Non-equilibrium statistical mechanics of classical nuclei interacting with the quantum electron gas

Kinetic equations governing time evolution of positions and momenta of atoms in extended systems are derived using quantum-classical ensembles within the Non-Equilibrium Statistical Operator Method (NESOM). Ions are treated classically, while their electrons quantum mechanically; however, the statistical operator is not factorised in any way and no simplifying assumptions are made concerning the electronic subsystem. Using this method, we derive kinetic equations of motion for the classical degrees of freedom (atoms) which account fully for the interaction and energy exchange with the quantum variables (electrons). Our equations, alongside the usual Newtonian-like terms normally associated with the Ehrenfest dynamics, contain additional terms, proportional to the atoms velocities, which can be associated with the electronic friction. Possible ways of calculating the friction forces which are shown to be given via complicated non-equilibrium correlation functions, are discussed. In particular, we demonstrate that the correlation functions are directly related to the thermodynamic Matsubara Green's functions, and this relationship allows for the diagrammatic methods to be used in treating electron-electron interaction perturbatively when calculating the correlation functions. This work also generalises previous attempts, mostly based on model systems, of introducing the electronic friction into Molecular Dynamics equations of atoms.Comment: 18 page

Magnetorheological properties of ferrofluids containing clustered particles

A theoretical model is proposed to describe experimental data on the magnetorheological properties of magnetic fluids containing clustered particles consisting of single-domain ferromagnetic nanoparticles distributed in a polymeric shell 80-100 nm in diameter. These fluids combine the sedimentation stability typical of nanodisperse ferrofluids with the high sensitivity of rheological parameters to magnetic fields. The developed model explains the experimentally found long-term rheological relaxation and residual stress that is retained after the medium ceases to flow. © 2013 Pleiades Publishing, Ltd

A temperature behavior of the frustrated translational mode of adsorbate and the nature of the "adsorbate-substrate" interaction

A temperature behavior of the frustrated translational mode (T-mode) of a light particle, coupled by different regimes of ohmicity to the surface, is studied within a formalism of the generalized diffusion coefficients. The memory effects of the adsorbate motion are considered to be the main reason of the T-mode origin. Numerical calculations yield a thermally induced shift and broadening of the T-mode, which is found to be linear in temperature for Ohmic and super-Ohmic systems and nonlinear for strongly sub-Ohmic ones. We obtain analytical expressions for the T-mode shift and width at weak coupling for the systems with integer "ohmicity" indexes n=0-2 in zero temperature and high temperature limits. We provide an explanation of the experimentally observed blue- or red-shifts of the T-mode on the basis of a comparative analysis of two typical times of the system evolution: a time of decay of the "velocity-velocity" autocorrelation function, and a correlation time of the thermal bath random forces. A relation of the T-mode to the multiple jumps of the adsorbate is discussed, and generalization of conditions of the multiple hopping to the case of quantum surface diffusion is performed.Comment: 12 pages, 4 figure

Patterns in soft and biological matters

The issue is devoted to theoretical, computer and experimental studies of internal heterogeneous patterns, their morphology and evolution in various soft physical systems-organic and inorganic materials (e.g. alloys, polymers, cell cultures, biological tissues as well as metastable and composite materials). The importance of these studies is determined by the significant role of internal structures on the macroscopic properties and behaviour of natural and manufactured tissues and materials. Modern methods of computer modelling, statistical physics, heat and mass transfer, statistical hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Non-equilibrium patterns which appear during macroscopic transport and hydrodynamic flow, chemical reactions, external physical fields (magnetic, electrical, thermal and hydrodynamic) and the impact of external noise on pattern evolution are the foci of this issue. Special attention is paid to pattern formation in biological systems (such as drug transport, hydrodynamic patterns in blood and pattern dynamics in protein and insulin crystals) and to the development of a scientific background for progressive methods of cancer and insult therapy (magnetic hyperthermia for cancer therapy; magnetically induced drug delivery in thrombosed blood vessels). The present issue includes works on pattern growth and their evolution in systems with complex internal structures, including stochastic dynamics, and the influence of internal structures on the external static, dynamic magnetic and mechanical properties of these systems. © 2020 The Author(s) Published by the Royal Society. All rights reserved.Russian Science Foundation, RSF: 18-19-00008Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present paper. Competing interests. The authors declare that they have no competing interests. Funding. This work was supported by the Russian Science Foundation (project no. 18-19-00008)

