Two-dimensional mesoscopic dusty plasma clusters: Structure and phase transitions

A two-dimensional mesoscopic cluster of “dusty plasma” particles, which can be interpreted as a system of microparticles in an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors are found for clusters of N=22–40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as first-order or second-order phase transitions with respect to the parameter R. The disorder (“melting”) of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed. Zh. éksp. Teor. Fiz. 116, 1300–1312 (October 1999)     

Effects of dust-charge gradient and polarization forces on the waves and Jeans instability in strongly coupled dusty plasma

The effects of dust charge gradient (DCG) force and polarization force have been investigated on the properties of dust acoustic wave (DAW) and linear Jeans instability in strongly coupled dusty plasma. In the kinetic regime, DCG and polarization forces modify the DAW mode and couple with compressional viscoelastic wave mode. The Jeans instability criterion and critical wavenumber have been modified due to DCG force, polarization force and strong coupling effects. The results have been discussed in the warm photodisassociation region and in the laboratory complex plasmas. The strong correlation effect and the charge variation parameter stabilize the growth rate of Jeans instability. But, the polarization parameter stabilize the growth rate for positively charged dust grains and destabilize for negatively charged dust grains. The implications of charge gradient and polarization parameters are discussed for lower and higher charges in the laboratory complex plasma which decreases the growth of the propagating DAW.     

Modular conformal scaling group evidenced in lepton-quark mass

Lepton-quark mass may reflect a correspondence in spacetime structure described by a modular conformal scaling group. Stemming in part from a spacetime line element correspondenceds → (expλ _n)ds in which the eight quantitiesλ ₀,λ ₁, ...,λ ₇ constitute a closed set under a modular addition, the associated formula for lepton-quark mass (yielding values at the 1 GeV scale for the leptons and lighter quarks and at the physical pole for the top) is conjectured to bem=m _fQ²(exp −λ _n), wherem _f=10.245 TeV is the progenitor fermion mass,Q is the charge number of the lepton or quark, and the modular group parameterλ _n is indexed by a fermion principal quantum numbern that depends on three mutually independent projection operators.     

Jeans stability of dusty space plasmas

The Jeans stability of dusty plasmas is re-considered. In contrast to a gas, a dusty plasma can support a plethora of wave modes each potentially able to impart to the dust particles the randomising energy necessary to avoid Jeans collapse on some length scale. Consequently, the analysis of the stability to Jeans collapse is many-fold more complex in a dusty plasma than it is for a charge-neutral gas. After recalling some of the fundamental ideas related to the ordinary Jeans instability in neutral gases, we extend the discussion to plasmas containing charged dust grains. Besides the usual Jeans criterion based upon thermal agitation, we consider two other ways of countering the gravitational collapse: (i) via the excitation of dust-acoustic modes and (ii) via a novel Alfvén-Jeans instability, where perturbations of the dust mass-loaded magnetic field counter the effects of self-gravitation. These two mechanisms yield different minimum threshold length scales for the onset of instability/condensation. It is pointed out that for the study of the Jeans instability produced by density enhancements induced in the plasma by the presence of normal wave modes, even more prohibitive plasma size constraints must necessarily be satisfied.     

Effect of electric field on the rheological and dielectric properties of a liquid crystal exhibiting nematic-to-smectic-A phase transition

We report simultaneous measurements of shear viscosity (η) and dielectric constant (ε) of octyloxy cyanobiphenyl (8OCB) in the nematic (N) and smectic-A (SmA) phases as functions of temperature and electric field. With increasing electric field η increases in the N phase whereas it decreases in the SmA phase and saturates beyond a particular field in both the phases. The flow curves in the intermediate-field range show two Newtonian regimes in the N phase. The temperature-dependent behavior of η and ε at zero or at small electric field suggests the occurrence of several structures that results from precessional motion of the director along the neutral direction as reported in similar other system. We show that the precessional motions are gradually suppressed with increasing electric field and the effective viscosity resembles with the Miesowicz viscosity η ₁ at high enough electric field. In the intermediate field range the temperature-dependent η exhibits anomalous behavior across the N-SmA phase transition which is attributed to the large contribution of Leslie coefficient α ₁.     

Translational and rotational diffusion in supercooled orthoterphenyl close to the glass transition

Self diffusion coefficients in supercooled orthoterphenyl (OTP) have been determined down toD _t =3·10^–14 m²s^–1 using a¹H-NMR technique applying static field gradients up to 53T m^–1 In a range of more than two decades theD _t values agree with those of photochromic tracer molecules of the same size determined by forced Rayleigh scattering down to the glass transition temperatureT _g . A change of mechanism is found for translational diffusion atT _c 1.2T _g whereD _t is proportional to the inverse shear viscosity ^–1 atT>T _c butD _t with =0.75 atT<T _c . Rotational correlation times determined by²H-NMR stimulated echo techniques in deuterated OTP remain proportinal to ^–1 down toT _g . Our results are discussed in relation with mode coupling theory and with models of cooperative motion at the glass transition.     

The 1/D expansion for low-dimensional classical magnets

The physical characteristics of two-dimensional classical ferro- and antiferro-magnets have been calculated in the whole temperature range by an analytical approach based on the expansion in powers of 1/D, whereD is the number of spin components. This approach works rather well since it yields exact results for antiferromagnetic susceptibility and specific heat atT=0 already in the first order in 1/D and it is consistent with HTSE at high temperatures. For the quantities singular atT=0, such as ferromagnetic susceptibility and correlation length, the 1/D expansion supports their general-D functional form in the low-temperature range obtained by Fukugita and Oyanagi. The critical index calculated in the first order in 1/D proves to be temperature dependent: =20/(D) (=T/T _c ^(MFT) ,T _c ^(MFT) =J ₀/D, J ₀ is the zero Fourier component of the exchange interaction).     

