mikhail vasin

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Competition of glass and crystal: Phase‐field model

Mathematical Methods in the Applied Sciences

The phase‐field model for the description of the solidification processes with the glass‐crystal ... more The phase‐field model for the description of the solidification processes with the glass‐crystal competition is suggested. The model combines the first‐order phase transition model in the phase‐field formalism and gauge‐field theory of glass transition. We present a self‐consistent system of stochastic motion equations for unconserved order parameters describing the crystal‐like short‐range ordering and vitrification. It is shown that the model qualitatively describes the glass‐crystal competition during quenching with finite cooling speed. The nucleation of the crystalline phase at slow cooling speeds and low undercoolings proceeds by a fluctuation mechanism. The model demonstrates the tendency to amorphization with the increase of its cooling rate.

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Soft model of solidification with the order–disorder states competition

Mathematical Methods in the Applied Sciences, 2021

A theoretical model is proposed that describes the kinetics of the formation and evolution of com... more A theoretical model is proposed that describes the kinetics of the formation and evolution of competing phases, one of which is a disordered system of topologically stable excitations (vortices) and the second one is an ordered (crystalline) phase. This model is intended to be the simplest model which can demonstrate such important characteristics of solidification process as a sensitivity to the cooling speed, natural appearance of the relaxation times of kinetic phase transformations, and particular features of the rapidly solidified systems. The model was studied numerically showing the crucial properties relevant to the obtained in the experiments on the amorphization in metals. In the present work, we derive a general form of the system's Hamiltonian and stochastic dynamical equations to describe the rapid solidification and a competing formation of amorphous and crystalline phases. The numerical study of the formation of both phases shows the competition of inherited phase...

Field theory of dissipative systems with gapped momentum states

Physical Review D, 2020

We develop a field theory with dissipation based on a finite range of wave propagation and associ... more We develop a field theory with dissipation based on a finite range of wave propagation and associated gapped momentum states in the wave spectrum. We analyze the properties of the Lagrangian and the Hamiltonian with two scalar fields in different representations and show how the new properties of the twofield Lagrangian are related to Keldysh-Schwinger formalism. The proposed theory is non-Hermitian, and we discuss its properties related to PT symmetry. The calculated correlation functions show a decaying oscillatory behavior related to gapped momentum states. We corroborate this result using path integration. The interaction potential becomes short-ranged due to dissipation. Finally, we observe that the proposed field theory represents a departure from the harmonic paradigm and discuss the implications of our theory for the Lagrangian formulation of hydrodynamics.

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Description of glass transition kinetics in 3DXYmodel in terms of gauge field theory

Physica A: Statistical Mechanics and its Applications, 2019

We consider a gauge theory of the glass transition in the frustrated XY model being simplest mode... more We consider a gauge theory of the glass transition in the frustrated XY model being simplest model containing topologically nontrivial excitations. We describe the transition kinetics and find that the three-dimensional system exhibits the Vogel-Fulcher-Tamman criticality heralding its freezing into a spin glass. We analytically show that the system demonstrates all glass transition properties, like the logarithmic relaxation, and corresponding behavior of linear and non-linear susceptibility. The mode-coupling theory equation in the Zwanziger-Mori representation also is derived in framework of our approach. Our findings provide insights into the topological origin of glass formation, that allows to make progress in understanding glass-transition processes in more intricate systems.

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Quantum critical dynamics of the boson system in the Ginzburg–Landau model

Physica A: Statistical Mechanics and its Applications, 2014

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Multi-critical dynamics of the Boson system in the vicinity of the second-order quantum phase transition

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Dynamical heterogeneity in terms of gauge theory of glass transition

Physica A: Statistical Mechanics and its Applications, 2015

In this paper the phenomenon of dynamic heterogeneity in supercooled liquid systems is considered... more In this paper the phenomenon of dynamic heterogeneity in supercooled liquid systems is considered in terms of the recently proposed gauge theory of glass transition. The physical interpretation of the dynamic scaling is considered. It is shown that the development of the dynamic heterogeneity occurs due to the growth areas in which molecular motion is correlated due to the elastic interaction described by the gauge field. We obtains the analytical expressions for the dependence of the number of dynamically correlated atoms as the function on the system relaxation time, and the time dependence of the dynamic susceptibility near the glass transition. It is shown that the relaxation consists two processes: α-relaxation process corresponding to the joint motion of the domains disordered with each other, and β-relaxation process corresponding to the motion inside these domains.

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Quantum-classical crossover close to quantum critical point

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Gauge theory of glass transition

Journal of Statistical Mechanics: Theory and Experiment, 2011

An analytical approach, which develops the gauge model of the glass transition phenomenon, is sug... more An analytical approach, which develops the gauge model of the glass transition phenomenon, is suggested. It is based on the quantum field theory and critical dynamics methods. The suggested mechanism of glass transition is based on the interaction of the local magnetization field with the massive gauge field, which describes frustration-induced plastic deformation. The example of the three-dimensional Heisenberg model with trapped disorder is considered. It is shown that the glass transition appears when the fluctuations scale reaches the frustrations scale, and the mass of the gauge field becomes equal to zero. The Vogel-Fulcher-Tammann relation for the glass transition kinetics and critical exponent for non-linear susceptibility, 1.7 γ < 3, are derived in the framework of the suggested approach.

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Gauge theory approach to glass transition

Journal of Physics: Conference Series, 2012

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Gapped momentum states

Physics Reports, 2020

Important properties of a particle, wave or a statistical system depend on the form of a dispersi... more Important properties of a particle, wave or a statistical system depend on the form of a dispersion relation (DR). Two commonly-discussed dispersion relations are the gapless phonon-like DR and the DR with the energy or frequency gap. More recently, the third and intriguing type of DR has been emerging in different areas of physics: the DR with the gap in momentum, or k-space. It has been increasingly appreciated that gapped momentum states (GMS) have important implications for dynamical and thermodynamic properties of the system. Here, we review the origin of this phenomenon in a range of physical systems, starting from ordinary liquids to holographic models. We observe how GMS emerge in the Maxwell-Frenkel approach to liquid viscoelasticity, relate the k-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space and vice versa. We subsequently discuss how GMS emerge in the two-field description which is analogous to the quantum formulation of dissipation in the Keldysh-Schwinger approach. We discuss experimental evidence for GMS, including the direct evidence of gapped

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