Spin-wave theory for finite classical magnets and superparamagnetic relation

Analytical calculations based on finite-size spin-wave theory and Monte Carlo (MC) simulations are performed to investigate the validity of the well-known relation m(H, T) = M(H, T)B _D[M(H, T) H/T] between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models (B _D(x) is the Langevin function, D is the number of spin components, is the number of atoms in the particle). It follows from general arguments and from our analytical results for the Heisenberg model at T≪T _c that this relation is not exact for any finite D and nonzero temperature. Nevertheless, corrections to this formula remain very small practically in the whole range T < T _c if ≫ 1, as confirmed by our Monte Carlo calculations. At T T _c/4 there is a good agreement between the MC and finite-size spin-wave calculations for the field dependence of m and M for the Heisenberg model with free boundary conditions. Received 1st December 2000     

A classical theory of hard squares

A simple phenomenological theory of the hard-square lattice gas is obtained by analyzing a low-order corner transfer matrix variational approximation. The free energy is of Landau type and expressions are obtained for the order parameter and densities. In this approximation, the model exhibits a critical point atz _c =4(3 + 23)/9 with critical exponents given by the classical values: =0_disc,=1/2, =1, =3.     

A study of the parameterisation of the uniaxial model of superparamagnetic relaxation

Mössbauer spectra of the iron storage protein ferritin taken over a range of temperatures exhibit the characteristic behaviour of superparamagnetic relaxation, and can be used to investigate a model for the superparamagnetic relaxation of a sample of small magnetic particles. A computer program is used to calculate a series of Mössbauer spectra based on the relaxation model, and these theoretical spectra are then fitted simultaneously to all the variable temperature experimental spectra, with the parameters of the uniaxial anisotropy model as the only variables.     

Dynamics of superparamagnetic filaments with finite magnetic relaxation time

In this paper we formulate a model of superparamagnetic filaments with internal dissipative torques due to the action of a rotating magnetic field. It is shown that spirals are formed at both ends of the filament due to the action of the internal torques. These spirals propagate to the center of the filament and collide, forming a compact cluster that rotates in accordance with the rotating magnetic field. These results are in agreement with recent experiments with chains of superparamagnetic beads in a rotating magnetic field.     

A relaxation theory of Stark broadening by ions

A theory of Stark broadening in plasmas is presented in which the effects of broadening by ion perturbers are treated in a manner similar to the relaxation theory or unified theory for electrons. An expression is derived for Fano's broadening operator M(ω) which does not contain the projection operators or cumulants of previous forms. To obtain a calculable expression for M(ω), an approximation is made in which small, second-order fluctuation terms are replaced by their adiabatic limits. Sample calculations are presented for the first two members of the Lyman and Balmer series of hydrogen which show reasonable agreement with experiment, although the “dip” of the β-lines is still too pronounced.     

A relaxation theory of plasma-broadened He II lines

The relaxation theory of plasma line broadening developed by Smith and Hooper, and extended by Smith, is applied to a charged radiator. The 304 Å Lyman alpha line of He II is chosen as an example. The radiator is assumed perturbed only by electronic and ionic electric microfields. The ions are treated in the static approximation. Two-component ion microfield distribution functions that allow for the presence of both He⁺ and He⁺⁺ perturbers are employed. The fact that the radiator is charged complicates the treatment of electron perturbation; two different approaches are included. The first neglects the effect of the charge of the radiator on the perturbing electron and assumes that the perturbing electrons can be represented by momentum wave functions. This method corresponds to Smith's treatment of the electron perturbers in neutral hydrogen. The second includes the effect of the charge of the radiator on the perturbing electrons and represents the perturbing electrons by Coulomb wave functions; this calculation requires evaluation of free-free gaunt factors. The theory, with both the momentum and Coulomb perturber wave functions, predicts a blue asymmetry in the near wings of the line. These two approaches can be compared with the classical path approach of Griem and Shen.     

Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

Nonlinear classical theory of electromagnetism

A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere.     

