We consider a two-dimensional degenerate electron gas in the presence of perpendicular random mag... more We consider a two-dimensional degenerate electron gas in the presence of perpendicular random magnetic field. The magnetic fleld disorder which is assumed to be Gaussian is characterized by two parameters. The first is proportional to the amplitude of local magnetic field fluctuations. The second one characterizes the disorder on the longer scale-we call it the screening length. Using the Kubo formula for the conductivity we have found a class of diagrams which leads to the long time tails in the current-current correlation function. For short times in comparison with the diffusion time corresponding to the screening length this function behaves like logarithm of time, for longer times it decays like t-1 which of course brings into question the diffusive character of the behavior of the charged particle in random magnetic field widely assumed in the literature.
ABSTRACT Electrons interacting with a domain wall in ferromagnetic metals are considered theoreti... more ABSTRACT Electrons interacting with a domain wall in ferromagnetic metals are considered theoretically. In the framework of semiclassical approximation and taking into account Coulomb interaction between electrons, we calculate the spin and charge distribution near the domain wall as well as the local conductivity. We show that the conductivity is significantly modified near the wall and also depends on electron–electron interaction.
Diffusion of a classical particle on a simple Bravais lattice in the presence of a single disloca... more Diffusion of a classical particle on a simple Bravais lattice in the presence of a single dislocation line is analyzed using the Fokker-Plánckequation derived from the continuous theory ofdislocations. It is shown that in the d=2 case the diffusion coefficient is enhanced. This prediction is confirmed by the Monte Carlo simulation of the same diffusion process. A possible generalizationof our results is briefly outlined.
The one-dimensional Potts chain dynamics is analysed by means of the direct space renormalisation... more The one-dimensional Potts chain dynamics is analysed by means of the direct space renormalisation technique. In contrast to previous work one needs no restriction on the value of the Potts dimensionality q. They use the generalised Glauber kinetics for the chain and find that the value of the dynamical critical exponent z is not universal, i.e. it depends on both
Journal of Physics: Condensed Matter, Aug 13, 2009
Following our earlier gauge field theory analysis of the diffusion and interactions of classical ... more Following our earlier gauge field theory analysis of the diffusion and interactions of classical and quantum waves with topological defects in solids (screw and edge dislocations), we present the analysis of the interaction of a classical spin wave with a screw dislocation studied within the Heisenberg ferromagnet model in which spins are located on a lattice containing dislocations. We show that the spin wave interaction with the screw dislocation shows a similarity to the Aharonov-Bohm-like deflection found previously for scattering of acoustic waves on the same type of defects.
The diffusion coefficient of the O/W(1 1 0) system at low temperatures, below critical point, exh... more The diffusion coefficient of the O/W(1 1 0) system at low temperatures, below critical point, exhibits some interesting properties. It is observed that the activation energy of the diffusion process increases rapidly at the phase transition from disordered to the ordered (2 • 1) phase. It is possible to model this rapid change in the activation energy, by proper choice of the transition probabilities in the lattice gas model. This rapid increase of the activation energy is visible as the change of the scaling of the diffusion curves. In the present work we use the same transition rates to calculate the diffusion coefficient at higher densities from 0.5 to 1. Scaling function shows how the activation energy varies with density. The density dependence of the activation energy changes its character on coming from lower to higher temperatures, what can be related to the changes in the phase diagram.
Physica A: Statistical Mechanics and its Applications, 1977
This work contains a discussion of the Vlasov approximation for the system of particles interacti... more This work contains a discussion of the Vlasov approximation for the system of particles interacting not only via the pair-wise central potential, but also via the velocity dependent interactions (V.D.I). The VDI are assumed to be similar in nature to those encountered in the classical plasma when the higher order in (v/c) corrections to the Coulomb forces are taken into account. Using the Klimontovich formulation of the many-body dynamics, we derive the general equation of motion for the exact one-particle distribution function N(r, v, t) and we discuss the Vlasov approximation to this equation in some detail. The linearization of the Vlasov equation and the derivation of the dispersion relations for longitudinal and transverse waves are also presented while the detailed analysis of the solutions and of the stability problem is postponed to the following publication.
Equation (5) should read 4I(p, 0) = QX'-(I/lxx; I) +e~J d('sink~(('-()/Ix'x, 'i. The paragraph st... more Equation (5) should read 4I(p, 0) = QX'-(I/lxx; I) +e~J d('sink~(('-()/Ix'x, 'i. The paragraph starting on line 14 on p. 694 is incorrect and should be replaced by the following: We are interested in the wake field trailing behind the N bunches on the z axis. However, the integral in Eq. (5) includes (=0 and therefore is logarithmically divergent when p = 0. This is certainly unphysical. The origin of this symptom is due to the lack of any thermal effects in our cold-fluid model. Thus Eq. (5) is not applicable to the region within a Debye length from the axis. When we bear this in mind, Eq. (5) reads
This paper contains an analysis of a new model of collisional broadening of spectral lines in whi... more This paper contains an analysis of a new model of collisional broadening of spectral lines in which the effect of the velocity-changing collisions is treated within the Boltzmann-Lorentz model, borrowed from the kinetic theory of gases. The simultaneous occurrence of the velocity modulations and the effects of interaction during the collisions is investigated in detail.
