Nikolai Nikolaevich Bogolubov

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• Doctor of Sciences
• Professor (Full) at Russian Academy of Sciences

We study a novel charged hadronic string model within the least action principle and the vacuum field theory approach based on the classical R.P. Feynman’s proper time paradigm. It is stated that the hadronic string model allows the conformal local coordinates, with respect to which the resulting string dynamics is described by means of the linear...

Исследованы спектральные свойства флуоресцентного излучения двухуровневой квантовой системы с нарушенной инверсионной пространственной симметрией, которая может быть реализована в виде модели одноэлектронного двухуровневого атома, оператор электрического дипольного момента которого имеет перманентные, не равные друг другу диагональные матричные эле...

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...

In this communication, we consider a pair of entangled quantum systems, each described by the su(1) Lie algebra, interacting with two two-level atoms. We discuss in detail the influence of the detuning terms on the system and derive from the Heisenberg equations of motion the expressions of various operators corresponding to the dynamics. Solving t...

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...

We consider magnetic systems with the SU(3) symmetry of the exchange interaction. For degenerate equilibriums with broken magnetic and phase symmetries, we formulate classification equations for the order parameter using the concept of residual symmetry. Based on them, we obtain an explicit form of the equilibrium values of the order parameters of...

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...

In paper the evolution of N identical in mass and charge particles interacting wia generalized Yukawa potential is investigated. The system of particles is considered in a finite area. Using the semi group theory, we prove the existence of a unique solution of the chain of quantum kinetic equations for correlation matrices.

A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged p...

We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point particle dynamics using the developed field theory concepts. There is also described a new approach to the classica...

The existence of a unique solution, in terms of initial data of the hierarchy of quantum kinetic equations for correlation matrices with Coulomb potential, has been proven. The proof is based on nonrelativistic quantum mechanics and application of semigroup theory methods.

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...

We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point particle dynamics using the developed field theory concepts. There is also described a new approach to the classica...

The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum field theory approach. The electron inertia problem is analyzed within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle. The modified Abraham- Lor...

The classical Maxwell electromagnetic field and the Lorentz-type force equations are rederived in the framework of the Feynman proper time paradigm and the related vacuum field theory approach. The classical Ampere law origin is rederived, and its relationship with the Feynman proper time paradigm is discussed. The electron inertia problem is analy...

The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum …eld theory approach. The electron inertia problem is analyzed within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle. The modi…ed Abraham-Lorent...

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...

In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superco...

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respective...

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrodinger equation, respectively.

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 to describing nonlinear Lax type integrable dynamical systems of modern mathematical and theoretical physics, based on the Marsden–Weinstein reduction method on canonically symplectic manifolds with group symmetry, is proposed. Its natural relationship with the well-known Adler–Kostant–Souriau–Berezin–Kirillov method and the associated...

We study the dynamics of systems consisting of interacting two-level atoms and a field (microcavities). Such systems include the Jaynes-Cummings model. We formulate the problem and present a short history of it, derive a generalized kinetic equation for the system, find its solution, and show that this model allows describing photon emission and ab...

The equilibrium properties of a system of interacting bosons are studied from a microscopic point of view. We calculate the superfluid density in the Bogolyubov model of imperfect Bose gas. The model superstable Hamiltonian is considered. We examine the case of some pair potential and find the estimate for temperature and density in the λ-point.

The paper is devoted to the investigation of dynamics of system, consisting of interacting two-level atoms and field (cavity field). To such system covers also Jaynes-Cummings model. In this paper, evolution of two-level many bosons system interacting with a field is investigated by means of generalized kinetic equation. On base of the Bogolyubov's...

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...

We use the Bogolyubov approximating Hamiltonian method to rigorous study the equilibrium properties of imperfect Bose gases. We calculate the pressure of the mean field Bose gas model. This model in external potential is considered. Key wordsBose-condensation-approximating Hamiltonian method

Construction of a kinetic equation for a dynamical system interacting with a boson field in the case of spatial inhomogeneity is based on a method expounded in [1–3]. In the present article, it is shown that approaches considered in [1, 2] can be generalized for the case of spatial inhomogeneity. An arbitrary operator function that depends on the m...

