arXiv subjects

Kirill A. Kazakov

Publications and source records attributed to Kirill A. Kazakov.

At least 37 records · Page 2Linked to original sources

arXiv2008

On-Shell Description of Unsteady Flames

The problem of non-perturbative description of unsteady premixed flames with arbitrary gas expansion is solved in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas velocity jumps given on it, we show that the front dynamics can be determined without having to solve the flow equations in the bulk. On the basis of the Thomson circulation theorem, an implicit integral representation of the gas velocity downstream is constructed. It is then simplified by a successive stripping of the potential contributions to obtain an explicit expression for the vortex component near the flame front. We prove that the unknown potential component is left bounded and divergence-free by this procedure, and hence can be eliminated using the dispersion relation for its on-shell value (i.e., the value along the flame front). The resulting system of integro-differential equations relates the on-shell fuel velocity and the front position. As limiting cases, these equations contain all theoretical results on flame dynamics established so far, including the linear equation describing the Darrieus-Landau instability of planar flames, and the nonlinear Sivashinsky-Clavin equation for flames with weak gas expansion.

physics.flu-dyn↗

arXiv2007

Quantum Theory of Flicker Noise in Metal Films

Flicker (1/f^gamma) voltage noise spectrum is derived from finite-temperature quantum electromagnetic fluctuations produced by elementary charge carriers in external electric field. It is suggested that deviations of the frequency exponent γfrom unity, observed in thin metal films, can be attributed to quantum backreaction of the conducting medium on the fluctuating field of the charge carrier. This backreaction is described phenomenologically in terms of the effective momentum space dimensionality, D. Using the dimensional continuation technique, it is shown that the combined action of the photon heat bath and external field results in a 1/f^gamma-contribution to the spectral density of the two-point correlation function of electromagnetic field. The frequency exponent is found to be equal to 1 + delta, where delta = 3 - D is a reduction of the momentum space dimensionality. This result is applied to the case of a biased conducting sample, and a general expression for the voltage power spectrum is obtained which possesses all characteristic properties of observed flicker noise spectra. The range of validity of this expression covers well the whole measured frequency band. Gauge independence of the power spectrum is proved. It is shown that the obtained results naturally resolve the problem of divergence of the total noise power. A detailed comparison with the experimental data on flicker noise measurements in metal films is given.

cond-mat.mes-hall↗

arXiv2007

Quantum fluctuations of Coulomb Potential as a Source of Flicker Noise. The Influence of Heat Bath

The power spectrum of finite-temperature quantum electromagnetic fluctuations produced by elementary charge carriers under the influence of external electric field is investigated. It is found that under the combined action of the photon heat bath and the external field, the low-frequency asymptotic of the power spectrum is modified both qualitatively and quantitatively. The new term in the power spectrum is inversely proportional to, but is odd in frequency. It comes from the connected part of the correlation function, and is related to the temperature and external field corrections to the photon and charge carrier propagators. In application to the case of a biased conducting sample, this term gives rise to a contribution to the voltage power spectrum which is proportional to the absolute system temperature, the charge carrier mobility, the bias voltage squared, and a factor describing dependence of the noise intensity on the sample geometry. It is verified that the derived expression is in agreement with the experimental data on 1/f-noise measurements in metal films.

quant-ph↗

arXiv2006

Quantum Fluctuations of Coulomb Potential as a Source of Flicker Noise. The Influence of External Electric Field

Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in the whole measured frequency band, the power spectrum of fluctuations exhibits an inverse frequency dependence. A general argument is given showing that for all practically relevant values of the electric field, the power spectrum of induced fluctuations is proportional to the field strength squared. As an illustration, the power spectrum is calculated explicitly using the kinetic model with the relaxation-type collision term. Finally, it is shown that the magnitude of fluctuations produced by a sample generally has a Gaussian distribution around its mean value, and its dependence on the sample geometry is determined. In particular, it is demonstrated that for geometrically similar samples, the power spectrum is inversely proportional to the sample volume. Application of the obtained results to the problem of flicker noise is discussed.

