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Gamayun O.,Lancaster University | Gamayun O.,Bogoliubov Institute for Theoretical Physics | Pronko A.G.,Va Steklov Mathematical Institute | Zvonarev M.B.,University Paris - Sud | Zvonarev M.B.,French National Center for Scientific Research
Nuclear Physics B | Year: 2015

We consider a one-dimensional gas of spin-1/2 fermions interacting through δ-function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the spin-down fermion. This impurity Green's function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators. © 2015 The Authors.

Bogoliubov N.,Va Steklov Mathematical Institute | Timonen J.,University of Jyväskylä
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2011

A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q-boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size. © 2011 The Royal Society.

Soldatov A.V.,Va Steklov Mathematical Institute
Condensed Matter Physics | Year: 2010

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 massive analytical and numerical computations of experimentally measurable properties of realistic polarons, such as inverse effective mass tensor and excitation gap, and can be elaborated even further, without major alterations, to allow for treatment of multitudinous polaron-like models, those describing polarons of various sorts placed in external magnetic and electric fields among them. © A.V. Soldatov.

Soldatov A.V.,Va Steklov Mathematical Institute
Physics of Particles and Nuclei | Year: 2010

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 arbitrary values of the electron-phonon interaction constant. These bound estimates allow for explicit numerical evaluation at all orders. In conjunction with numerous well-known upper bound estimates for the energy spectral curve of the Fröhlich polaron as a function of the interaction constant and the polaron total momentum, the aforesaid improvable lower bound estimates might provide one with virtually precise magnitude for the energy of the slow-moving polaron. Possible generalization to the case of the Fröhlich polaron in external magnetic field is outlined. © 2010 Pleiades Publishing, Ltd.

Seregin G.,University of Oxford | Seregin G.,Va Steklov Mathematical Institute
Nonlinearity | Year: 2016

It is shown that any smooth solution to the stationary Navier-Stokes system in R3 with the velocity, belonging to L6 and BMO-1, must be zero. © 2016 IOP Publishing Ltd & London Mathematical Society Printed in the UK.

Bogolubov N.N.,Va Steklov Mathematical Institute | Soldatov A.V.,Va Steklov Mathematical Institute
Physics of Particles and Nuclei Letters | Year: 2016

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 master equation derived within this approach is tractable numerically and can be readily used to derive a set of ordinary differential equations for various relevant physical variables belonging to the subsystem of magnetic moments. Upon further analysis of the thus obtained variational master equation, an influence of the macroscopic filling of the selected Bose field mode at low enough temperatures on the relaxation dynamics of magnetic moments was revealed. © 2016, Pleiades Publishing, Ltd.

Levin V.A.,Institute for Automatics and Control Processes | Afonina N.E.,Moscow State University | Gromov V.G.,Moscow State University | Smekhov G.D.,Moscow State University | And 2 more authors.
Combustion Science and Technology | Year: 2010

Complex results are presented in numerical and experimental flow dynamic research and thrust characteristics of jet engine model thrust device with ring nozzle working on equilibrium combustion products of acetylene-air mixtures. Experiments with thrust device models were performed in a pulse aerodynamic laboratory facility. Calculations of viscous flow were based on a program complex including the programs of Navier-Stokes equations and numerical integration for various models of gas environment added by the equations of chemical kinetics. As a result, the main details of flow dynamic, stationary flow structure, and thrust characteristics of the ring nozzle have been established. The comparison of experimental and calculated data has been made to verify the mathematical models and computation method. Copyright © 2010 Taylor & Francis Group, LLC.

Bogolubov N.N.,Va Steklov Mathematical Institute | Soldatov A.V.,Va Steklov Mathematical Institute
Conference Proceedings - 2011 IEEE 2nd International Conference on Photonics, ICP 2011 | Year: 2011

Upper bound estimates for the ground state energy of quantized Frhlich'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 allows for generalization to the case of the Frhlich polaron model in external magnetic Held as well as to various quantum models of polarons confined by external potentials, thus forming polaronic quantum dots. © 2011 IEEE.

Sankovich D.P.,Va Steklov Mathematical Institute
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2013

We use infrared bounds method to study the existence of a Bose condensation phase transition in a three-dimensional lattice model of interacting bosons. Upper bound (local Gaussian domination) is presented on the Bogolyubov inner product of creation and annihilation bosonic operators in momentum space. We focus on the situation with a non-negative chemical potential. The presence of a Bose condensation is established for sufficiently small superstable interaction potential. A special case of the model considered is the Bose-Hubbard model. © 2013 Elsevier B.V. All rights reserved.

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