Table of contents

We consider three two-level atoms (A, B, and C) initially in the W entanglement state, then one of them, C, is injected into a high-Q cavity to make resonant interaction to entangle with the other two atoms A and B that are far away from the cavity. The entanglement swapping or disentanglement can be realized by carrying out measurements on C and selecting appropriate interaction time of C with the coherent field.

A new family of the supramolecular antiferromagnetically exchange-coupled dimer of single-molecules magnets, [Mn₄]₂, really behave as a quantum mechanical coupled system and can be used for quantum computation [Tiron et al (2003) Phys. Rev. Lett. 91 227203]. We study the time evolution of [Mn₄]₂ dimer interacting with an injected electron by solving the time-dependent Schrödinger equations. We find that the variations of [Mn₄]₂ dimer magnetization and the electron spin crucially depend on the exchange interaction strength. Time evolution of the entanglement between the injected electron and supramolecular dimer [Mn₄]₂ is evaluated. It is observed that entanglement oscillates in time and is closely related to the spin variation of injected electron. From these characteristics the technique for the reversing and read-out of supramolecular dimer [Mn₄]₂ spin states is suggested.

We show a deterministic secure direct communication protocol using single qubit in a mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized by the current technologies.

We propose a scheme to teleport probabilistically an unknown two-particle three-level entangled state by using two partial entangled two-particle three-level states as the quantum channel. This scheme can be directly generalized to teleport an unknown N-particle three-level entangled state by using N partial-entangled two-particle three-level states as the quantum channel.

Through a mapping relation between the triple sine-Gordon and ϕ⁵ model, we discuss the equation in detail. A series of solitary wave solutions for the triple sine-Gordon equation is obtained by the existing ones of the ϕ⁵ model. Some detailed solitary wave solutions are given for some special coefficients which have significance in physics.

The eccentricity of the centre of mass from the geometric centre of a spherical attracting mass in determining the Newtonian gravitational constant G is tested by means of an electronic balance. The experimental result shows that the eccentricity of the sample is about 0.31 μm with uncertainty of 0.05 μm. Two density distribution models are discussed to estimate the uncertainty to G by the eccentricities of the attracting masses.

Capillary forces are significantly dominant in adhesive forces measured with an atomic force microscope (AFM) in ambient air, which are always thought to be dependent on water film thickness, relative humidity, and the free energy of water film. We study the nature of the pull-off force on a variety of surfaces as a function of tip velocity. It is found that the capillary forces are of relatively strong dependence on tip velocity. The present experiment is expected to provide a better understanding of the work mechanism of AFM in ambient air.

The global colour model in free space is extended to finite temperature to study the deconfinement and chiral phase transitions at high temperature T and zero chemical potential in the mean field approximation. Both possibilities of coincidence and non-coincidence of the two distinct phase transitions are found when the model parameters are varied in a certain range. The underlying mechanisms of the coincidence and noncoincidence are analysed and discussed. The validity of the T-dependent model propagator as the input is also discussed.

We present an SU(3)_F meson mass formula from random phase approximation. Both the mesons of ground-state pseudoscalar octet and ground-state vector octet are described quite well by this mass formula. We also estimate the current and constituent quark masses from the naive quark model and the PCAC relation.

Excited states in ¹⁴²Pm are investigated via the ¹²⁸Te(¹⁹F, 5n)¹⁴²Pm reaction at beam energies from 75 to 95 MeV by using techniques of in-beam γ-ray spectroscopy. Measurements of γ-ray excitation function, X–γ and γ–γ–t coincidences are performed with 10 BGO(AC)HPGe detectors. Decay of the previously known 67-μs isomer in ¹⁴²Pm is observed and added into the new level scheme. This isomer is definitely placed at the excitation energy of 2828.5 keV. The spin of this isomer is suggested to be 13 ℏ according to the measured γ-ray anisotropies.

Hanbury–Brown–Twiss (HBT) results of the nucleon–nucleon correlation function have been presented for the nuclear reactions with neutron-rich projectiles using an event-generator, i.e. the isospin-dependent quantum molecular dynamics model. A good agreement of our calculation for the two-halo-neutron correlation function of ¹¹Li with the experimental data has been reached. In addition, we explore the relationship between the single-neutron separation energy and the strength of the HBT results. It is feasible to investigate the exotic structure of neutron-rich nuclei with the HBT method.

