Effect of anomalously slow motions of particles with spins of 1/2 on the shape of the magnetic resonance line of pairs of particles

A non-Markovian version of the Liouville stochastic equation was used to analyze spin relaxation in a pair of particles with spins 1/2 and the dipole-dipole interaction between the spins. The particles were involved in anomalously slow stochastic relative rotation described by the angular correlation function K(t) ～ 1/t ^α with α < 1. The Liouville stochastic equation could be used to describe memory effects in the kinetic dependence of rotational relaxation resulting in a very slow descent of K(t). Our analysis showed that the anomalous relative motion of radicals manifested itself in special features of the shape of the magnetic resonance line of the particle pair.     

Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.     

Optimal control-based states transfer for non-Markovian quantum system

Utilizing the method of optimal control, we investigate the tactics of state transfer in the non-Markovian quantum system with phase relaxation and energy dissipative relaxation. The influence of Ohmic reservoir with Lorentz–Drude regularization is numerically studied. Owing to the decoherence and memory effects of non-Markovian channel, the purity of quantum state attenuates damply in the free evolution. The numerical simulations indicate that arbitrary state transfer for non-Markovian system can be realized under the optimal control function by a proper external control field with a success rate of more than 98 percent. When the right control field and function is implemented, not only the decoherence is compensated completely but also the purity of quantum states are maintained in the process of state transfer.     

Influences of magnetic particle–particle interactions on orientational distributions and rheological properties for a colloidal dispersion composed of rod-like particle with a magnetic moment normal to the particle axis

We have investigated mainly the influences of magnetic particle–particle interactions on the orientational distribution and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane since the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the increase in the viscosity because the mean-field vector has only a component along the magnetic field direction.     

Non-Markovianity and Indivisible Quantum dynamics of a Apin-S System

Using a measure for the divisibility of a dynamical map,we study the non-Markovian character of a quantum evolution of a spin-S system,which is in an external field and weakly coupled to a bosonic bath with a certain temperature.The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation.Besides the influence of the environmental spectral density function,the external field and low temperatures can afect the quantum non-Markovianity.It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Non-Markovianity and Indivisible Quantum dynamics of a Apin-S System

Using a measure for the divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a spin-S system, which is in an external field and weakly coupled to a bosonic bath with a certain temperature. The finite-temperature dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. Besides the influence of the environmental spectral density function, the external field and low temperatures can affect the quantum non-Markovianity. It is found out that the non-Markovian feature of a dynamical map of a high-dimensional spin system is noticeable in contrast to that of a low-dimension spin system.     

Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

Negative viscosity due to magnetic properties of a non-dilute suspension composed of ferromagnetic rod-like particles with magnetic moment normal to the particle axis

The negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis, have been investigated. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rod-like particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.     

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) ? 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.     

On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion

Differential equations governing the time evolution of distribution functions for Brownian motion in the full phase space were first derived independently by Klein and Kramers. From these so-called Fokker-Planck equations one may derive the reduced differential equations in coordinate space known as Smoluchowski equations. Many such derivations have previously been reported, but these either involved unnecessary assumptions or approximations, or were performed incompletely. We employ an iterative reduction scheme, free of assumptions, and calculate formally exact corrections to the Smoluchowski equations for many-particle systems with and without hydrodynamic interaction, and for a single particle in an external field. In the absence of hydrodynamic interaction, the lowest order corrections have been expressed explicitly in terms of the coordinate space distribution function. An additional application of the method is made to the reduction of the stress tensor used in evaluating the intrinsic viscosity of particles in solution. Most of the present work is based on classical Brownian motion theory, but brief consideration is given in an appendix to some recent developments regarding non-Markovian equations for Brownian motion.Supported by the National Science Foundation.     

Dirac particle with memory: Proper time non-locality

A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function. This function takes into account that the behavior of the particle at proper time can depend not only at the present time, but also on the history of changes on finite time interval. In this case the Dirac particle can be considered an open quantum system with non-Markovian dynamics. The violation of the semigroup property of dynamic maps is a characteristic property of dynamics with memory. We use the Fock-Schwinger proper time method and derivatives of non-integer orders with respect to proper time. The fractional differential equation, which describes the Dirac particle with memory, and the expression of its exact solution are suggested. The asymptotic behavior of the proposed solutions is described.     