The polaron model in ionic crystal is studied in the Bogolubov representation using a special RPA-approxima- tion. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at nite temperature is calculated analytically. The polaron free energy in the constant magnetic eld at nite tem- perature is also di...

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k = 0 mode operator ^ a0 is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufcient conditions which ensure the appearance of the Bose condensate in the model. For some temperatures and some posit...

We analyze the approximating Hamiltonian method for Bose sys-tems. Within the framework of this method, the pressure for the mean field model of an imperfect boson gas is calculated. The problem is considered by the systematic application of the Bogolyubov–Ginibre approximation.

Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed e...

The polaron model in ionic crystal is studied in the N. Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is al...

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm.The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to e...

Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is con...

The linear polaron model is an excellent example of an exactly soluble, yet nontrivial polaron system. It serves as a trial system or zero-level approximation in many sophisticated methods of polaron investigation. This book analyzes, in particular, the possibility of reduction of the full polaron Hamiltonian to the linear one, and introduces a spe...

We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point particle dynamics using the developed field theory concepts. There is also described a new approach to the classica...

The backgrounds of quantum mathematics, a new discipline in mathematical physics, are discussed and analyzed from both historical and analytical points of view. The magic properties of the second quantization method, invented by Fock in 1934, are demonstrated, and an impressive application to the theory of nonlinear dynamical systems is considered.

We consider the possibilities of the formation of quasistationary distributions of particles over energy with power asymptotics in nonequilibrium systems and dynamical systems with couplings. It is shown that the Tsallis distribution is related to the exact solutions of a kinetic equation of the Boltzmann type and those of covariant kinetic equatio...

We show that the Bogolyubov generating functional method is a very efficient tool for studying distribution functions of both equilibrium and nonequilibrium states of classical many-particle dynamical systems. In some cases, the Bogolyubov generating functionals can be represented by means of infinite Ursell-Mayer diagram expansions, whose converge...

The analytic aspects of the Bogoliubov generating functional equations and their transformation properties within the Bogoliubov canonical transformation method are studied. The classical Bogoliubov idea [2] to use the Wigner density operator transformation for studying the non equilibrium distribution functions within the Bogoliubov canonical tran...

We show that the Bogoliubov microscopic theory of superfluidity of liquid 4He allows quantum fluctuations of both condensate and excitations. Comparison of those fluctuations leads to an equation determining the mean number of atoms with zero momentum in a self-consistent way. Obtained results are in good agreement with the experiments on Bose-Eins...

We study the differential-geometric aspects of generalized de Rham-Hodge complexes naturally related to integrable multidimensional differential systems of the M. Gromov type, as well as the geometric structure of the Chern characteristic classes. Special differential invariants of the Chern type are constructed, their importance for the integrabil...

We show that the Bogoliubov microscopic theory of superfluidity of liquid ⁴ He allows quantum fluctuations of both condensate and excitations. Comparison of those fluctuations leads to an equation determining the mean number of atoms with zero momentum in a self-consistent way. Obtained results are in good agreement with the experiments...

A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle fl...

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...

The name of the prominent twentieth century theorist Academician Nikolai Nikolaevich Bogolyubov and his creative works are intimately intertwined with the development of modern methods of investigating fundamental problems of statistical mechanics, the physics of condensed matter, nonlinear mechanics, quantum field theory, the theory of dispersion...

The differential-geometric and topological structure of Delsarte transmutation operators, and the Gelfand-Levitan-Marchenko-type equations associated with them, are studied by using a generalized de Rham-Hodge differential complex. The relationships to spectral theory and special Berezansky-type congruence properties of Delsarte transmuted operator...

A discussion is made on the appearance of strong effective magnetic field with a new quantum state induced by the zero-point plasma oscillation in semi-localized half-filling electron system in the 2D network of circular molecular orbits. With the help of numerical calculation we study the appearance of superconductivity in the Cu and Ru oxide supe...