On the basis of the Dirac equation, the analytic continuation in the coupling constant method is employed to investigate the energies and widths of single-particle resonant in square-well, harmonic-oscillator, and Woods–Saxon potentials. The influences of the coupling constant interval and the Padé approximant order are analysed. It is shown that, by properly choosing the coupling constant interval and the Padé approximant order, stable and convergent energies and widths of single-particle resonant states can be obtained, which makes the application of the analytic continuation in the coupling constant for the relativistic mean field theory possible.

The survival probability of the superheavy compound nuclei with Z = 114 is studied with the statistical model. It is found that the survival probability shows drastic odd–even effects. The odd-A compound nuclei have higher survival probability by evaporating three neutrons as compared with their neigbouring even-A compound nuclei.

Raman spectra of binary sodium silicates are calculated by self-consistent field (SCF) molecular orbital ab initio calculation of the quantum chemical method with several poly silicon–oxygen tetrahedral model clusters when both the basis sets of 6-31 G and 6-31 G(d) are applied. The symmetric stretching vibrational frequency of non-bridging oxygen in a high frequency range and its Raman optical activity and scattering cross section are deduced and analysed. The correlation between this vibrational Raman shift and its microscopic environment of the silicon–oxygen tetrahedron is found based on interior stress of configuration, which depends on the connecting topology of adjacent silicon–oxygen tetrahedra (SiOT). A newly established empirical stress index of tetrahedron is introduced to elucidate the above relationship.

The point-to-point Feynman quantum propagator ⟨q₁|exp(−iHt/ℏ)|q₂⟩ has an analytic form only for quadratic potentials. We apply the split operator approach to obtain a propagator matrix for arbitrary potentials for non-uniform grids, which are particularly useful for real physical potentials with both rapid-varying and smooth regions. We exemplify our method with the wave propagation function and the extraction of an eigenvalue and an eigenfunction of a Morse system modelling diatomic molecules.

The semirigid vibrating rotor target (SVRT) model proposed by Zhang [J. Chem. Phys. 111 (1999) 3929] is applied to study the dynamics of dissociative adsorption for CH₄ on a flat and static Ni(100) surface. The molecule CH₄ is treated as a semirigid vibrating rotor CH₃-H, and the London–Eyring–Polanyi–Sato potential energy surface is utilized. The numerical calculation for the reaction system is carried out by using the time-dependent wave packet approach, and the propagation of wave packets is obtained by the split-operator method. The results demonstrate many important properties of the CH₄ molecule dissociation process on the metal Ni. The dissociation probability is a strongly increasing function of the incident kinetic energy, and is enhanced significantly when the molecule CH₄ is excited, which denotes the clear vibration-excitation effect, as observed in the molecular beam studies of Holmblad et al. [J. Chem. Phys. 102 (1995) 8255] The isotopic effect is also studied for molecules CH₄ and CD₄ at the ground rovibrational states.

We present high-order harmonic generation spectra resulted from a single-electron model molecular ion exposed to intense laser fields by numerically solving a one-dimensional time-dependent Schrödinger equation. There are three plateaus in the spectra and the maximal cutoff energy is I_p+8.5U_p, when the inter-nuclear distance R equals πα₀/2. Here I_p is the ionization potential and U_p = E₀²/(4ω²) is the ponderomotive potential with E₀ and ω being the laser electric field amplitude and the central frequency. The harmonic structures are well interpreted by a modified three-step model in which the effects of the electron reflected by the non-parent ion are stressed.

The absolute optical oscillator strength density spectrum of HBr in the valence shell energy region of 4.5–20 eV has been determined by a high-resolution fast electron energy loss spectrometer. The optical oscillator strengths for the broad a³Π+A¹Π dissociation peak and the discrete transitions of b ³Π₁(ν' = 0) and C¹Π(ν' = 0,1,2) are reported. It has been manifested clearly that the optical oscillator strengths of some transitions for the previous photoabsorption method are subject to severe line-saturation effects.

A polarization controlled switchable multiwavelength erbium-doped fibre laser with overlapping cavities is proposed. The wavelengths are specified by two Bragg gratings in polarization-maintaining PANDA fibre. The proposed laser can be designed to be operated in stable four-wavelength or wavelength switching modes only by simple adjustment of two polarization controllers. For wavelength switching, four single-wavelength, six dual-wavelength, and four three-wavelength operations have been obtained. The minimum wavelength spacing is only about 0.4 nm.