Vortex rings and plasma toroidal vortices in homogeneous infinite media. III. Diffusion anisotropy effect in vortices

The effect of diffusion anisotropy of material particles in toroidal vortices (TVs) is experimentally studied in plasma TVs in air, in vortex rings in air and water. The essence of this effect consists in the fact that diffusion coefficients of material particles in TVs in the direction perpendicular to the rotation axis D _⊥ are much lower than in the direction parallel to this axis D _‖. The coefficient D _⊥ is determined for propane molecules in air TVs, and the dependence of the coefficient D _⊥ of ink particles in water TVs on the rotation angular velocity ω is studied. It is shown that the coefficient D _⊥ can decrease with increasing ω by a factor of 10–25 in comparison with the coefficient D _‖.     

Kraus Operator-Sum Representation and Time Evolution of Distribution Functions in Phase-Sensitive Reservoirs

Using the thermal entangled state representation 〈η|, we examine the master equation (ME) describing phase-sensitive reservoirs. We present the analytical expression of solution to the ME, i.e., the Kraus operator-sum representation of density operator ρ is given, and its normalization is also proved by using the IWOP technique. Further, by converting the characteristic function χ(λ) into an overlap between two “pure states” in enlarged Fock space, i.e., χ(λ)=〈η _=−λ |ρ|η ₌₀〉, we consider time evolution of distribution functions, such as Wigner, Q- and P-function. As applications, the photon-count distribution and the evolution of Wigner function of photon-added coherent state are examined in phase-sensitive reservoirs. It is shown that the Wigner function has a negative value when kt\leqslant\frac 12ln( 1+m_￥) \kappa t\leqslant\frac {1}{2}\ln ( 1+\mu_{\infty}) is satisfied, where μ _∞ depends on the squeezing parameter |M|² of environment, and increases as the increase of |M|.     

Representation of complex number imaginary unit and supermatrix solution to the Yang-Baxter equation

The double complex number imaginary unitJ _D is treated as a special matrixM(J _D ); by considering the matrixM(ε) corresponding to the hyperbolic complex imaginary unit ε, a supermatrix solution to the Yang-Baxter equation is constructed.     

Electrical conductivity and dielectric constant of A-type Nd2O3

The measurements of electrical conductivity (σ) from 300 to 1200 K and dielectric constant (ε′) from 4·2 to 1200 K of A-type Nd₂O₂ pellets are reported here. Electrical conductivity (σ) data can be explained in terms of impurity. The dielectric constant (ε′) increases slowly up to 500 K as is expected for ionic solids. The increase ofε′ becomes much faster above 500 K, which is attributed to space charge polarization of thermally generated charge carriers.     

Multi-Hamiltonian structure of kdv hierarchy by Drienfeld-Sokolov formalism

Conserved quantities and the multi-Hamiltonian structure for the integrable coupled kdv system which is associated with the isospectral flow [(∑ _i=0 ^N−1 ε _i λ ⁱ )∂² + ∑ _i=0 ^N−l V ₁λ ⁱ ]φ=λ ^N φ are deduced by the Drienfeld-Sokolov formalism.     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Space-charge relaxation and electrical conduction in?K0.5Na0.5NbO3 at high temperatures

Sodium potassium niobate K_0.5Na_0.5NbO₃(KNN) ceramic was synthesized by a solid-state technique. The X-ray diffraction of the sample at room temperature showed a monoclinic phase. The real part (ε′) and imaginary part (ε″) of dielectric permittivity of the sample were measured in a frequency range from 40 Hz to 1 MHz and in a temperature range from 350 to 850 K. The ε′ deviated from Curie–Weiss law above 702 K, due to additional dielectric contributions resulting from universal dielectric response and thermally activated space charges at high temperatures. This anomaly arose from a Debye dielectric dispersion that slowed down following an Arrhenius law. We have established a link between the dielectric relaxation and the conductivity.     

Equation of state of fluid helium at high temperatures and densities

Helium, hydrogen, and their isotopes are the simplest monoatomic and diatomic molecules. It is relatively easy to describe their properties using the basic principles of quantum mechanics. In condensed matter physics, hydrogen and helium serve as the models for the condensed matter properties at extreme conditions so that both experi- mental and theoretical physicists pay much attention to the study of their properties[1], especially the insulator-metal transition of hydrogen[2]. The aim to st…     

Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff

We study the Dirac operator D ₀ in an external potential V, coupled to a quantized radiation field with energy H _f and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the operator D ₀+α · A+V +λ H _f with λ ∈{0, 1}, that the essential self-adjointness is not affected by the behavior of V at ∞.      

Measurement of electric field strengths in a waveguide by means of the dynamic Stark effect in hydrogen and neutral helium spectral lines

The dynamic Stark effect of the spectral lines H_β and of the neutral helium lines λ=402.6 nm (2³ P ⁰−5³ D) and λ=438.8 nm (2¹ P ⁰−5¹ D) emitted from a discharge tube was used for probing rf electric fields in a transverse waveguide. Calculations accounting for the pertubation of the atomic states by strong unidirectional fields prove to be suitable in order to interprete the main experimental results. If the waveguide is terminated with a metallic reflector and the plasma in the discharge tube becomes overdense—then representing a slightly permeable mirror—a resonant enhancement of the electric field strength may be achieved by tuning. This enhancement is well recognizable in the spectral line contours.