The problem of the liquid-glass transformation continues to be a challenging one. It has been rec... more The problem of the liquid-glass transformation continues to be a challenging one. It has been recently tackled by several high-powered theories such as mode-mode coupling. By contrast, the present model employs the intuitive picture of local orientational order in supercooled liquids and combines this with a variant of the Maxwell model of viscoelasticity. The resulting dynamic theory provides a simple scenario of how the viscosity of a supercooled liquid is enhanced due to its tendency to order orientationally. An important by-product is an expression for the glass-transition temperature in terms of the microscopic parameters of the theory, via which a connection with the formal, spin-glass theoretical approach can be established. The model leads to expressions for the dynamical modes in a supercooled liquidquantities of direct experimental interest.
Following an earlier discussion of the mixed canonical and dissipative description of the many-pa... more Following an earlier discussion of the mixed canonical and dissipative description of the many-panicle dynamics we present a variant approach to the dynamics of a system with internal degrees of freedom. This is illustrated on the example of classical particles equipped with classical spin.
In this paper, we propose a novel algebraic and geometric description for the dissipative dynamic... more In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for constrained dissipative systems through an extension of the Dirac brackets concept, and we present a new formula for calculating Dirac brackets. This formula is particularly useful in the description of dynamical systems with many second-class constraints. After presenting the necessary formal background we illustrate our method on several examples taken from particle dynamics, continuum media physics and wave mechanics.
We present a novel canonical description of the incompressible fluid dynamics. This description u... more We present a novel canonical description of the incompressible fluid dynamics. This description uses the dynamical constraints, in our case reflecting incompressibility assumption, and leads to replacement of usual hydrodynamical Poisson brackets for density and velocity fields with Dirac brackets. The resulting equations are then known nonlinear, and nonlocal in space, equations for incompressible fluid velocity.
We consider a two-dimensional degenerate electron gas in the presence of perpendicular random mag... more We consider a two-dimensional degenerate electron gas in the presence of perpendicular random magnetic field. The magnetic fleld disorder which is assumed to be Gaussian is characterized by two parameters. The first is proportional to the amplitude of local magnetic field fluctuations. The second one characterizes the disorder on the longer scale-we call it the screening length. Using the Kubo formula for the conductivity we have found a class of diagrams which leads to the long time tails in the current-current correlation function. For short times in comparison with the diffusion time corresponding to the screening length this function behaves like logarithm of time, for longer times it decays like t-1 which of course brings into question the diffusive character of the behavior of the charged particle in random magnetic field widely assumed in the literature.
ABSTRACT Electrons interacting with a domain wall in ferromagnetic metals are considered theoreti... more ABSTRACT Electrons interacting with a domain wall in ferromagnetic metals are considered theoretically. In the framework of semiclassical approximation and taking into account Coulomb interaction between electrons, we calculate the spin and charge distribution near the domain wall as well as the local conductivity. We show that the conductivity is significantly modified near the wall and also depends on electron–electron interaction.
Diffusion of a classical particle on a simple Bravais lattice in the presence of a single disloca... more Diffusion of a classical particle on a simple Bravais lattice in the presence of a single dislocation line is analyzed using the Fokker-Plánckequation derived from the continuous theory ofdislocations. It is shown that in the d=2 case the diffusion coefficient is enhanced. This prediction is confirmed by the Monte Carlo simulation of the same diffusion process. A possible generalizationof our results is briefly outlined.
The one-dimensional Potts chain dynamics is analysed by means of the direct space renormalisation... more The one-dimensional Potts chain dynamics is analysed by means of the direct space renormalisation technique. In contrast to previous work one needs no restriction on the value of the Potts dimensionality q. They use the generalised Glauber kinetics for the chain and find that the value of the dynamical critical exponent z is not universal, i.e. it depends on both
Journal of Physics: Condensed Matter, Aug 13, 2009
Following our earlier gauge field theory analysis of the diffusion and interactions of classical ... more Following our earlier gauge field theory analysis of the diffusion and interactions of classical and quantum waves with topological defects in solids (screw and edge dislocations), we present the analysis of the interaction of a classical spin wave with a screw dislocation studied within the Heisenberg ferromagnet model in which spins are located on a lattice containing dislocations. We show that the spin wave interaction with the screw dislocation shows a similarity to the Aharonov-Bohm-like deflection found previously for scattering of acoustic waves on the same type of defects.