We apply a new method consisting of a coordinate transformation and two-step scheme to simulate numerically Z-scan characteristics of a nonlinear medium. A comparison of numerical results obtained by this new method with those by the conventional numerical method is made. The results show that the new scheme yields a large, orders-of-magnitude range improvement in computational speed and accuracy for the analysis of the closed-aperture and open-aperture Z-scan characteristics, compared with the conventional numerical method.

One-dimensional photonic crystal of second-order nonlinearity is studied. Among the three waves of the parametric interaction process of down-conversion with a nondispersive medium, two gap-edge localized modes and one travelling-mode are proposed, and an exact phase matching condition is realized using the periodic condition of the Bloch phase. Numerical simulation is implemented by the slow-envelope finite difference time domain method. In the case of a pulse wave pump of amplitude half-width 5.2×10⁻¹³ s, an intense optical parametric pulse with half-width about 5×10⁻¹⁴ s is observed.

Moiré fibre Bragg gratings are made in a single mode fibre and a polarization-maintaining fibre respectively, using an excimer KrF laser and a phase mask. Two gratings are written at the same location of the optical fibre. The wavelength spacing can be finely tuned from 0 to 1.86 nm by straining the optical fibre during UV illumination.

Determination of an ultra-low mean photon number is an important issue, either for precise optical measurement or understanding the interaction between individual atoms and photons inside an optical cavity. By utilizing a homemade balanced optical heterodyne detection system, the cw minimum measurable power of 3.6 fW has been reached, whereas the minimum mean photon number of ⟨n⟩ = 0.0014 in our micro-cavity with finesse of 2×10⁵ and optical length of 48 μm can be realized.

From Maxwell's equations and macroscopic polarization, we obtain the wave equations describing the propagation of strong light in an isotopic chiral fibre with weak spatial dispersion. By considering the possible nonlinear and dispersive effects, the nonlinear Schrödinger equations for the left- and right-circularly polarized components are derived. The mechanism to form the chiral optical solitons is discussed. The self-induced optical rotation of solitons in the chiral fibre is emphasized. An all-optical switch is proposed.

We investigate the photoinduced anisotropy of a photochromic material of pyrrylfulgide/PMMA films. It is proven that when the film is illuminated with a linear polarization light, an optical axis that has the same polarization as the excitation light could be induced in the film. A matrix of light spots with different polarizations is recorded on the pyrrylfulgide/PMMA film. When reading out with non-polarization light, the matrix of light spots shows no information of patterns. However, when reading out with different linear polarization lights, different patterns could be observed. The experiment confirms that the pyrrylfulgide/PMMA film could be used to record two different polarization patterns in a matrix of spots. This property may be applied in camouflage technology.

Inversion of Rayleigh waves is studied for the first time by using the genetic algorithm based on the intensities of the fundamental and/or higher modes. The relations of all modes to the medium structure are investigated. It is emphasized that the higher modes and mode jumping should be considered in the inversion when the low-velocity layers are contained in the stratified half space. Shear wave velocity and thickness of each layer are inverted by the genetic algorithm. Compared with the least square method, the genetic algorithm has several advantages. It usually does not depend on the initial models and the global optimal solutions can be obtained easily. The influences of some parameters on the inversion are also analysed and some useful results are presented.

The linear instability analysis of the Rayleigh–Marangoni–Bénard convection in a two-layer system of silicon oil 10 cS and fluorinert FC70 liquids are performed in a larger range of two-layer depth ratios H_r from 0.2 to 5.0 for different total depth H⩽12 mm. Our results are different from the previous study on the Rayleigh–Bénard instability and show strong effects of thermocapillary force at the interface on the time-dependent oscillations arising from the onset of instability convection.

On the basis of incompressible viscid magnetohydrodynamic equations, a formula is developed to study the mitigation of viscosity on the Rayleigh–Taylor instability in Z pinches. The results indicate that in the whole wavenumber region, the viscosity effect can mitigate the instability. In addition, we compare the viscosity effect with the finite Larmor radius effect [Chin. Phys. Lett. 19 (2002) 217], and the calculation results show that in the temperature region of interest, the former is stronger than the latter. Moreover, for heavy wire-array implosion the viscosity effect is stronger than the finite Larmor radius one, because the former is proportional to m_i^1/2 and the latter is independent of m_i.