We study the film-thickness dependence of ||c dielectric polarization of La1.95Sr0.05CuO4 thin film crystal, and find the existence of special film thicknesses where the polarization reveals a large amplitude alternate change with sign change. At the special thicknesses, we find interference patterns in the polarization-charge dependence of the fil...

The superconductivity Hamiltonian model with attraction is investigated. An asymptotic relation for average calculation is constructed in the model and the approximating Hamiltonians are presented.

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...

The derivation of the non-magnetic Laughlin state and other macroscopic quantum states in the semi-localized 2D electron system in the network of circular molecular orbits is made by the study of zero-point plasma oscillation. In the imaginary time representation, the electric field is transformed to the vector potential. After the cancellation of...

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...

Recently discovered new type of high temperature superconductors have circular molecular orbits in each unit site of 2D s/p electron system. We discuss a new model of superconductivity caused by the correlated state of electrons in the 2D interconnection of circular orbits. This model gives an estimation of the superfluidity transition temperature:...

Recently discovered new type of high temperature superconductors have circular molecular orbits in each unit site of 2D s/p electron system. We discuss a new model of superconductivity caused by the correlated state of electrons in the 2D interconnection of circular orbits. This model gives an estimation of the superfluidity transition temperature:...

Our theoretical study reports on the quantum interference effect expected to be found in the correlated state of the hole-doped electron system in 2D networks of circular molecular orbits, where the ground state of the system is described by a FQHE-like state. When the phase-correlation length λθ is larger than the incompressibility length λQ, the...

It is well known that cuprate-oxide high temperature superconductors are characterized by a 2D d-electron system in the CuO2 network where the probability amplitude of d electrons extends crosswise from each Cu ion. Recently a new trend of high temperature superconductivity [1,2] is attracting attention where (i) non-d electron system seems to be r...

We begin with a discussion on the approximating Hamiltonian method in the case of four-fermion interaction. Namely, we consider a general class of models with four-fermion pair interaction for which an asymptotically exact solution can be constructed. A definition of the asymptotically exact solution as well as methods of its construction for this...

Recently quantum computing has attracted wide attention [1]. It was shown that any quantum computer can be composed based on the combination of “controlled NOT gates” [2,3], where the quantum state is processed using a control bit and target bit. In order that a gate acquires practical feasibility, the decoherence time τd ≡ 1/γ of the quantum state...

A new model is proposed on the recently found non-cuprate high temperature superconductivity in crystal with 2D conduction plane which is composed of the planar connection of many circular localized orbits. Our findings are as follows: (i) the ground state of the doped 2D particle system in zero point oscillation is similar to the particle state in...

Some years ago Zakharov and Gibbon observed a very nice relation between the Benney type equation in hydrodynamics and the Vlasov equation of kinetic theory. These equations are generalized and put into the framework of infinite-dimensional Lie algebras associated to Lie algebra structures on rings of functions on finite-dimensional manifolds. This...

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...

The model of a ladder configuration three-level atom interacting with a two-mode near-resonant radiation field is treated. It is shown that the operator equations of motion can be solved explicitly. The dynamical behaviour of the photon numbers and level populations is studied for various initial conditions.

The generation of a squeezed state via non-degenerate four-wave mixing in a system of three-level atoms is discussed. The condition for receiving a nearly perfect squeezing is shown.

We study swept-volume dynamical systems for which several hydrodynamical models are formulated. The properties of those hydrodynamical models are studied by means of the algebraic Kostant – Symes technique. A differential-geometric description of swept volumes dynamical systems are devised based on the Cartan Movina frame approach. Для динамiчних с...

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...

A general variational method is proposed for investigating the surface polaron ground state valid for any coupling strength of an electron-surface-optical-phonon interaction and for any height of a barrier potential at the crystal boundary. The ground states of the surface polaron at the infinitely high barrier potential and of the surface polaron...

Here we propose a method of constructing a second order approximation for ground state energy for a class of model Hamiltonian with linear type interaction on bose operators in the strong coupling case. For the application of the above method we have considered polaron model and propose constructing a set of nonlinear differential equations for def...

CONTENTS §1. Introduction §2. Theory of open systems §3. Kinetic theory and hydrodynamics §4. Quantum statistical mechanics References