Heisenberg Group and Energy-Momentum Conservative Law in de-Sitter Spaces In Memory of the 100th Anniversary of Einstein‘s Special Relativity and the 70th Anniversary of Dirac‘s de-Sitter Spaces and Their Boundaries

In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.     

75th Anniversary of Boris Lazarevich Ioffe’s Birthday

News Items

75th Anniversary of Boris Lazarevich Ioffe’s Birthday     

High-Order Hamilton＇s Principle and the Hamilton＇s Principle of High-Order Lagrangian Function

In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton＇s principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton＇s principle. Finally, the Hamilton＇s principle of high-order Lagrangian function is given.     

A Thermodynamic Analysis of the Validity of Wenzel and Cassie＇s Equations ＊

Wettable properties of a considered solid on its contact angle （CA） can be analyzed theoretically using the classical Wenzel and Cassie＇s equations. However, recent strong interest in superhydrophobic surfaces has demanded a re-examination of the applicability of the two equations. We report a thermodynamic analysis to determine the universality, in particular, the limitations of the two equations. Using some special surfaces, we demonstrate that the two equations are valid for micro-scale heterogeneous structures, however they are invalid for macro-scale heterogeneous surfaces. Furthermore, the present calculations suggest that fundamental thermodynamic analysis is the most powerful and reliable approach to determine the comprehensive wettability for various structurally patterned surfaces.     

Measuring the Wigner Functions of Two-Mode Cavity Fields and Testing the Bell＇s Inequalities

We propose a scheme for measuring the Wigner function of a two-mode cavity field. The scheme bases on the interaction between the two-mode cavity field and three-level atoms. We find a simple relation between the Wigner function and the atomic population. One can obtain the Wigner function by measuring the atomic population with a micromaser-like experiment and doing a numerical integral. By using the two-mode Wigner function one can obtain the Clauser-Horne combination and test the Bell‘s inequalities. We test our equations with a two-mode entanglement state and the results are rather good.     

Sommerfeld＇s Quantum Condition of Action and the Spectra of Quantum Schwarzschild Black Hole

If the situation of quantum gravity nowadays is nearly the same as that of quantum mechanics in its early time of Bohr and Sommerfeld, then a first-step study of the quantum gravity under Sommerfeld‘s quantum condition of action might be helpful. We present the spectra of quantum Schwarzschild black hole in non-relativistic quantum mechanics. It is found that the quantum of area is 8π/3 lp^2, the quantum of entropy is 2π/4kB, and the Hawking evaporation will cease when the black hole reaches the ground state m=1/2√3mp.     

NMR analogue of the generalized Grover＇s algorithm of multiple marked states and its application

The generalized Grover‘s algorithm for the case in which there are multiple marked states is demonstrated on a nuclear magnetic resonance (NMR) quantum computer. The Walsh-Hadamard transform and the phase inversion are all replaced. NMR analogues of Einstein-Podolsky-Rosen states (pseudo-EPR states) are synthesized using the above algorithm.     

Green’s Function for the Hodge Laplacian on Some Classes of Riemannian and Lorentzian Symmetric Spaces

We compute the Green’s function for the wave equation on forms on the symmetric spaces M × Σ, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and Σ is a simply connected Riemannian surface of constant curvature. Our approach is based on a generalization to the case of differential forms of the method of spherical means and on the use of Riesz distributions on manifolds. The radial part of the Green’s function is governed by a fourth order analogue of the Heun equation.     

Algebraic structure and Poisson＇s theory of mechanico-electrical systems

The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange--Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.     

Thermal transport property of investigated by molecular Ge34 and d-Ge dynamics and the Slack＇s equation

In this study, we evaluate the values of lattice thermal conductivity κL of type Ⅱ Ge clathrate （Ge34） and diamond phase Ge crystal （d-Ce） with the equilibrium molecular dynamics （EMD） method and the Slack＇s equation. The key parameters of the Slack＇s equation are derived from the thermodynamic properties obtained from the lattice dynamics （LD） calculations. The empirical Tersoff＇s potential is used in both EMD and LD simulations. The thermal conductivities of d-Ge calculated by both methods are in accordance with the experimental values. The predictions of the Slack＇s equation are consistent with the EMD results above 250 K for both Ge34 and d-Ge. In a temperature range of 200-1000 K, the κL value of d-Ge is about several times larger than that of Ge34.     

Construction of a New Set of fpc＇s for the Composite Pair

A new set of fpc is introduced to build the orthogonal set of basis for the states with many S and D pairs in the microscopic theory of low-lying collective motion.     