quant-ph↗

arXiv2005

Quantum Fluctuations of a Coulomb Potential as a Source of Flicker Noise

The power spectrum of quantum fluctuations of the electromagnetic field produced by an elementary particle is determined. It is found that in a wide range of practically important frequencies the power spectrum of fluctuations exhibits an inverse frequency dependence. The magnitude of fluctuations produced by a conducting sample is shown to have a Gaussian distribution around its mean value, and its dependence on the sample geometry is determined. In particular, it is demonstrated that for geometrically similar samples the power spectrum is inversely proportional to the sample volume. It is argued also that the magnitude of fluctuations induced by external electric field is proportional to the field strength squared. A comparison with experimental data on flicker noise measurements in continuous metal films is made.

physics.data-an↗

arXiv2004

On-Shell Description of Stationary Flames

The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral, a simple explicit expression for the vortex mode of the burnt gas flow near the flame front is obtained. Furthermore, a dispersion relation for the potential mode at the flame front is written down, thus reducing the initial system of bulk equations and jump conditions for the flow variables to a set of integro-differential equations for the flame front position and the flow velocity at the front. The developed approach is applied to the case of thin flames. Finally, an asymptotic expansion of the derived equations is carried out in the case θ\to 1 where θis the gas expansion coefficient, and a single equation for the front position is obtained in the second post-Sivashinsky approximation. It is demonstrated, in particular, how the well-known problem of correct normalization of the front velocity is resolved in the new approach. It is verified also that in the first post-Sivashinsky approximation, the new equation reduces to the Sivashinsky-Clavin equation corrected according to Cambray and Joulin. Analytical solutions of the derived equations are found, and compared with the results of numerical simulations.

physics.flu-dyn↗

arXiv2004

Long-Range Behavior in Quantum Gravity

Quantum gravity effects of zeroth order in the Planck constant are investigated in the framework of the low-energy effective theory. A special emphasis is placed on establishing the correspondence between classical and quantum theories, for which purpose transformation properties of the \hbar^0-order radiative contributions to the effective gravitational field under deformations of a reference frame are determined. Using the Batalin-Vilkovisky formalism it is shown that the one-loop contributions violate the principle of general covariance, in the sense that the quantities which are classically invariant under such deformations take generally different values in different reference frames. In particular, variation of the scalar curvature under transitions between different reference frames is calculated explicitly. Furthermore, the long-range properties of the two-point correlation function of the gravitational field are examined. Using the Schwinger-Keldysh formalism it is proved that this function is finite in the coincidence limit outside the region of particle localization. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly, and the relative value of the root mean square fluctuation of the Newton potential is found to be 1/\sqrt{2}. It shown also that in the case of a macroscopic gravitating body, the terms violating general covariance, and the field fluctuation are both suppressed by a factor 1/N, where N is the number of particles in the body. This leads naturally to a macroscopic formulation of the correspondence between classical and quantum theories of gravitation. As an application of the obtained results, the secular precession of a test particle orbit in the field of a black hole is determined.

gr-qc↗

arXiv2004

Quantum Fluctuations of a Coulomb potential

Long-range properties of the two-point correlation function of the electromagnetic field produced by an elementary particle are investigated. Using the Schwinger-Keldysh formalism it is shown that this function is finite in the coincidence limit outside the region of particle localization. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly, and its gauge independence is proved. The leading contribution turns out to be of zero order in the Planck constant, and the relative value of the root mean square fluctuation of the Coulomb potential is found to be 1/\sqrt{2}, confirming the result obtained previously within the S-matrix approach. It is shown also that in the case of a macroscopic body, the \hbar^0 part of the correlation function is suppressed by a factor 1/N, where N is the number of particles in the body. Relation of the obtained results to the problem of measurability of the electromagnetic field is mentioned.

hep-th↗

arXiv2003

Gauge dependence of effective gravitational field.II. Point-like measuring device

The role of the measurement process in resolving the gauge ambiguity of the effective gravitational potential is reexamined. The motion of a classical point-like particle in the field of an arbitrary linear source, and in the field of another point-like particle is investigated. It is shown that in both cases the value of the gravitational field read off from the one-loop effective action of the testing particle depends on the Feynman weighting parameter. The found dependence is essential in that it persists in the expression for the gravitational potential. This result disproves the general conjecture about gauge independence of the effective equations of motion of classical point-like particles.