Spatial distribution of hot electrons with energies above 50 keV are investigated by an ethanol micro-droplet spray irradiated by linearly and elliptically polarized 150 fs laser pulses at an intensity of 10¹⁶W/cm². Two symmetric hot electron jets with respect to the laser propagation direction are observed in the polarization plane for a linearly polarized laser field and in the plane of the long electric vector for an elliptically polarized laser field, respectively. Particle-in-cell simulations suggest that the resonance absorption on the spherical surface of the droplets is mainly responsible for the generation of the double-jet emission of hot electrons.

We theoretically investigate the dust charging in the sheath of an electronegative plasma, by using a single dust grain model based on a previous sheath structure [Chin. Phys. Lett 20 (2003) 1537] in which cold positive ions and hot negative ions have been assumed. It is found that dust grains are first charged negatively at the sheath edge and then begin to be charged positively in the sheath. Moreover, both the temperature ratio of electrons to negative ions and the density ratio of negative ions to positive ions have effects on the neutral point of the dust charge.

A nanocrystalline model for microstructures of liquid metals is constructed. According to the nanocrystalline model, the intensity curves of x-ray diffraction (XRD) on liquid Cu, Al and Al₆₅Cu₂₀Fe₁₅ alloy are derived by broadening the XRD peaks of these metals in some crystal structures. These broadening intensity curves are identical with the results measured by an x-ray diffractometer on these liquid metals. The present results indicate that the nanocrystal model may be helpful to understand the microstructures of liquid metals and that there is a close correlation between the short-range orders (SROs) of these liquid metals and some crystal lattice structures. That is, the SRO structures of liquid Cu, Al and Al₆₅Cu₂₀Fe₁₅ alloy are fcc, bcc and icosahedron, respectively.

In terms of a single-π orbital model, an analytical expression of the lowest-lying conduction-band and the highest-lying valence-band is derived for single wall carbon nanotubes under both the uniaxial and torsional strains. We observe not only semiconductor–metal transitions in primary metallic tubes, but also insulator–metal transitions in semiconducting tubes. Additionally, an indirect transition of electrons and a quantized electron-resonance have been expected in optical spectrum experiments of the nanotubes.

Lateral stress of LY-12 aluminium alloy under plate impact shock loading was measured. Based on the measured data, the Hugoniot relation and shear strength were obtained. The result has demonstrated that the shear strength of the tested material increases remarkably with the increasing longitudinal stress. This means that the assumption of constant shear strength usually adopted in shock stress calculation is not suitable for the present material.

The effects of surfactants on the phase separation of surfactant–water–oil systems have been investigated by using discontinuous molecular dynamic simulations. The phase separation speed and equilibrium configuration are dependent on the surfactant concentration and conformation. The equilibrium concentration of surfactants at the interface remains constant. With the increasing surfactant concentration, the equilibrium configuration crosses over from the disperse phase to the bicontinuous one. The crossover concentration is estimated. The conformation of the surfactant has little effect on the equilibrium concentration of surfactants at the interface, while it affects the equilibrium configuration after phase separation.

An advanced ac calorimetric method to measure thermal diffusivity of a thin sample is developed by using an optical reflectivity technique. A modulated infrared laser is used to heat the front surface of a foil specimen. The reflectivity of a continuous-wave He–Ne laser at the rear surface of the specimen is detected by a photoreceiver. According to the temperature dependence of reflectivity, the ac temperature response is obtained. Thermal diffusivity is deduced from a one-dimensional heat conduction equation. A stainless-steel foil and a copper foil are chosen as the samples. The present results agree well with the data in the literature.

We investigate the effects of Er₂O₃ on electrical properties of the SnO₂.CoO.Ta₂O₅ varistor system sintered at 1400 degrees C. It is found that all the samples have excellent nonlinear electrical characteristics and the sample with 0.50 mol% Er₂O₃ has the best nonlinear electrical property and the highest nonlinear coefficient (α = 43.7). The high nonlinear coefficient value obtained in the system indicates that the SnO₂-based varistor is a candidate for ZnO-based varistors in commercial applications. Er₂O₃ additive can significantly affect the average grain size. With increasing Er₂O₃ concentration from 0.10 mol% to 1.00 mol%, the average grain size decreases from 21.2 μm to 10.6 μm, the breakdown electrical field increases from 208 V/mm to 459 V/mm, and the relative electrical permittivity decreases from 2440 to 1210. The reason that the grain size decreases with increasing Er₂O₃ concentration is explained. Also, we present a modified defect barrier model to illustrate the grain-boundary barrier formation of Er₂O₃-doped SnO₂ based varistors.