Local orientational order in the Stockmayer liquid

Phase behaviour of the Stockmayer fluid is studied with a method similar to the Monte-Carlo annealing scheme. We introduce a novel order parameter which is sensitive to the local co-orientation of the dipoles of particles in the fluid. We exhibit a phase diagram based on the behaviour of the order parameter in the density region 0.1 \leq {\rho}\ast \leq 0.32. Specifically, we observe and analyse a second order locally disordered fluid \rightarrow locally oriented fluid phase transition.Comment: 13 pages, 7 figure

Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectric

The theory of anomalous Hall effect for the heat transfer in a paramagnetic dielectric, discovered experimentally in [1], is developed. The appearance of the phonon heat flux normal to both the temperature gradient and the magnetic field is connected with the interaction of magnetic ions with the crystal field oscillations. In crystals with an arbitrary phonon spectrum this interaction creates the elliptical polarization of phonons. The kinetics related to phonon scattering induced by the spin-phonon interaction determines an origin of the off-diagonal phonon density matrix. The combination of the both factors is decisive for the phenomenon under consideration.Comment: 5 pages; typos and abstract correcte

Matching of nonthermal initial conditions and hydrodynamic stage in ultrarelativistic heavy-ion collisions

A simple approach is proposed allowing actual calculations of the preequilibrium dynamics in ultrarelativistic heavy-ion collisions to be performed for a far-from-equilibrium initial state. The method is based on the phenomenological macroscopic equations that describe the relaxation dynamics of the energy-momentum tensor and are motivated by Boltzmann kinetics in the relaxation-time approximation. It gives the possibility to match smoothly a nonthermal initial state to the hydrodynamics of the quark gluon plasma. The model contains two parameters, the duration of the prehydrodynamic stage and the initial value of the relaxation-time parameter, and allows one to assess the energy-momentum tensor at a supposed time of initialization of the hydrodynamics.Comment: 16 pages, minor corrections, to appear in Phys. Rev.

Theoretical Study of the Magnetization Dynamics of Nondilute Ferrofluids

The paper is devoted to the theoretical investigation of the magnetodipolar interparticle interaction effect on magnetization dynamics in moderately concentrated ferrofluids. We consider a homogenous (without particle aggregates) ferrofluid consisting of identical spherical particles and employ a rigid dipole model, where the magnetic moment of a particle is fixed with respect to the particle itself. In particular, for the magnetization relaxation after the external field is instantly switched off, we show that the magnetodipolar interaction leads to the increase of the initial magnetization relaxation time. For the complex ac susceptibility χ (ω) = χ′ (ω) +i χ″ (ω) we find that this interaction leads to an overall increase of χ″ (ω) and shifts the χ″ (ω) peak towards lower frequencies. Comparing results obtained with our analytical approach (second order virial expansion) to numerical simulation data (Langevin dynamics method), we demonstrate that the employed virial expansion approximation gives a good qualitative description of the ferrofluid magnetization dynamics and provides a satisfactory quantitative agreement with numerical simulations for the dc magnetization relaxation, up to the particle volume fraction ∼10%, and for the ac susceptibility, up to 5%. © 2009 The American Physical Society.This work has been done under the financial support of RFFI, Grants No. 06-01-00125, No. 07-02-00079, No. 07-01-960769Ural, No. 08-02-00647, Fund CRDF, No. PG07-005-02

Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons

The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weyl's symbol of considered operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the last function the integral Wigner- Liouville's type equation has been derived. The numerical procedure for solving this equation combining both molecular dynamics and Monte Carlo methods has been developed. For electrons in disordered systems of scatterers the numerical results have been obtained for series of the average values of the quantum operators including position and momentum dispersions, average energy, energy distribution function as well as for the frequency dependencies of tensor of electron conductivity and permittivity according to quantum Kubo formula. Zero or very small value of static conductivity have been considered as the manifestation of Anderson localization of electrons in 1D case. Independent evidence of Anderson localization comes from the behaviour of the calculated time dependence of position dispersion.Comment: 8 pages, 10 figure

Exponential Decay of Correlations in a Model for Strongly Disordered 2D Nematic Elastomers

Lattice Monte-Carlo simulations were performed to study the equilibrium ordering in a two-dimensional nematic system with quenched random disorder. When the disordering field, which competes against the aligning effect of the Frank elasticity, is sufficiently strong, the long-range correlation of the director orientation is found to decay as a simple exponential, Exp[-r/x]. The correlation length {x} itself also decays exponentially with increasing strength of the disordering field. This result represents a new type of behavior, distinct from the Gaussian and power-law decays predicted by some theories.Comment: Latex file (4 pages) + 2 EPS figure