Julia Sets in Parameter Spaces

Given a complex number λ of modulus 1, we show that the bifurcation locus of the one parameter family {f _b (z)=λz+b z ²+z ³} _{b ∈ ℂ} contains quasi-conformal copies of the quadratic Julia set J(λz+z ²). As a corollary, we show that when the Julia set J(λz+z ²) is not locally connected (for example when z↦λz+z ² has a Cremer point at 0), the bifurcation locus is not locally connected. To our knowledge, this is the first example of complex analytic parameter space of dimension 1, with connected but non-locally connected bifurcation locus. We also show that the set of complex numbers λ of modulus 1, for which at least one of the parameter rays has a non-trivial accumulation set, contains a dense G _δ subset of S ¹. Received: 22 September 2000 / Accepted: 16 January 2001     

Optical magnetometer with submicron spatial resolution based on Rb vapors

It is shown experimentally that use of fluorescence and transmission spectra obtained from nanocells with the thickness of column of rubidium atomic vapor L = λ/2 and L = λ, respectively (λ = 794 nm is the wavelength of laser radiation close to resonance with D ₁-line transition of Rb atoms), by means of a narrowband diode laser allows spectral separation and study of variations of probabilities of atomic transitions between ground and excited states of hfs of D ₁ lines of ⁸⁵Rb and ⁸⁷Rb atoms in the range of magnetic fields from 10 to 5000 G. Small thickness of atomic vapor column (∼390 nm and ∼794 nm) allows applying permanent magnets simplifying essentially creation of strong magnetic fields. Advantages of this technique are discussed as compared with the technique of saturated absorption. The obtained results show that a nanocell with submicrom thickness of vapor column may serve as a basis for designing a magnetometer with submicron local spatial resolution which is important in case of measuring strongly inhomogeneous magnetic fields. Experimental data are in good agreement with the theoretical results.     

Selective excitation of the 62 D 3/2 state of the atomic thallium beam

The absorption of the tunable narrow-band laser radiation with λ = 276.9 nm at the 6² P _1/2 → 62 D _3/2 transition in the atomic thallium beam is experimentally studied. The isotopic selectivity and efficiency of the excitation of the 6² D _3/2 state is investigated. The splittings between the ²⁰³Tl and ²⁰⁵Tl isotopes were found to be Δv = 0.98 and 1.25 GHz for the transitions with the nuclear momenta F = 1 → F = 1, 2 and F = 0 → F = 1, respectively, which is sufficient for a relatively high isotopic selectivity of the 6² D _3/2 state excitation with the subsequent ionization for the laser separation of the thallium isotopes. The effects that lead to the broadening of the resonance and a decrease in the selectivity are analyzed. The main contribution is related to the field broadening by the laser radiation, which limits the mean laser power density.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Relativistic star solutions in higher-dimensional pseudospheroidal space-time

We obtain relativistic solutions of a class of compact stars in hydrostatic equilibrium in higher dimensions by assuming a pseudospheroidal geometry for the spacetime. The space-time geometry is assumed to be (D − 1) pseudospheroid immersed in a D-dimensional Euclidean space. The spheroidicity parameter (λ) plays an important role in determining the equation of state of the matter content and the maximum radius of such stars. It is found that the core density of compact objects is approximately proportional to the square of the space-time dimensions (D), i.e., core of the star is denser in higher dimensions than that in conventional four dimensions. The central density of a compact star is also found to depend on the parameter λ. One obtains a physically interesting solution satisfying the acoustic condition when λ lies in the range λ > (D + 1)/(D − 3) for the space-time dimensions ranging from D = 4 to 8 and (D + 1)/(D − 3) < λ < (D ² − 4D + 3)/(D ² − 8D − 1) for space-time dimensions ≥9. The non-negativity of the energy density (ρ) constrains the parameter with a lower limit (λ > 1). We note that in the case of a superdense compact object the number of space-time dimensions cannot be taken infinitely large, which is a different result from the braneworld model.     

The Beam Propagation Factor of Nonparaxial Truncated Flattened Gaussian Beams

By using the second-order moment of the power density, the beam width, far-field divergence angle and M² factor of nonparaxial truncated flattened Gaussian (FG) beams are derived analytically. It is shown that the M² factor of nonparaxial truncated FG beams depends not only on the truncation parameter δ and beam order N, but also on the initial waist-width to wavelength ratio w₀/λ. The far-field divergence angle approaches an asymptotic value of θ_max=63.435° when the truncation parameter δ → 0. For the special cases of N = 0 and δ → ∞ our results reduce to those of nonparaxial truncated Gaussian beams and nonparaxial untruncated FG beams, respectively.     

