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M. Yu. Nalimov

Publications and source records attributed to M. Yu. Nalimov.

10 recordsLinked to original sources
arXiv2023

Dynamical description of the phase transition into the superconducting state

Dynamical equations that are valid in the vicinity of the phase transition into the superconducting state are given. Probable effects of the field of charge carriers' magnetic interactions and the field of temperature fluctuations were taken into account. The order of the phase transition is discussed. Considerations in favor of the applicability of the stochastic dynamical model A to describe the dynamics of this phase transition are given.

cond-mat.supr-con↗
arXiv2023

Composite operators of stochastic model A

By means of the field-theoretic renormalization group, we study the damping of the viscosity coefficient near the superfluid phase transition. We utilize the fact that in the infrared region, the complex model used to describe the phase transition belongs to the same universality class as the well-known stochastic model A. This allows us a determination of the critical behavior of viscosity using composite operators for model A. Our analysis is based on the $\varepsilon$-expansion near the upper critical dimension $d_c = 4$ of model A. The critical exponent of viscosity is then calculated from the critical dimensions of composite operators of massless two-component model A. In particular, we present results for critical dimensions of a selected class of composite operators with the canonical dimension $8$ to the leading order.

cond-mat.stat-mech↗
arXiv2016

Renormalization group calculation of dynamic exponent in the models E and F with hydrodynamic fluctuations

The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation for the anomalous dimension $γ_λ$ and fixed-points' structure. The dynamic exponent $z$ is calculated in the turbulent regime and stability of the fixed points for the standard model E is discussed.

cond-mat.stat-mech↗
arXiv2016

Influence of Hydrodynamic Fluctuations on the Phase Transition in Models E and F of Critical Dynamics

We use the renormalization group method to study model E of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using Martin-Siggia-Rose theorem, we obtain a field- theoretical model that allows a perturbative renormalization group analysis. By direct power counting and an analysis of ultraviolet divergences, we show that the model is multiplicatively renormalizable, and we use a two-parameter expansion in $\varepsilon$ and $δ$ to calculate renormalization constants. Here, $\varepsilon$ is a deviation from the critical dimension four, and $δ$ is a deviation from the Kolmogorov regime. We present the results of the one-loop approximation and part of the fixed-point structure. We briefly discuss the possible effect of velocity fluctuations on the large-scale behavior of the model.

cond-mat.stat-mech↗
arXiv2015

Superfluid Phase Transition with Activated Velocity Fluctuations: Renormalization Group Approach

A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within perturbative renormal- ization group method. The double $(ε,δ)$-expansion scheme is employed, where is a deviation from space dimension $4$ and $δ$ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value $4/3$.

cond-mat.stat-mech↗
arXiv2015

Renormalization-group investigation of a superconducting $U(r)$-phase transition using five loops calculations

We have studied a Fermi system with attractive $U(r)$-symmetric interaction at the finite temperatures by the quantum field renormalization group (RG) method. The RG functions have been calculated in the framework of dimensional regularization and minimal subtraction scheme up to five loops. It has been found that for $r\geq 4$ the RG flux leaves the system's stability region -- the system undergoes a first order phase transition. To estimate the temperature of the transition to superconducting or superfluid phase the RG analysis for composite operators has been performed using three-loops approximation. As the result this analysis shows that for $3D$ systems estimated phase transition temperature is higher then well known theoretical estimations based on continuous phase transition formalism.

cond-mat.stat-mech↗
arXiv2004

Instantons for Dynamic Models from B to H

Instanton analysis is applied to models B--H of critical dynamics. It is shown that the static instanton of the massless $ϕ^{4}$ model determines the large-order asymptotes of the perturbation expansion of these near-equilibrium dynamic models leading to factorial growth with the order of perturbation theory.

hep-th↗
arXiv2004

Kraichnan model of passive scalar advection

A simple model of a passive scalar quantity advected by a Gaussian non-solenoidal ("compressible") velocity field is considered. Large order asymptotes of quantum-field expansions are investigated by instanton approach. The existence of finite convergence radius of the series is proved, a position and a type of the corresponding singularity of the series in the regularization parameter are determined. Anomalous exponents of the main contributions to the structural functions are resummed using new information about the series convergence and two known orders of the expansion.

nlin.CD↗
arXiv1998

Renormalization Group, Operator Product Expansion, and Anomalous Scaling in a Model of Advected Passive Scalar

Field theoretical renormalization group methods are applied to the Obukhov--Kraichnan model of a passive scalar advected by the Gaussian velocity field with the covariance $<{\bf v}(t,{\bf x}){\bf v}(t',{\bf x})> - < v(t,{\bf x}){\bf v}(t',x')> \proptoδ(t-t')| x-x'|^{\eps}$. Inertial range anomalous scaling for the structure functions and various pair correlators is established as a consequence of the existence in the corresponding operator product expansions of ``dangerous'' composite operators [powers of the local dissipation rate], whose negative critical dimensions determine anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order $\eps^{2}$ of the $\eps$ expansion. Generalization of the results obtained to the case of a ``slow'' velocity field is also presented.

chao-dyn↗