate dynamical and thermodynamical properties of models with four-fermion interaction of general type. The approach combines ideas of the standard Bogolubov's approximating Hamiltonian method for the models with separable interaction with the method of Hartree-Fock approximation based on the ideas...

An algorithm is proposed that allows us to derive the convergent sequence of upper bounds for the ground state energy of a quantum system. The algorithm generalizes the well-known variational principle of quantum mechanics and moreover provides qualitative, and under some additional conditions even quantitative, characteristics of the spectrum of a...

We present very simple methods to derive upper bounds of the ground state energy for the Froehlich polaron theory. The obtained bounds are proved to be uniform for all values of the interactions parameter.

Single mode colored-loss-noise dye-laser models with and without an additive quantum noise term are treated by means of a new version of an approximate effective Markovian equation for the whole range of noise intensifies and correlation time. The steady state probability density is derived and various scenarios of possible noise-induced, nonequili...

The formalism presented in this paper for deriving a kinetic equation for a dynamical system with multiplicative colored noise is to quite a degree universal. It can be used to investigate nonequilibrium phase transitions induced by both additive and multiplicative colored noise. The formalism can be used to describe, the behavior of a system under...

A generalization of a model Hamiltonian of the nuclear quadrupole interaction is proposed. It enables one to describe the effects of the resonance dependence of the constant of longitudinal relaxation of a system of nuclear spins on the magnitude of the external magnetic field. The part played by acoustic phonons at low temperature is discussed.

A model is considered for the interaction of a single-mode boson field with a system of electrons placed at the nodes of an N-node lattice. Bogolyubov's approximating-Hamiltonian method is used to obtain an expression exact in the thermodynamic limit for the free-energy density in the system for the case of an arbitrary electron concentration (0 le...

Applicability of the method of intermediate problems to investigation of the energy spectrum and eigenstates of a two-electron two-dimensional quantum dot (QD) formed by a parabolic confining potential is discussed. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of l...