A finite-dimensional canonical formalism in the classical field theory

A canonical formalism based on the geometrical approach to the calculus of variations is given. The notion of multi-phase space is introduced which enables to define whole the canonical structure (physical quantities, Poisson bracket, canonical fields) without use of functional derivatives. All definitions are of pure geometrical (finite dimensional) character.The observable algebra (physical quantities algebra) obtained here is much smaller then the algebra of all (sufficiently smooth) functionals on the space of states, derived from the standard infinite-dimensional formulation. As it is known, the latter is much too large for purposes of quantization. As the examples prove, our algebra could be an adequate start-point for quantization.For simplifying the language the notion of observable-valued distribution is introduced. Many concrete physical examples are given. E.g. it is shown that some problems connected with gauge in electrodynamics are automatically solved in this approach. The introduced language allows to obtain the Noether theorem in a most natural way.     

A simple theory of spin-wave relaxation in ferromagnetic metals

The anisotropic exchange interaction between localized spins and conduction electrons is described by an appropriate spin hamiltonian. This is used to calculate the lifetime of magnons for arbitrary values of Λ_eq, where Λ_e is the electron mean free path and q the magnon wavevector. At Λ_eq ? 1, this lifetime depends on the angle between q and the saturation magnetization. The antisymmetric part of anisotropic exchange (Dzialoshinsky-Moriya interaction) may dominate the relaxation of spin-waves of large q. The complicated band structure of transition metals gives rise to a magnon lifetime independent of Λ_e. The contribution of isotropic exchange is also considered.     

The effect of an oblique magnetic field on the superparamagnetic relaxation time

The effect of a constant magnetic field, applied at an angle ψ to the easy axis of magnetization, on the Néel relaxation time τ of a single domain ferromagnetic particle with uniaxial anisotropy is investigated by calculating the smallest non-vanishing eigenvalue of the appropriate Fokker-Planck equation as a function of ψ. The curve of λ₁ versus ψ is symmetric about ψ = 90°. Thus the maximum decrease in τ occurs at ψ = 45° with maximum increase to a value exceeding that at ψ = 0, at ψ = 90°, the ψ = 0 value being again attained at ψ = 180°. The results are shown to be consistent with the behaviour predicted by the Kramers theory of the rate of escape of particles over potential barriers. This theory when applied to the potential barriers for the ψ = 90° orientation for rotation in space yields a simple approximate formula for the escape rate which is in reasonable agreement with the exact λ₁ calculated from the Fokker-Planck equation.     

广义经典力学与非完整力学的统一理论

建立广义经典力学与非完整力学的统一理论———广义非完整力学理论,构造其基本框架.提出广义非完整力学的Чeтаeв(Chetaev)定义,建立广义非完整力学系统的Routh方程和正则方程.给出广义非完整力学系统的非等时变分方程,证明由广义非完整力学系统的第一积分可以构造积分不变量.研究广义非完整力学系统作用量的非等时变分,给出系统的Poincar啨Cartan积分变量关系和积分不变量,进而给出等时变分下系统的Poincar啨积分变量关系和通用积分不变量.给出一些推论,表明广义经典力学和一阶至高阶非完整力学的相关结论均为广义非完整力学理论的特款. 关键词： 广义非完整力学 广义Чeтаeв定义 运动方程 积分不变量     

A critical experimental study of the classical tactile threshold theory

Background  

The tactile sense is being used in a variety of applications involving tactile human-machine interfaces. In a significant number of publications the classical threshold concept plays a central role in modelling and explaining psychophysical experimental results such as in stochastic resonance (SR) phenomena. In SR, noise enhances detection of sub-threshold stimuli and the phenomenon is explained stating that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. We designed an experiment to test the validity of the classical vibrotactile threshold. Using a second choice experiment, we show that individuals can order sensorial events below the level known as the classical threshold. If the observer's sensorial system is not activated by stimuli below the threshold, then a second choice could not be above the chance level. Nevertheless, our experimental results are above that chance level contradicting the definition of the classical tactile threshold.     

Quark-gluon transport theory I. The classical theory

A classical relativistic kinetic theory for a plasma with non-Abelian gauge interactions is formulated. After the local equilibrium solutions for the quark distribution function are found, the associated moment equations and their near-equilibrium expansion, leading to a set of relativistic chromohydrodynamical equations for viscous colored fluids, are studied.