非均匀量子等离子体中的非线性波

本文探讨具有温度和密度梯度的非均匀量子等离子体系统, 获得了该系统在离子与中子碰撞频率较低情况下的二维非线性流体动力学方程． 求得了非均匀量子等离子体中的电势的冲击、爆炸和旋涡解．分析讨论了在致密天体物理环境中静电势的变化, 结果表明电势的冲击波的幅度和爆炸波的宽度,都随密度的增大(即随无维量子参量的减小)而增大, 但随漂移速度的增大(即随密度和温度梯度的增大)而减小; 静电势随时空相位的增大而趋向于稳定值, 系统最后达到稳定的状态． 旋涡解表明,旋涡静电势的时空分布呈现稳定的周期性的旋涡流．     

Vortex Street in Homogeneous Dense Dusty Magnetoplasma

For studying the vortex structure in uniform dense dusty astrophysical conditions, a two-dimensional nonlinear equation is derived employing the quantum magnetoplasma hydrodynamic model and considering the strong collisional effect. The coherent vortex solution is obtained by perturbation analysis method. It is shown that the distribution of the electrostatic potential forms spatially a periodic vortex street, and is controlled temporally by the arbitrary function of time that may lead to abundant spacial distributions. It is found that the dust charge number, collision frequency, electron Fermi wavelength and quantum correction all play significant roles to the spatial distribution of vortex street.     

Dust acoustic waves in collisional uniform dense magnetoplasma

In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral collisions. The linear dispersion relation indicates that the scale lengths of the system are revised by the quantum parameter, and that the wave motion decays gradually leading the system to a stable state eventually. The variations of the dispersion frequency with the dust concentration, collision frequency, and magnetic field strength are discussed. For the coherent nonlinear dust acoustic waves, new analytic solutions are obtained, and it is found that big shock waves and wide explosive waves may be easily produced in the background of high dusty density, strong magnetic field, and weak collision. The relevance of the obtained results is referred to dense dusty astrophysical circumstances.     

Sheared Flow Driven Drift Instability and Vortices in Dusty Plasmas with Opposite Polarity

Low-frequency electrostatic drift waves are studied in an inhomogeneous dust magnetoplasma containing dust with components of opposite polarity. The drift waves are driven by the magnetic-field-aligned (parallel) sheared flows in the presence of electrons and ions. Due to sheared flow in the linear regime, the electrostatic dust drift waves become unstable. The conditions of mode instability, with the effects of dust streaming and opposite polarity, are studied. These are excited modes which gain large amplitudes and exhibit interactions among themselves. The interaction is governed by the Hasegawa-Mima (HM) nonlinear equation with vector nonlinearity. The stationary solutions of the HM equation in the form of a vortex chain and a dipolar vortex, including effects of dust polarity and electron (ion) temperatures, are studied. The relevance of the present work to space and laboratory four component dusty plasmas is noted.     

Exact vortex solitons in a quasi-two-dimensional Bose–Einstein condensate with spatially inhomogeneous cubic–quintic nonlinearity

The exact vortex soliton solutions of the quasi-two-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities are constructed by similarity transformation. It is demonstrated that spatially inhomogeneous cubic–quintic nonlinearity can support exact vortex solitons in which there are two quantum numbers S and m. The radius structures and density distributions of these vortex solitons are studied, and it is shown that the number of ring structure of the vortex solitons increases by one with increasing the “radial quantum number” m by one.     

Characteristic parameters of drift vortices coupled to Alfvén waves in an inhomogeneous space plasma

We present detailed measurements of ion scale vortices of drift type coupled to Alfvén waves in an inhomogeneous and collisionless space magnetoplasma. The two free parameters of a dipolar vortex, intensity and spatial radius, are measured. The vortices are driven by a strong density gradient on a boundary layer with scale size of the same order as the vortex diameter. Observations of vortices off the gradient show that symmetry-breaking conditions in a real inhomogeneous plasma can lead not only to cross-field but also to cross-boundary anomalous transport of particles and energy.     

Lateral phase drift of the topological charge density in stochastic optical fields

The statistical distributions of optical vortices or topological charge in stochastic optical fields can be inhomogeneous in both transverse directions. Such two-dimensional inhomogeneous vortex or topological charge distributions evolve in a complex way during free-space propagation. While the evolution of one-dimensional topological charge densities can be described by a linear diffusion process, the evolution of two-dimensional topological charge densities exhibits some additional nonlinear dynamics. Here we propose a phase drift mechanism as a partial explanation for this additional nonlinear dynamics. Numerical results are presented in support of this proposal.     

