Cross-relaxation in multiple pulse NQR spin-locking

The experimental and theoretical NQR multiple-pulse spin locking study of cross-relaxation process in solids containing nuclei of two different sorts I?>?1/2 and S?=?1/2 coupled by the dipole–dipole interactions and influenced by an external magnetic field. Two coupled equations for the inverse spin temperatures of the both spin systems describing the mutual spin lattice relaxation and the cross-relaxation were obtained using the method of the nonequilibrium state operator. It is shown that the relaxation process is realized with non-exponential time dependence describing by a sum of two exponents. The cross relaxation time is calculated as a function of the multiple-pulse field parameters which agree with the experimental data. The calculated magnetization cross relaxation time vs the strength of the applied magnetic field agrees well with the obtained experimental data.     

Solution of the Electrodiffusion Equations in the Quasi-Stationary Approximation

The electrodiffusion equations are solved together with the equation for the current running through the boundary of the examined system with the environment. The complete system of equations allows the volt-ampere characteristic of the system to be obtained for an arbitrary time dependence of the external potential. The procedure of finding the first-order approximation is developed to solve the system of electrodiffusion equations.     

Solution of the System of Electrodiffusion Equations

The solution of the electrodiffusion equations together with the Poisson equation is examined. It is demonstrated that in the main approximation in a small parameter, the solution is reduced to that of two first-order differential equations. The obtained equations allow the transition processes in systems of charged particles to be examined for an arbitrary time dependence of the external potential.     

Relaxation of physical systems in relative-number state representation

The relaxation properties of physical systems in the Liouville space are investigated in terms of the relative-number state representation. An arbitrary state can be expressed by superposition of relative-number states. In the absence of an time-dependent external field, all components with non-zero relative-numbers decay to zero with time, and any stationary state can be expressed only in terms of zero relative-number states. The phase canonically conjugate to the relative-number is completely uncertain in a stationary state. It is thought that relaxation from an arbitrary initial state to a stationary state is described as some kind of phase relaxation process. Such a phase relaxation process is explicitly described by the phase operator formalism within the framework of the relative-number state representation.     

Spin 3/2 Field Equation: Separation and Solution in a Class of Lema?tre–Tolman–Bondi Cosmologies

The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin field equation is suggested.     

Asymmetry of the shape of surroundings as a mechanism for generating directed motion

A mechanism for generating a directed motion of a Brownian particle in an asymmetric channel under the action of a varying force field is considered. The setup implementing such a mechanism resembles typical Brownian motors using asymmetry of the energy potential (ratchet effect). It is shown that under certain conditions, the asymmetry of the shape may ensure the maximal level of rectification for a large intensity of the external field drawing the system from equilibrium. The main question formulated here is the dependence of the rectifying ability of such a mechanism on the external action parameters and, above all, on the form of the time dependence. The results obtained here for a sine signal and an aperiodic train of pulses are compared with the previous results obtained by the authors for bipolar rectangular pulses. General estimates obtained for pulses of an arbitrary shape determine its influence on the velocity of directed motion. Analysis of the proposed mechanism is based of the combination of analytic calculations for a strong external field with simulation by the method of Brownian dynamics for arbitrary parameters.     

Dirac-graphene quasiparticles in strong slow-light pulse

An analytical Volkov's solution of the massless Dirac equation for graphene in the field of slow-light pulse with arbitrary time dependence is obtained. Exact solutions are presented for special cases of monochromatic field and a single-cycle pulse. Following the Fock-Schwinger proper time method, the Green's function for quasiparticles is derived with the account of the influence an external classical electromagnetic wave field.     

The influence of external fields on the orientational relaxation of nematic liquid crystals

The relaxation of the director field n, the velocity field v, and the shear and normal components of the stress tensor is theoretically investigated by numerically solving the system of nonlinear hydrodynamic equations. These equations describe the director reorientation with allowance made for the field of velocities induced by the rotation of the director field. The relaxation time and the influence of the velocity field on the relaxation processes are analyzed for a number of hydrodynamic regimes, which arise in a liquid-crystal cell under the effect of external electric and magnetic fields.     

Anisotropy of the submillimeter conductivity of warm carriers in n-type gallium arsenide

The submillimeter conductivity of warm electrons in GaAs at 300 K shows a pronounced dependence on the orientation of the high-frequency field relative to an applied d.c. field. Calculations based on the momentum and energy balance equations can explain the measured data and allow a determination of the energy relaxation time.     

Lagrangian dynamics of spinning particles and polarized media in general relativity

The general form of the Lagrangian equations of motion is derived for a spinning particle having arbitrary multipole structure in arbitrary external fields. It is then shown how these equations, together with the complete system of field equations can be recovered from a fourdimensional action integral representing a polarized dustlike medium interacting with an arbitrary set of fields. These general results are then specialized to the case of Einstein-Maxwell fields in order to obtain the general-relativistic extension of Lorentz's dielectric theory.     