The unintentionally doped samples of Al_0.22Ga_0.78N/GaN/Al_0.22Ga_0.78N/GaN multi-heterostructures have been designed and fabricated. The polarization induced charge and free-carrier charge distributions have been demonstrated and the energy band profile has also been calculated. The results indicate the existence of two-dimensional electron gas (2DEG) and hole well at the heterointerfaces. By means of variable temperature Hall measurements, the carrier mobility and the sheet carrier density were measured from 300 to 77 K. The significant increment of carrier mobility at low temperature also verified the existence of the 2DEG.

Organic thin-film field-effect transistors (OTFTs) with pentacene as the semiconductor have been fabricated for driving an organic light-emitting diode (OLED). The driving circuit includes two OTFTs and one storage capacitor. The field-effect mobility of the transistors in the driving circuit is more than 0.3 cm²/Vs, and the on/off ratio is larger than 10⁴. The light-emission area of the OLED is 0.04 mm² and the brightness is larger than 400 cd/m² when the selected line voltage, data line voltage and drive voltage all are -40 V. The responding characteristics and holding characteristics are also researched when the selected line voltage and the date line voltage are changed.

Well-characterized surface intrinsic Josephson junctions (IJJs) on Bi₂Sr₂CaCu₂O_8+δ single crystals are fabricated by in situ cryogenic cleavage of the crystals and immediate evaporation of Au films on the crystal surface. Magnetic field dependences of the critical currents of the surface and inner IJJs are carefully measured. We find that the critical current behaviour of the surface IJJs in magnetic field is quite different from that of the inner junctions. The behaviour of the inner IJJs can be understood to be of large stacked junctions described by the coupled sine-Gordon equations, while the surface IJJs behave like a separate single large junction. These results indicate that the coupling between the surface IJJ and the inner IJJs is weaker than the coupling among the inner junctions.

Arrays of Ni nanowires with different wire diameters were prepared by electrodepositing the corresponding material into cylindrical pores of anodic alumina templates. A transition of the easy magnetization direction has been observed from the wire axis to the transverse direction when the wire diameter increases. It is analytically obtained that this phenomenon is mainly originated from the competition of shape anisotropy and the magnetostatic coupling among the Ni wires. Based on dipolar interaction model, numerical calculation is performed to study the interaction among the nanowires, and the result is in agreement with the experimental data.

Quasi-one-dimensional Fe₃O₄ nanowires in diameter of about 200 nm were assembled into anodic aluminium oxide templates via electrodepositing and heat-treating processes. The nanowires have a polycrystalline spinel structure with a = 8.317 Å, and each nanowire is composed of fine Fe₃O₄ crystallites with size of about 30 nm. The magnetic moments of Fe₃O₄ crystallites in nanowires have a preferred orientation leaning to the wire axis but not parallel to the wire axis. Mössbauer spectra (MS) were used to verify the presence of Fe₃O₄ further and the existence of superparamagnetic particles in nanowires. A perpendicular magnetic anisotropy was observed obviously. Temperature dependence of the magnetic moments (M–T) shows that the Verwey transition for the Fe₃O₄ nanowires occurs at 50 K, and the behaviour of the M–T curve is different from that of other magnetite materials. These characteristic magnetic properties of Fe₃O₄ nanowires are mainly due to the reduced dimension and the configuration of preferred orientation in the nanowires caused by the shape anisotropy.

We prepare two kinds of Co₃O₄ antiferromagnetic nanocrystallite systems with different surface structures: one grain surface is covered by polymer decomposition residues (PDRs) (referred to as CS) and the other is naked (NS). It has been found that the magnetic properties of the CS sample deviate greatly from those of the NS sample. For example, the CS sample exhibits an open loop up to 8 T at 4.2 K, while the two branches of the hysteresis loop for the NS sample superpose together when the field is in excess of 3 T. The average permanent magnetic moments per Co₃O₄ cell for the CS sample are about three times larger than that of the NS sample. The coercivity and loop shift for the CS sample are enhanced remarkably in comparison with the NS sample, i.e., from 73.8 and 11.0 kA/m for the NS sample to 116.5 and 25.5 kA/m for the CS sample, respectively. The anomalous magnetic properties and their enhancements for the CS sample are attributed to the surface spin pinning effect by PDRs.