Microwave energy channeling in plasma waveguides created by a high-power UV laser in the atmosphere

The grazing mode of microwave propagation in a hollow plasma waveguide formed by ionization of atmospheric air with a small easily ionized additive by strong UV pulses of the Garpun KrF laser (λ = 248 nm, the pulse duration and energy are ∼70 ns and ∼50 J) was experimentally demonstrated for the first time. The annular laser beam produced a hollow tube ∼10 cm in diameter with an electron density of ∼10¹² cm⁻³ in a plasma wall ∼1 cm thick, over whichmicrowave radiation with λ _mw ∼ 8 mm was transmitted to a distance of 60 m. Themicrowave signal transmitted by the waveguide was amplified by a factor of 6 in comparison with propagation in free space.     

Investigation of Rb <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript> atomic lines in strong magnetic fields by fluorescence from a half-wave-thick cell

It has been experimentally demonstrated that the use of the effect of significant narrowing of the fluorescence spectrum from a nanocell that contains a column of atomic Rb vapor with a thickness of L = 0.5λ (where λ = 794 nm is the wavelength of laser radiation, whose frequency is resonant with the atomic transition of the D ₁ line of Rb) and the application of narrowband diode lasers allow the spectral separation and investigation of changes in probabilities of optical atomic transitions between levels of the hyperfine structure of the D ₁ line of ⁸⁷Rb and ⁸⁵Rb atoms in external magnetic fields of 10–2500 Gs (for example, for one of transitions, the probability increases ∼17 times). Small column thicknesses (∼390 nm) allow the application of permanent magnets, which facilitates significantly the creation of strong magnetic fields. Experimental results are in a good agreement with the theoretical values. The advantages of this method over other existing methods are noted. The results obtained show that a magnetometer with a local spatial resolution of ∼390 nm can be created based on a nanocell with the column thickness L = 0.5λ. This result is important for mapping strongly inhomogeneous magnetic fields.     

Laser dye stability. Part 5

Photodegradation parameters that relate bleaching and absorption at the lasing wavelength λ_l have been examined for over 30 different coumarin and quinolone laser dyes in a number of solvents. Quinolone dyes were found to bleach faster than the coumarin dyes. The effect of chemical substituents was found to affect bleaching of the coumarin dyes only to a small (20%) extent in ethanol. The major effect of chemical substituents was in the conversion of a dye to products absorbing at λ_l. Effects of solvent, cover gas, and changes in fluorescent quantum yields are discussed. Of particular interest is the photodegradation parameterA, the ratio of the percent absorption at λ_l to the total input energy per dm³. Combined with τ, the total input energy per dm³ required for a laser to reach half its original intensity, it was found thatAτ=1.2±0.9 for all of the dyes independent of dye concentration in all of the solvents tested. It appears that where bleaching of the dye is only of the order of 10–20%, the absorption at λ_l is 1.2% when our dye laser has reached one-half of its initial output. It is consequently possible to estimate τ values of new dyes by the use ofA terms through the relationshipA ₁τ₁=A ₂τ₂ where τ₁ of Dye 1 has been calibrated in the same dye laser system.     

Entropic Repulsion for the High Dimensional Gaussian Lattice Field Between Two Walls

The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝ^λ _N , λ _N = [−N, N] ^d ∩ ℤ ^d and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ _N where L is large enough but finite. We also study the same problem for two layered interfaces case.     

Laser-induced cavities and solitons in overcritical hydrogen plasma

A picosecond CO₂ laser was used successfully in a number of experiments exploring advanced methods of particle acceleration [1]. Proton acceleration from gas-jet plasma exemplifies another advantage of employing the increase in laser wavelength from the optical to the mid-IR region. Recent theoretical- and experimental-studies of ion acceleration from laser-generated plasma point to better ways to control the ion beam’s energy when plasma approaches the critical density. Studying this regime with solid-state lasers is problematic due to the dearth of plasma sources at the critical electron density ∼10²¹ cm⁻³, corresponding to laser wavelength λ = 1 μm. CO₂ laser offers a solution. The CO₂ laser’s 10 μm wavelength shifts the critical plasma density to 10¹⁹ cm⁻³, a value attainable with gas jets. Capitalizing on this approach, we focused a circular polarized 1-TW CO₂ laser beam onto a hydrogen gas jet and observed a monoenergetic proton beam in the 1–2 MeV range. Simultaneously, we optically probed the laser/plasma interaction region with visible light, revealing holes bored by radiation pressure, as well as quasi-stationary soliton-like plasma formations. Our findings from 2D PIC simulations agree with experimental results and aid in their interpretation.     

Pulsed lasers operating by the atomic transitions of inert gases on pumping by a self-sustained transverse discharge

This paper presents the results of experimental studies of lasing by the atomic transitions of inert gases in mixtures ofHe−NF ₃ (λ=706.5 nm),Ne−NF ₃ (585.3 nm), andAr−NF ₃ (750.4 nm). It has been shown that when an inert-gas-halide mixture is excited by a self-sustained discharge, the electronegative gas provides depopulation of the lower laser level and simultaneously increases the pumping efficiency. Based on investigations of the spontaneous emission and lasing, on measurements of the density and temperature of the gas-discharge plasma electrons, and on an analysis of the process rates, it is concluded that the processes of electron excitation play a dominant role in the population of the upper laser level. Institute of High-Current Electronics, Siberian Division of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 60–63, April, 2000.     