Weyl Spinor and Solution of Massless Free Field Equations

The massless field equations for arbitrary spin in curved space-time arereconsidered. The general solution of the field equation in Robertson-Walkerspace-time that was previously determined is briefly discussed after explicitlyshowing that the Weyl spinor vanishes. The case of the Lemaître-Tolman-Bondispace-time is studied in detail. The general expression of the corresponding Weylspinor is obtained and some particular situations exploited. The spin-3/2 andspin-2 massless field equations are solved explicitly. The solutions are simplifiedby the existence of nontrivial algebraic constraints. The angular part of theequations is separated by the usual separation method and integrated directly.The other equations that are not separated in the radial and time dependence arereduced to a simple form. The results obtained are extended, as a consequenceof previous results, to the case of arbitrary spin. The solution of the general caseessentially reduces to the treatment of spin 3/2 and spin 2.     

Supersonic flows with small perturbations in the presence of external effects in the flow. Part 1: “Thin body of revolution”

Axisymmetric supersonic flow about a thin body of revolution with an external energy supply and an external force localized near the body surface is considered in the linear approximation. An analytic theory is constructed for calculating spatial fields of flow parameters in this case for an arbitrary dependence of external effects on the longitudinal coordinate. Formulas are derived for the pressure ratio on the surface of the thin body of revolution. The results of calculations based on the analytic theory are in good agreement with numerical data obtained from the solution of hydrodynamic equations in the Euler approximation.     

Distribution function for random interaction fields in disordered magnets: Spin and macrospin glass

Systems with an arbitrary dependence of exchange integral on the distance between atoms which are randomly scattered in an amorphous substance are investigated by averaging over random fields of interaction in the framework of the Ising model. This method is also used for describing long-term magnetization relaxation in a system of single-domain particles scattered in a nonmagnetic matrix. Random field distribution functions are obtained for the dipole-dipole and the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions. Long-term relaxation in macrospin glasses is investigated.     

A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field

Quantum characteristics of a charged particle subjected to a singular oscillator potential under an external magnetic field is investigated via SU(1,1) Lie algebraic approach together with the invariant operator and the unitary transformation methods. The system we managed is somewhat complicated since we considered not only the time-variation of the effective mass of the system but also the dependence of the external magnetic field on time in an arbitrary fashion. In this case, the system is a kind of time-dependent Hamiltonian systems which require more delicate treatment when we study it. The complete wave functions are obtained without relying on the methods of perturbation and/or approximation, and the global phases of the system are identified. To promote the understanding of our development, we applied it to a particular case, assuming that the effective mass slowly varies with time under a time-dependent magnetic field.     

Dielectric properties of monocrystal diglycine nitrate near the phase transition point in the frequency range 1 Hz-10 MHz

In this paper, the dielectric properties of the polar cut of the monocrystal of diglycine nitrate (DGN), depending on the temperature, the frequency of the applied external field and the measuring time, were studied. Using the Havriliak—Negami equation, an approximation of the experimental frequency dependencies of permittivity was made. For each temperature point, a relaxation time spectrum is obtained. The temperature dependence of relaxation time values near the Curie point was found.     

Non-perturbative renormalization group calculation of the scalar self-energy

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.     

Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.     

Nonlinear response of superparamagnetic particles to a sudden change of a high constant magnetic field

For a system of superparamagnetic particles in a high external constant magnetic field, a technique for calculating the nonlinear response to a sudden change in the field direction and magnitude is proposed. A set of momentary equations for the averaged spherical harmonics, which is derived from the Fokker-Planck equation for the magnetization-orientation distribution function is the basis of this technique. As an example, the nonlinear response of a system of particles with anisotropy of the easy-axis type is examined. For this case, a solution to the momentary equations is obtained by using matrix continued fractions. The magnetization relaxation time and the spectrum of the relaxation function are calculated for typical values of anisotropy, dissipation, and nonlinearity parameters. It is shown that the magnetization kinetics is essentially dependent on these parameters.     

Complex magnetic susceptibility of uniaxial superparamagnetic particles in a strong static magnetic field

The magnetic relaxation of a system of single-domain ferromagnetic particles in the presence of a strong static magnetic field directed at an arbitrary angle relative to the particle anisotropy axis is investigated. A system of linear difference-differential equations for the moments (averaged spherical harmonics) is derived without recourse to the Fokker-Planck equation by averaging Gilbert’s equations with a fluctuating field. An exact solution (in terms of matrix continuous fractions) is found for this system. The relaxation times and spectra of the complex magnetic susceptibility are calculated. Fiz. Tverd. Tela (St. Petersburg) 40, 1642–1649 (September 1998)