Coupling Coefficients for Ion-Cyclotron Alfvén Waves

Magnetohydrodynamic equations for plasmas with large Larmor radii are used to derive the wave coupling coefficients. The results generalize those of previous works.     

The Stability of the Relativistic Alfvén Waves

Within the framework of the special relativity, the system of reference comoving with Alfvén wave is defined and the form of the perturbations with respect to this system are deduced. The system of equations corresponding to the interaction of the waves, in the case when the relativistic Alfvén wave can generate new Alfvén waves and magnetosonic waves, is obtained in the most general form. In the one-dimensional case the time dependent perturbation method is used for obtain the dispersion equation for the relativistic coupled waves (decay processes). Finally, by solving numerically the dimensionless dispersion equation, the instability domains of the Alfvén waves are obtained. It is shown that there are possible decay processes and modulational instabilities.     

An Exactly Solvable Model of Disordered System

An exactly solvable model of disordered system with infinite-ranged interaction is solved. We find that almost every eigenvector is localized.     

MHD Wave Interaction within a Plasma Perturbed by Alfvén Waves

The interaction between fast magnetoacoustic waves within a plasma with periodical nonhomogeneities, perturbed by Alfvén waves has been studied. It has been ascertained the appearance of phenomena of a decay instability and an instability involving an increase of the amplitude oscillations. A study of the influence of perturbed plasma parameters on these instability phenomena has been made. It has been found that the optimal perturbing frequency for giving rise to the instability phenomenon is twice the frequency of fast magnetoacoustic waves.     

Alfvén Pulses in the Ionospheric Waveguide

Exact explicit solutions, describing the propagation of wideband non-sinusoidal waveforms in the ionospheric Alfvén waveguide by means of non-separable electromagnetic fields, are presented. The dispersive modulation of these fields is shown to result in the formation of quasimonochromatic oscillations at the wings of the Alfvén pulses. The frequencies of these oscillations are close to the cut off frequencies of the waveguide.     

An Exactly Solvable Spin-1 Model under External Magnetic Field

A two-fold Cayley tree with fully q-coordinated sites is constructed and thespin-1 Blume-Capel model in the presence of an external magnetic field issolved exactly. The relevant properties such as magnetization m and squaremagnetic moment q are investigated as functions of temperature and externalmagnetic field both for ferromagnetic and antiferromagnetic couplings. Inthe study, we propose a possible mechanism of the plateau based on theexchange couplings.     

An Exactly Solvable Spin-1 Model under External Magnetic Field

A two-fold Cayley tree with fully q-coordinated sites is constructed and the spin-1 Blume-Capel model in the presence of an external magnetic field is solved exactly. The relevant properties such as magnetization m and square magnetic moment q are investigated as functions of temperature and external magnetic fieId both for ferromagnetic and antiferromagnetic couplings. In the study, we propose a possible mechanism of the plateau based on the exchange couplings.     

Relation between Hall-magnetohydrodynamics and the kinetic Alfvén wave

Effects of a finite ion temperature on the Hall magnetohydrodynamics (MHD), which breaks down for a finite ion temperature, are clarified in terms of a rigorous three-field kinetic dispersion relation. The MHD mode equation becomes anisotropic with respect to the ion pressure because of the double adiabaticity in ion dynamics.     

Surface Tension of a Metal-Electrolyte Boundary: Exactly Solvable Model

An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The information gained from the mapping provides an explicit form of the surface tension in the plasma-stability regime.     

Surface Tension of an Ideal Dielectric-Electrolyte Boundary: Exactly Solvable Model

The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant <2, in contact with a dielectric wall of dielectric constant =0. The model is mapped onto an integrable sine-Gordon theory with a free Neumann boundary condition. Using recent results on a reflection relationship between the boundary Liouville and sine-Gordon theories, an explicit expression is derived for the surface tension at a rectilinear dielectric – Coulomb gas interface. This expression reproduces the Debye-Hückel 0 limit and the exact result at the bulk collapse border, the free-fermion point =2, where the surface tension keeps a finite value. The surface collapse, identified with the divergence of the surface tension, occurs at =3.     

三维精确可解统计模型──Baxter－Bazhanov模型的可积性条件

从手征Ｐｏｔｔｓ模型推导出三维精确可解Ｂａｘｔｅｒ－Ｂａｚｈａｎｏｖ模型的“可逆性”及“星一方”关系,从而说明其可积性条件──四面体方程是手征Ｐｏｔｔｓ模型星──三角关系的一个结论．若把玻尔兹曼权参变数表示为Ｚａｍｏｌｏｄｃｈｉｋｏｖ角变量形式,其附加条件自然成立．值得指出的是,由本文处理方法可以得出三维可解统计模型的星－三角关系,它包含了Ｂａｚｈａｎｏｖ和Ｂａｘｔｅｒ的结论．     

Stationary Regimes of Nonlinear Alfvén Oscillations in a Driven System with Discrete Spectrum

Driven stationary Alfvén oscillations in a system with discrete spectrum are considered in the approximation of weak nonlinearity. The correction to the eigenfrequency of small oscillations, proportional to the square of their amplitude, is derived with the help of the perturbative approach. The dependence of the amplitude versus the frequency of the driving force is found to have two bifurcation points at which the amplitude exhibits finite variation under the action of infinitesimal deviation of the driver frequency. It is shown that the bifurcation is possible only when the unstable processes of interaction of the initial standing Alfvén wave with small perturbations are stabilized to the third order in the wave amplitude. Conditions of the stabilization, as a consequence of a finite length of the system or due to dissipation, of three- and four-wave parametric instabilities are discussed.     