Instability of plasma-dust systems with a macroparticle charge gradient

An analysis is made of various self-oscillations which appear in plasma-dust systems with spatially varying macroparticle charges. The conditions of establishment and the nature of the evolution of the two main types of instability of these systems are analyzed. Particular attention is paid to cases of vortex particle motion. Dust systems having parameters similar to those in laboratory experiments are modeled numerically. Calculations were made for charged particles in an external electric field and in the Earth’s gravitational field using a molecular dynamics method.     

A numerical method for the analysis of polydisperse aerosol particles charging in a coaxial electrode system

In this paper, charging kinetics of polydisperse aerosol particles in a corona field of a coaxial electrode system is numerically analyzed for a logarithmic normal distribution of aerosol particle size. The particle charging and the particle current are calculated by using a charging model considering ion concentration and particle mobility. Particle charging profiles under varying ion density and electrical field intensity distributions of the charging chamber were revealed. A low charging profile in the transition region of bipolar corona field was demonstrated in the simulation results.     

The Fokker-Planck equation in the second-order pitch angle approximation and its exact solution

The diffusive particle propagation and its pitch angle scattering is studied using kinetic equation of the Fokker-Planck form. The case is considered when charged particles preferable propagate along the strong mean magnetic field direction and undergo the pitch angle scattering with respect to it. The paper deals with solution of the equation for particle distribution function in the second-order approximation in the pitch angle. The exact analytical solution is obtained in an integral form. The well-known solution in the first-order pitch angle approximation can be restored performing the small time limit in the result. Unlike the first-order solution the obtained solution in the second approximation rightly shows that the pitch angle diffusion is closely connected with the particle transport along the mean magnetic field. The expression for particle density for the point instantaneous unidirectional source also has been obtained.     

The kinetic boundary layer for the Fokker-Planck equation: Selectively absorbing boundaries

We study the joint distribution function for position and velocity of a Brownian particle near a wall. The wall absorbs all particles that hit it with sufficiently high velocity and reflects all slower ones, either specularly or diffusely. We determine in particular stationary distributions in the absence of external forces. Appreciable deviations from local equilibrium occur in a kinetic boundary layer near the wall; its details depend strongly on the way in which the slow particles are reflected. The resulting effective absorption rate is calculated and compared with the result of approximations analogous to the transition state theory of chemical reactions. The method used is a generalization of the one used in an earlier paper for the case of a completely absorbing wall; a numerical algorithm based on an expansion of the distribution function in terms of a presumably complete set of boundary layer solutions.     

The fluctuation kinetics of formation of nanoparticles: Particle-size distribution

A stochastic simulation of the growth of particles on a uniform cubic lattice was performed by the Monte Carlo method. Changes in the width of the distribution (M _w /M _n ) as the size of particles increased were extremal in character. Distribution narrowing occurred much more slowly than in classic polymerization. An empirical equation relating the number of free vacancies of a growing particle and its mean size was obtained. The introduction of a stabilizer deactivating free vacancies of a growing particle caused the appearance of a critical phenomenon. At stabilizer concentrations higher than critical, large-sized particles could not form. At stabilizer concentrations close to critical, the particle-size distribution was bimodal. This resulted in an anomalously larger distribution width.     

Method of projection operators in the theory of irreversible processes

The Zwanzig-Nakajima projection-operator method is extended to the case of time-dependent nonlinear projection operators. A method employing these operators is proposed for constructing the non-Markovian kinetic equation for a single-particle, time-dependent distribution function. An important assumption is made in the derivation of the equation regarding the factorization of the initial nonequilibrium distribution of the multi-particle system. An approximate kinetic equation is obtained for a slightly nonequilibrium system which asymptotically approaches the equilibrium canonical distribution at a fixed temperature. The effects of the self-consistent Vlasov field and the non-Markovian Fokker-Planck collision operator with a microscopic parameter appear in this equation. This is the first derivation of such an equation.     

Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory

The non-Markovian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal field theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.