Drift ion acoustic solitons in an inhomogeneous 2-D quantum magnetoplasma

Linear and nonlinear propagation characteristics of quantum drift ion acoustic waves are investigated in an inhomogeneous two-dimensional plasma employing the quantum hydrodynamic (QHD) model. In this regard, the dispersion relation of the drift ion acoustic waves is derived and limiting cases are discussed. In order to study the drift ion acoustic solitons, nonlinear quantum Kadomstev-Petviashvilli (KP) equation in an inhomogeneous quantum plasma is derived using the drift approximation. The solution of quantum KP equation using the tangent hyperbolic (tanh) method is also presented. The variation of the soliton with the quantum Bohm potential, the ratio of drift to soliton velocity in the co-moving frame, , and the increasing magnetic field are also investigated. It is found that the increasing number density decreases the amplitude of the soliton. It is also shown that the fast drift soliton (i.e., v_*>u) decreases whereas the slow drift soliton (i.e., v_*<u) increases the amplitude of the soliton. Finally, it is shown that the increasing magnetic field increases the amplitude of the quantum drift ion acoustic soliton. The stability of the quantum KP equation is also investigated. The relevance of the present investigation in dense astrophysical environments is also pointed out.     

Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas

The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg-de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron-ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.     

Quantum kinetic equation for nonequilibrium dense systems

Using the density matrix method in the form developed by Zubarev, equations of motion for nonequilibrium quantum systems with continuous short range interactions are derived which describe kinetic and hydrodynamic processes in a consistent way. The T-matrix as well as the two-particle density matrix determining the nonequilibrium collision integral are obtained in the ladder approximation including the Hartree-Fock corrections and the Pauli blocking for intermediate states. It is shown that in this approximation the total energy is conserved. The developed approach to the kinetic theory of dense quantum systems is able to reproduce the virial corrections consistent with the generalized Beth-Uhlenbeck approximation in equilibrium. The contribution of many-particle correlations to the drift term in the quantum kinetic equation for dense systems is discussed.     

Resistive drift instability and Rayleigh-Taylor instability in a dusty plasma

The resistive drift instability and the Rayleigh-Taylor instability are studied self-consistently in a magnetized inhomogeneous dusty plasma. The effect of grain charge fluctuations is taken into consideration. It is found that the presence of the dust grains in the plasma can significantly affect the resistive drift instability but less significantly the Rayleigh-Taylor instability. Further, the grain charge fluctuation has a tendency to stabilize both instabilities.     

Effect of multicomponent dust grains in a cold quantum dusty plasma

By employing the quantum hydrodynamic model for electron-ion-dust plasma,we derive a dispersion relation of the quantum dusty plasma.The effects of the dust size distribution on the dispersion relation in a cold quantum dusty plasma are studied.Both analytical and numerical results are given to compare the differences between the dusty plasma by considering the dust size distribution and the mono-sized dusty plasma.It is shown that many system parameters can significantly influence the dispersion relation of the quantum dusty plasma.     

Spontaneous rotating vortex lattices in a pumped decaying condensate

Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behavior. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyze the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a finite pumping spot. However if the pumping spot is larger than the Thomas-Fermi cloud radius, then rotationally symmetric solutions are replaced by solutions with spontaneous arrays of vortices. These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry.     

多个子玻色-爱因斯坦凝聚气体膨胀叠加形成的量子涡旋现象研究

基于二维模型,研究了多个子玻色-爱因斯坦凝聚气体在谐振势阱内膨胀叠加形成的量子涡旋现象.运用传播子方法,分析了对称分布的三个子玻色-爱因斯坦凝聚气体膨胀叠加形成宏观量子涡旋的物理过程,得到量子涡旋随时间演化的规律;发现涡旋核分布在谐振势阱内出现振荡;涡旋与反涡旋随时间演化而相互转变,并对这些现象进行了物理分析.     

Drift wave turbulence in a dense semi-classical magnetoplasma

A semi-classical nonlinear collisional drift wave model for dense magnetized plasmas is developed and solved numerically. The effects of fluid electron density fluctuations associated with quantum statistical pressure and quantum Bohm force are included, and their influences on the collisional drift wave instability and the resulting fully developed nanoscale drift wave turbulence are discussed. It is found that the quantum effects increase the growth rate of the collisional drift wave instability, and introduce a finite de Broglie length screening on the drift wave turbulent density perturbations. The relevance to nanoscale turbulence in nonuniform dense magnetoplasmas is discussed.     