Quantum Decoherence of Macroscopic Object Induced by Inner Environments: an Exactly Solvable Model

We revisit the quantum decoherence problem of the center of mass motion of a macroscopic object,which is modelled as a one-dimensional atom chain.Induced by the coupling of the center of mass (C.M) motion with the inner degrees of freedom,this inner-environment-induced decoherence is reflected by the localization of the C.M wave packet.We show that,the C.M motion is coupled to the inner states only when the chain has interaction with the external potential.This result provides a realistic mechanism for the analysis of the inner-environment-induced localization of a macroscopic object.     

Information-Theoretic Features of Many Fermion Systems: An Exploration Based on Exactly Solvable Models

Finite quantum many fermion systems are essential for our current understanding of Nature. They are at the core of molecular, atomic, and nuclear physics. In recent years, the application of information and complexity measures to the study of diverse types of many-fermion systems has opened a line of research that elucidates new aspects of the structure and behavior of this class of physical systems. In this work we explore the main features of information and information-based complexity indicators in exactly soluble many-fermion models of the Lipkin kind. Models of this kind have been extremely useful in shedding light on the intricacies of quantum many body physics. Models of the Lipkin kind play, for finite systems, a role similar to the one played by the celebrated Hubbard model of solid state physics. We consider two many fermion systems and show how their differences can be best appreciated by recourse to information theoretic tools. We appeal to information measures as tools to compare the structural details of different fermion systems. We will discover that few fermion systems are endowed by a much larger complexity-degree than many fermion ones. The same happens with the coupling-constants strengths. Complexity augments as they decrease, without reaching zero. Also, the behavior of the two lowest lying energy states are crucial in evaluating the system’s complexity.     

A Solvable Model of Interface Depinning in Random Media

We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written directly for an infinite system. For a flat distribution of random local forces the value of the depinning threshold can be obtained exactly. In the case of parallel dynamics (all unstable sites move simultaneously), due to the discrete character of the interface heights allowed in the model, the motion of the center of mass is non-uniform in time in the moving phase close to the threshold, and the mean interface velocity vanishes with a square-root singularity.     

Dispersion of kinetic Alfvén wave in a rotating plasma with an inhomogeneous magnetic field

The effects of inhomogeneity of a magnetic field on the dispersion of kinetic Alfvén waves (KAWs) in a rotating plasma is investigated under the framework of magnetohydrodynamic theory. The magnetic field should be in a non‐uniform state if the centrifugal force is balanced only by the magnetic pressure. The inhomogeneity of the magnetic field increases the frequency of KAW and drives it into an unstable state. The growth rate of KAW varies non‐monotonously with respect to the distance. The KAW will be excited in a certain region with maximum growth rate. And the growth rate of KAW in the region near and far from the centre of rotation approaches zero. These results will be helpful in understanding the properties of KAWs in rotating astrophysical and laboratory plasmas.     

Dispersion Relations for Drift-Alfvén and Drift-Acoustic Waves in Arbitrary Directions

A dispersion equation for low-frequency waves in a fully ionized plasma with slowly varying density and magnetic field is derived from the two-fluid equations. The solutions are discussed in several limiting cases. Phase-velocity and refractive index surfaces are presented for the fast and slow magneto-acoustic waves and for the shear-Alfvén wave, influenced by the inhomogeneity drifts.     

Quantum Tunneling in Time-Dependent Potential Barrier: a General Formulation and Some Exactly Solvable Models

Quantum tunneling in one spatial dimension in the presence of time-dependent potentials is investigated theoretically. First, a general multichannel formulation of the problem is given for harmonic time-dependence. The case of an oscillatory delta-function potential of constant strength is discussed at length and specific numerical calculations are presented for the reflection and transmission coefficients. Then other exactly solvable time-dependent potentials are obtained by carrying out successive unitary transformations. As an example of this class, a delta-function potential with time-dependent strength and boundary conditions is studied. Finally tunneling time-delay for time-dependent potentials is formulated in the multichannel situation, and also the concept of first passage time for the decay of a wave packet confined to one well of a double well potential is generalized for the case of time-dependent barrier and boundary conditions.     

Closure Approximations for Passive Scalar Turbulence: A Comparative Study on an Exactly Solvable Model with Complex Features

Some standard closure approximations used in turbulence theory are analyzed by examining systematically the predictions these approximations produce for a passive scalar advection model consisting of a shear flow with a fluctuating cross sweep. This model has a general geometric structure of a jet flow with transverse disturbances, which occur in a number of contexts, and it encompasses a wide variety of possible spatio-temporal statistical structures for the velocity field, including strong long-range correlations. Even though the Eulerian and Lagrangian velocity statistics are not equal and the passive scalar statistics exhibit broader-than-Gaussian intermittency, this model is nevertheless simple enough so that many passive scalar statistics can be computed exactly and compared systematically with the predictions of the closure approximations. Our comparative study illustrates the strength and weaknesses of the closure approximations and points out the physical phenomena that these approximations are able or not able to describe properly. In particular it is shown that the direct interaction approximation (DIA), one of the most sophisticated closure approximations available, fails to reproduce adequately the statistical features of the scalar and may even lead to absdurd predictions, even though the equations it produces are rather complicated and difficult to analyze. Two alternative closure approximations, the Modified DIA (MDIA) and the Renormalized Lagrangian Approximation (RLA), with different levels of sophistication, both are simpler to use than the DIA and perform better. In particular, it is shown that both closure approximations always reproduce exactly the second order statistics for the scalar and that the MDIA is even able to capture intermittency effects.