Annealing temperature effects on the structure and electrical resistance of Ge₂Sb₂Te₅ thin film were studied. The crystallization and melting temperature of the thin film are about 175 degrees C and 610 degrees C respectively. The structure of the as-deposited and the annealed film at different annealing temperatures are identified by the x-ray diffraction method. The thin film changes from an amorphous state to the fcc structure at about 200 degrees C, and then changes into the hexagonal close-packed (hcp) structure at about 400 degrees C. Electrical resistance of as-deposited thin film reaches as high as 1.7×10⁸ Ω/sq. Then it decreases to 1.6×10⁴ Ω/sq and 165 Ω/sq after the annealing process at 250 degrees C and 400 degrees C respectively. The current–voltage curve of the Ge₂Sb₂Te₅ thin film is also investigated. Due to the large resistance difference between the amorphous, the fcc crystalline and the hcp crystalline states, Ge₂Sb₂Te₅ film may be used to realize multilevel storage for Ovonic unified memory.

We report a new method to enhance the properties of the polyethyleneterephthalate (PET) substrates for flexible organic light-emitting diodes (OLEDs). By spin-coating a polyimide (PI) film between the PET and the indium–tin-oxide anode, the flexible substrate with a smooth surface, high transmission over the visible spectrum and good adhesion are achieved. We also compare the flexible OLEDs on different substrates. The diodes on the substrates with polyimide buffer layers exhibit a brightness of 7280 cd/m² at 15 V and the maximum efficiency of 2.64 cd/A.

Highly c-oriented nanocolumn structure ZnO films were successfully deposited on sapphire (0001) substrates by pulsed laser deposition at a substrate temperature of 500 degrees C and 200 mTorr oxygen pressure. X-ray diffraction, scanning electron microscopy, photoluminescence, and spectroscopic ellipsometry were used to characterize the ZnO films. The as-grown film is composed of well-aligned ZnO columns with diameters about 200–300 nm. Photoluminescence spectrum of the ZnO film exhibits a strong near-band-edge emission and a weak deep-level emission band. The optical refractive indices and the extinction coefficients are obtained by fitting the spectroscopic ellipsometry data using the Forouhi–Bloomer dispersion relation.

A supercontinuum extending from 350 nm to more than 1700 nm is generated in microstructured fibre (MF) with randomly distributed air holes in cladding and core by using 15-fs pulses of a 790-nm laser. The maximum total power of the supercontinuum is 63 mW with 288 mW pump power from a 100× microscope objective. The wavelength and power of visible light ranging in the supercontinuum can be tuned by adjusting the input end of random the MF (to change pump incident point or incident angle). In particular, white light has been observed. The polarization states and waveguide modes of the visible light change with adjustment of the pump incident point or incident angle.

We propose a scheme to simulate the dynamic process of the armature expansion of explosive magnetic flux compression generators. Values of the deflective angle and the velocity of expanding the innermost radius of copper cylinder (or armature) caused by explosives detonation are calculated, which are in good agreement with the experimental data. The calculated results show that there may be some dynamic processes that exist during explosive detonation.

We demonstrate that noise can be a benefit factor that enables us to hear weaker signals. We measured the hearing thresholds of subjects for pure tone in different noise levels. The results show that pure tone thresholds with noise of some levels are lower than that without noise. The largest down-shift of the threshold by noise among the examined subjects is 5.7 dB, and the smallest is 1.7 dB.

We discuss the effects of a laser gradient field on particle diffusion in solvent. A tightly focused laser beam may change both the local concentration and the diffusion time obtained in fluorescence correlation spectroscopy (FCS). A quantitative relation between the gradient field strength and the local particle concentration has been derived. Using the data generated by Monte Carlo simulations, we demonstrate that the quantitative relation can be used to obtain number density and polarizability of the particles by FCS experiments in the laser gradient field. A nonlinear growth of diffusion time with laser power is also shown by both the theoretical analysis and the simulations.

Some electromagnetic quantities in the black hole (BH) magnetosphere are discussed by considering the coexistence of the Blandford–Znajek process and the magnetic coupling process. These quantities are (i) flux of electromagnetic energy and angular momentum transferred between the BH and the disc, (ii) poloidal currents flowing on the horizon and disc, (iii) poloidal electric field on the horizon, (iv) toroidal magnetic field in the BH magnetosphere, and (v) voltage drop across the magnetic coupling region on the horizon. It turns out that these quantities are determined mainly by three parameters: (i) the positions relative to the corotation magnetic surface, (ii) the BH spin, and (iii) the power-law index for the variation of the magnetic field on the disc.