Propagation features of head-on collision dust acoustic solitary waves in four-component quantum plasmas

ABSTRACT

In framework of the extended Poincaré–Lighthill–Kuo, the properties of dust acoustic (DA) solitary wave’s interaction are investigated in four-component quantum dusty plasma. Two Korteweg–de Vries equations describing the colliding DA solitary waves are derived by eliminating the secularities. By knowing the explicit form of the solitary wave solutions, the leading phase changes, trajectories and phase shifts are obtained, accordingly. The effects of various physical parameters such as the quantum mechanical parameters, the charge ratio between positive and negative dust particles, the mass ratio between negative and positive dust particles and the ratio of electron to ion temperatures are studied extensively. Our findings showed that these parameters play a significant role on the characteristics and basic features of DA solitary waves such as phase shifts in trajectories due to collision. The obtained results may be beneficial to understand well the collision of DA solitary waves that may occur in laboratory plasmas, space plasma as well as in plasma applications.     

Quantum random walks and piecewise deterministic evolutions

In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard "coin" solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW.     

Dynamics of straight vortex filaments in a Bose–Einstein condensate with the Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating Bose–Einstein condensate existing in the Thomas–Fermi regime at zero temperature and obeying the Gross–Pitaevskii equation has been considered in the hydrodynamic “nonelastic” approximation. A noncanonical Hamilton equation of motion for the macroscopically averaged vorticity has been derived for a smoothly inhomogeneous array of filaments (vortex lattice) taking into account spatial nonuniformity of the equilibrium density of the condensate, which is determined by the trap potential. The minimum of the corresponding Hamiltonian describes the static configuration of the deformed vortex lattice against the preset density background. The condition of minimum can be reduced to a nonlinear second-order partial differential vector equation for which some exact and approximate solutions are obtained. It has been shown that if the condensate density has an anisotropic Gaussian profile, the equation of motion for the averaged vorticity has solutions in the form of a vector exhibiting a nontrivial time dependence, but homogeneous in space. An integral representation has also been obtained for the matrix Green function that determines the nonlocal Hamiltonian of a system of several quantized vortices of an arbitrary shape in a Bose–Einstein condensate with the Gaussian density. In particular, if all filaments are straight and oriented along one of the principal axes of the ellipsoid, we have a finitedimensional reduction that can describe the dynamics of the system of pointlike vortices against an inhomogeneous background. A simple approximate expression is proposed for the 2D Green function with an arbitrary density profile and is compared numerically with the exact result in the Gaussian case. The corresponding approximate equations of motion, describing the long-wavelength dynamics of interacting vortex filaments in condensates with a density depending only on transverse coordinates, have been derived.     

Entropy and Vacuum Radiation

It is shown that entropy increase in thermodynamic systems can plausibly be accounted for by the random action of vacuum radiation. A recent calculation by Rueda using stochastic electrodynamics (SED) shows that vacuum radiation causes a particle to undergo a rapid Brownian motion about its average dynamical trajectory. It is shown that the magnitude of spatial drift calculated by Rueda can also be predicted by assuming that the average magnitudes of random shifts in position and momentum of a particle correspond to the lower limits of the uncertainty relation. The latter analysis yields a plausible expression for the shift in momentum caused by vacuum radiation. It is shown that when the latter shift in momentum is magnified in particle interactions, the fractional change in each momentum component is on the order of unity within a few collision times, for gases and (plausibly) for denser systems over a very broad range of physical conditions. So any system of particles in this broad range of conditions would move to maximum entropy, subject to its thermodynamic constraints, within a few collision times. It is shown that the spatial drift caused by vacuum radiation, as predicted by the above SED calculation, can be macroscopic in some circumstances, and an experimental test of this effect is proposed. Consistency of the above results with quantum mechanics is discussed, and it is shown that the diffusion constant associated with the above Brownian drift is the same as that used in stochastic interpretations of the Schrödinger equation.     

Vortex fusion and giant vortex states in confined superconducting condensates

In a direct scanning tunneling spectroscopy experiment we address the problem of the quantum vortex phases in strongly confined superconductors. The strong confinement regime is achieved in in situ grown ultrathin single nanocrystals of Pb by tuning their lateral size to a few coherence lengths. Upon an external magnetic field, the scanning tunneling spectroscopy revealed novel ultradense arrangements of single Abrikosov vortices characterized by an intervortex distance up to 3 times shorter than the bulk critical one. At yet stronger confinement we discovered the giant vortex phase; the spatial evolution of the excitation tunneling spectra in the cores of these unusual quantum objects was explored. We anticipate the giant vortex phase to be a common feature of other confined quantum condensates such as superfluids, Bose-Einstein condensates of cold atoms, etc.