Response of the Earth＇s Magnetosphere and Ionosphere to Solar Wind Driver and Ionosphere Load： Results of Global MHD Simulations

Three-dimensional global magnetohydrodynamic simulations of the solar wind-magnetosphere-ionosphere system are carried out to explore the dependence of the magnetospheric reconnection voltage, the ionospheric transpolar potential, and the field aligned currents （FACs） on the solar wind driver and ionosphere load for the cases with pure southward interplanetary magnetic field （IMF）. It is shown that the reconnection voltage and the transpolar potential increase monotonically with decreasing Pedersen conductance （∑ p ）, increasing southward IMF strength （Bs） and solar wind speed （Vsw）. Moreover, both regions 1 and 2 FACs increase when Bs and vsw increase, whereas the two currents behave differently in response to ∑p. As ∑p increases, the region 1 FAC increases monotonically, but region 2 FAC shows a non-monotonic response to the increase of ∑p ： it first increases in the range of （0,5） Siemens and then decreases for ∑p 〉 5 Siemens.     

Effect of Particle＇s Size on the Structural and Dynamical Properties in 2D Dusty Plasma

In a two-dimensional （219） dusty plasma system, the size of particles is considered under two different interparticle potentials （Yukawa potential and Dressed potential）. The structural and dynamical characters are investigated by molecular dynamics simulation respectively. The results show that the 2D systems via Yukawa and Dressed potentials have a different critical coupling constant F corresponding to the systems beginning to coagulate and exhibit different crystal configurations. Also we find that the size of particles has little influence on the 2D system＇s structure characters.     

Anomalous Behaviour of the Spectra in Young＇s Double-Slit Interference Experiments

It is shown that an anomaly of the spectrum takes place in the interference field when Young‘s double-slit interference experiment is illuminated by spatially coherent polychromatic light. Specifically, drastic spectral changes (i.e. the spectral shifts exhibit a rapid transition) occur in the vicinity of the dark fringes. The potential applications of this spectral anomaly are also considered.     

Young＇s modulus surface and Poisson＇s ratio curve for tetragonal crystals

This paper gives the general expressions for the compliance s′ijkl, Young＇s modulus E（hkl） and Poisson＇s ratio v（hkl, θ） along arbitrary loading direction [hkl] for tetragonal crystals. The representation surface for which the length of the radius vector in the [hkl] direction equals E（hkl） and representation curve for which the length of the radius vector with angle θ deviated from the reference directions [001^-], [100], [001^-], [101^-] and [112^-] equals v（100, θ）, v（001, θ）, v（110,θ）, v（101,θ） and v（111, θ） respectively, are constructed for nine tetragonal crystals （ammonium dihydrogen arsenate, ammonium dihydrogen phosphate, barium titanate, indium, nickel sulfate, potassium dihydrogen arsenate, potassium dihydrogen phosphate, tin and zircon）. The characteristics of them are analysed in detail.     

Coupled—Channel Investigation of the Collision of Protons and Antiprotons with hydrogen—Like Atoms in the 2s States

The influence of the electric charge of both the projectile and the target nucleus on the cross section of the inelastic collision of protons and antiprotons with atoms is investigated at energies ranging from 1 to 2500Kev,The impact parameter method is used to analyse the cross sections of the excitation of the n=3 states of H atom and He^ ,Li^2 ions being initially in the excited 2s states.The calculated cross sections for hydrogen atome are compared with the other theoretical results based on coupled-channels methods.     

From extensive air showers to the characteristics of primary cosmic rays. To the 120th Anniversary of the Birth of D. V. Skobel’tsyn

The works by D.V. Skobel’tsyn that laid the foundation of the contemporary physics of cosmic rays and the physics of high energies are considered. Skobel’tsyn demonstrated that cosmic rays contain particles whose energy substantially surpasses the energies that are typical of radioactive decay, discovered the existence of air showers, i.e., when several particles hit an array simultaneously, and performed a series of investigations into extensive air showers that resulted in the discovery of a nuclear-cascade process in the atmosphere. The results that Skobel’tsyn obtained were of primary importance for the further development of cosmic-ray physics.     

Oscillation of Quasi-Steady Earth＇s Magnetosphere

A three-dimensional magnetohydrodynamics （MHD） code is designed specially for global simulations of the solar wind-magnetosphere-ionosphere system. The code possesses a high resolution in capturing MHD shocks and discontinuities and a low numerical dissipation in examining possible instabilities inherent in the system. The ionosphere is approximated by a spherical shell with uniform height-integrated conductance. The solar wind is steady, and the interplanetary magnetic field is either due northward or due southward. The code is then run to find solutions of the whole system. It is found that the system has never reached a steady state, but keeps oscillating with a period of about one hour in terms of density variation at the geosynchronous orbit. However, if a certain artificial resistivity is added either in the whole numerical box or in the reconnection sites only, the reconnections change from intermittent to steady regime and the oscillation disappears accordingly. We conclude that the Earth＇s magnetosphere tends to be in a ceaseless oscillation status because of the low dissipation property inherent in the magnetospheric plasma, and the oscillation may be driven by intermittent magnetic reconnections that occur somewhere in the magnetopause and/or the magnetotail.