Spin squeezing in finite temperature Bose-Einstein condensates: Scaling with the system size

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N →∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction ⟨N _nc⟩/N in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.     

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.     

Scale-free random graphs and Potts model

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight P_i ∝ i^-μ (0 < μ< 1) and an edge can connect verticesi andj with rateP _i P _j . Corresponding equilibrium ensemble is identified and the problem is solved by theq → 1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of λ > 3 and 2 < λ < 3, whereλ = 1 +μ ^-1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finiteN shows double peaks.     

On the surface properties of a nanodiamond

The dependences of the specific surface energy, the surface tension, and the surface pressure on the size, the surface shape, and the temperature of a nanodiamond with a free surface have been investigated using the Mie-Lennard-Jones interatomic interaction potential. The nanocrystal has the form of a parallelepiped faceted by the (100) planes with a square base. The number of atoms N in the nanocrystal varies from 5 to ∞. The isothermal isomorphic dependences of the specific surface energy, its isochoric derivative with respect to the temperature, the surface tension, and the surface pressure on the nanodiamond size have been calculated at temperatures ranging from 20 to 4300 K. According to the results of the calculations, the surface energy under this conditions is positive, which indicates that the nanodiamond cannot be fragmented at temperatures up to 4300 K. The surface pressure for the nanodiamond P _sf (N) ∼ N ^−1/3 is considerably less than the Laplace pressure P _ls (N)^−1/3 ∼ N ^−1/3 for the same nanocrystal at the given values of the temperature, the density, and the number of atoms N. As the temperature increases from 20 to 4300 K, the lowering of the isotherm P _sf (N) is considerably more pronounced than that of the isotherm P _ls (N). At high temperatures, the isotherm P _sf (N) changes the shape of the size dependence and goes to the range of extension of small nanocrystals. It has been demonstrated that the lattice parameter of the nanodiamond can either decrease or increase with a decrease in the nanocrystal size. The most significant change in the lattice parameter of the nanodiamond is observed at temperatures below 1000 K.     

Effects of sidelobes of focused flat-topped laser beams on vacuum electron acceleration

Using three-dimensional test particle simulations, we investigated electrons accelerated by a focused flat-top laser beam at different intensities and flatness levels of the beam profile before focusing in vacuum. The results show that the presence of sidelobes around the main focal spot of the focused flat-top laser beam influences the optimum (as far as electron acceleration is concerned) initial momentum (and incident angle) of electrons for acceleration. The difference of initial conditions between laser beams with and without sidelobes becomes evident when the laser field is strong enough (a₀>10, corresponding to intensities I>1×10²⁰ W/cm² for the laser wavelength λ=1 μm, where a₀ is a dimensionless parameter measuring laser intensity). The difference becomes more pronounced at increasing a₀. Because of the presence of sidelobes, there exist three typical CAS (capture and acceleration scenario) channels when a₀≥30 (corresponding to I>1×10²¹ W/cm² for λ=1 μm). The energy spread of the outgoing electrons is also discussed in detail. PACS 41.75.Jv; 42.60.Jf; 42.25.Fx     

Characterization of channel waveguides in Pr:YLiF<Subscript>4</Subscript> crystals fabricated by direct femtosecond laser writing

Single tracks and pairs of tracks are written in the volume of Pr-doped LiYF₄-crystals using tightly focused femtosecond laser radiation (λ=1045 nm, τ _p=400–500 fs, f=0.1–1 MHz). Waveguiding between the tracks is demonstrated and optimized by varying the distance between the tracks and the laser writing conditions. The stress-induced guiding mechanism is explained based on TEM, interference microscopy, near-field and far-field measurements. It is shown that the single-crystalline material is getting poly-crystalline under femtosecond laser irradiation. By measuring the lifetime of the ³P₁→³H₅ transition and the emission spectrum at excitation with λ=444 nm, no influence on these properties of the guided light is observed. This possibly enables the realization of a channel waveguide laser in the visible spectral range.     

The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant

Given two selfadjoint operators A and V=V ₊ -V _-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N ₊(λ,α), N _-(λ,α), N ₀(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger operators and its generalizations are given. Received: 9 April 1997 / Accepted: 26 August 1997     

Infrared laser emission in two-photon pumped sodium vapour

We report infrared laser emission in the region of 3 to 5 μm from sodium vapour optically pumped by a pulsed dye laser with wavelengths ranging from 585 to 610nm. Twophoton excitation processes are believed to be responsible for the primary excitation. Both molecular transitions (4 to 5 μm) between high lying states, and atomic transitions (5² S _1/2−4² P _3/2,1/2 at 3.41 μm) have been identified.