The diffusion coefficient of the O/W(1 1 0) system at low temperatures, below critical point, exh... more The diffusion coefficient of the O/W(1 1 0) system at low temperatures, below critical point, exhibits some interesting properties. It is observed that the activation energy of the diffusion process increases rapidly at the phase transition from disordered to the ordered (2 • 1) phase. It is possible to model this rapid change in the activation energy, by proper choice of the transition probabilities in the lattice gas model. This rapid increase of the activation energy is visible as the change of the scaling of the diffusion curves. In the present work we use the same transition rates to calculate the diffusion coefficient at higher densities from 0.5 to 1. Scaling function shows how the activation energy varies with density. The density dependence of the activation energy changes its character on coming from lower to higher temperatures, what can be related to the changes in the phase diagram.
Physica A: Statistical Mechanics and its Applications, 1977
This work contains a discussion of the Vlasov approximation for the system of particles interacti... more This work contains a discussion of the Vlasov approximation for the system of particles interacting not only via the pair-wise central potential, but also via the velocity dependent interactions (V.D.I). The VDI are assumed to be similar in nature to those encountered in the classical plasma when the higher order in (v/c) corrections to the Coulomb forces are taken into account. Using the Klimontovich formulation of the many-body dynamics, we derive the general equation of motion for the exact one-particle distribution function N(r, v, t) and we discuss the Vlasov approximation to this equation in some detail. The linearization of the Vlasov equation and the derivation of the dispersion relations for longitudinal and transverse waves are also presented while the detailed analysis of the solutions and of the stability problem is postponed to the following publication.
Equation (5) should read 4I(p, 0) = QX'-(I/lxx; I) +e~J d('sink~(('-()/Ix'x, 'i. The paragraph st... more Equation (5) should read 4I(p, 0) = QX'-(I/lxx; I) +e~J d('sink~(('-()/Ix'x, 'i. The paragraph starting on line 14 on p. 694 is incorrect and should be replaced by the following: We are interested in the wake field trailing behind the N bunches on the z axis. However, the integral in Eq. (5) includes (=0 and therefore is logarithmically divergent when p = 0. This is certainly unphysical. The origin of this symptom is due to the lack of any thermal effects in our cold-fluid model. Thus Eq. (5) is not applicable to the region within a Debye length from the axis. When we bear this in mind, Eq. (5) reads
This paper contains an analysis of a new model of collisional broadening of spectral lines in whi... more This paper contains an analysis of a new model of collisional broadening of spectral lines in which the effect of the velocity-changing collisions is treated within the Boltzmann-Lorentz model, borrowed from the kinetic theory of gases. The simultaneous occurrence of the velocity modulations and the effects of interaction during the collisions is investigated in detail.
The problem of the liquid-glass transformation continues to be a challenging one. It has been rec... more The problem of the liquid-glass transformation continues to be a challenging one. It has been recently tackled by several high-powered theories such as mode-mode coupling. By contrast, the present model employs the intuitive picture of local orientational order in supercooled liquids and combines this with a variant of the Maxwell model of viscoelasticity. The resulting dynamic theory provides a simple scenario of how the viscosity of a supercooled liquid is enhanced due to its tendency to order orientationally. An important by-product is an expression for the glass-transition temperature in terms of the microscopic parameters of the theory, via which a connection with the formal, spin-glass theoretical approach can be established. The model leads to expressions for the dynamical modes in a supercooled liquidquantities of direct experimental interest.
Following an earlier discussion of the mixed canonical and dissipative description of the many-pa... more Following an earlier discussion of the mixed canonical and dissipative description of the many-panicle dynamics we present a variant approach to the dynamics of a system with internal degrees of freedom. This is illustrated on the example of classical particles equipped with classical spin.
In this paper, we propose a novel algebraic and geometric description for the dissipative dynamic... more In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for constrained dissipative systems through an extension of the Dirac brackets concept, and we present a new formula for calculating Dirac brackets. This formula is particularly useful in the description of dynamical systems with many second-class constraints. After presenting the necessary formal background we illustrate our method on several examples taken from particle dynamics, continuum media physics and wave mechanics.
We present a novel canonical description of the incompressible fluid dynamics. This description u... more We present a novel canonical description of the incompressible fluid dynamics. This description uses the dynamical constraints, in our case reflecting incompressibility assumption, and leads to replacement of usual hydrodynamical Poisson brackets for density and velocity fields with Dirac brackets. The resulting equations are then known nonlinear, and nonlocal in space, equations for incompressible fluid velocity.
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