hep-th↗

arXiv2003

Classical Scale of Quantum Gravity

Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius r_g. The role of this scale in quantum domain is discussed in the context of the low-energy effective theory. The question of whether quantum gravity effects appear already at r_g leads to the question of correspondence between classical and quantum theories, which in turn can be unambiguously resolved considering the issue of general covariance. The O(\hbar^0) loop contributions turn out to violate the principle of general covariance, thus revealing their essentially quantum nature. The violation is O(1/N), where N is the number of particles in the body. This leads naturally to a macroscopic formulation of the correspondence principle.

hep-th↗

arXiv2003

Large Scale Evolution of Premixed Flames

The influence of the small scale ``cellular'' structure of premixed flames on their evolution at larger scales is investigated. A procedure of the space-time averaging of the flow variables over flame cells is introduced. It is proved that to the leading order in the flame front thickness, the form of dynamical equations for the averaged gas velocity and pressure, as well as of jump conditions for these quantities at the flame front, is the same as in the case of a zero-thickness flame propagating in an ideal fluid at constant velocity with respect to the fuel, equal to the adiabatic velocity of a plane flame times a factor describing increase of the flame front length due to the local front wrinkling. As an application, the large scale evolution of a flame in the gravitational field is investigated. A weakly nonlinear non-stationary equation for the averaged flame front position is derived. It is found that the leading nonlinear gravitational effects stabilize the flame propagating in the direction of the field. The resulting stationary flame configurations are determined analytically.

physics.flu-dyn↗

arXiv2002

Quantum Fluctuations of Effective Fields and the Correspondence Principle

The question of Bohr correspondence in quantum field theory is considered from a dynamical point of view. It is shown that the classical description of particle interactions is inapplicable even in the limit of large particles' masses because of finite quantum fluctuations of the fields produced. In particular, it is found that the relative value of the root mean square fluctuation of the Coulomb and Newton potentials of a massive particle is equal to 1/sqrt{2}. It is shown also that in the case of a macroscopic body, the quantum fluctuations are suppressed by a factor 1/sqrt{N}, where N is the number of particles in the body. An adequate macroscopic interpretation of the correspondence principle is given.

hep-th↗

arXiv2002

Closed Description of Stationary Flames

The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. A general method for deriving equations for the flame front position is developed. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral the flow structure near the flame front is determined, and a closed system of equations for the flame front position and a set of auxiliary quantities is obtained. This system is shown to be quasi-local, and its transverse representation is found. This representation allows reduction of the system to a single equation for the flame front position. The developed approach is applied to the case of zero-thickness flames.

physics.flu-dyn↗

arXiv2002

General Covariance in Quantum Gravity

The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge conditions fixing general invariance, are determined. It is found that the one-loop contributions violate the principle of general covariance, in the sense that the quantities which are classically invariant under such deformations take generally different values in different reference frames. The relative value of this violation is of the order 1/N, where N is the number of particles in a gravitating body.

hep-th↗

arXiv2002

Effective Gravitational Field of Black Holes

The problem of interpretation of the \hbar^0-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order \hbar^0 to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.

hep-th↗

arXiv2001

Nonlinear Theory of Flame Front Instability

Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be satisfied across the flame front, as well as correctly takes into account influence of vorticity, generated in the flame, on the flame front structure and flame velocity. Analytical solutions of the derived equation are found.

physics.flu-dyn↗

arXiv2001

Correspondence principle in quantum gravity

The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that this approach fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the correspondence principle is given directly in terms of the effective action. Gauge independence of the \hbar^0 part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed. Application to the black holes is discussed.

hep-th↗

arXiv2001

Nonlinear equation for curved stationary flames

A nonlinear equation describing curved stationary flames with arbitrary gas expansion $θ= ρ_{\rm fuel}/ρ_{\rm burnt}$, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for $θ\to 1,$ the new equation gives the true solution to the problem of stationary flame propagation with the accuracy of the sixth order in $θ- 1.$ In particular, it reproduces the stationary version of the well-known Sivashinsky equation at the second order corresponding to the approximation of zero vorticity production. At higher orders, the new equation describes influence of the vorticity drift behind the flame front on the front structure. Its asymptotic expansion is carried out explicitly, and the resulting equation is solved analytically at the third order. For arbitrary values of $θ,$ the highly nonlinear regime of fast flow burning is investigated, for which case a large flame velocity expansion of the nonlinear equation is proposed.

physics.flu-dyn↗