The Bose-Einstein condensation in a finite one-dimensional homogeneous system of noninteracting bosons

Condensation of the ideal Bose gas in a closed volume having the shape of a rectangular parallel-epiped of length L with a square base of side length l (L ? l) is theoretically studied within the framework of the Bose-Einstein statistics (grand canonical ensemble) and within the statistics of a canonical ensemble of bosons. Under the condition N(l/L)⁴ ? l, where N is the total number of gas particles, dependence of the average number of particles in the condensate on the temperature T in both statistics is expressed as a function of the ratio t=T/T ₁, where T ₁ is a certain characteristic temperature depending only on the longitudinal size L. Therefore, the condensation process exhibits a one-dimensional (1D) character. In the 1D regime, the average numbers of particles in condensates of the grand canonical and canonical ensembles coincide only in the limiting cases of t → 0 and t → ∞. The distribution function of the number of particles in the condensate of a canonical ensemble of bosons at t ≤1 has a resonance shape and qualitatively differs from the Bose-Einstein distribution. The former distribution begins to change in the region of t ～ 1 and acquires the shape of the Bose-Einstein distribution for t ? 1. This transformation proceeds gradually that is, the 1D condensation process exhibits no features characteristic of the phase transition in a 3D system. For N(l/L)⁴ ? 1, the process acquires a 3D character with respect to the average number of particles in the condensate, but the 1D character of the distribution function of the number of particles in the condensate of a canonical ensemble of bosons is retained at all N values.     

Reaction of molecular hydrogen with the 100 face of MoO3: I. Kinetics in the low pressure range (10−8–10−6 Torr) in the presence of platinum particles

Three successive processes are observed when the 100 face of a MoO₃ single crystal covered with a specific density of platinum particles of known diameter is exposed to molecular hydrogen in a pressure (P) domain between 10^?8 and 10^?6 Torr. During the first step, called the activation step, the rate process is a function of the surface area of the Pt particles and it is slightly thermally activated. During this activation step, H₂ dissociatively chemisorbed on the platinum surface and the hydrogen atoms are inserted into the MoO₃ surface layers. The inserted atom is partially ionized, the electrons given to the lattice reducing Mo⁶⁺ into Mo⁵⁺ and Mo⁴⁺. The rate of hydrogen insertion (V_a) in the activation step increases about linearly with time. The activation step is followed by a stationary step where V is independent of the extent of the Pt surface, V = 0.7Z(1?X), where Z is the number of collisions between H₂ and the MoO₃ surface and X the electronically reduced fraction of the surface area. $\text{X =}\text{a}\text{P}\text{(1 + a}\text{P}\text{)}$, where a is a function of the temperature only. In the stationary step, the platinum particles do not play any role and molecular hydrogen is dissociatively chemisorbed on the MoO₃ surface. The stationary step is followed by a deceleration step. The slowing down of the reaction rate is due to the formation of fractures within the crystal. During all these three steps, the surface is self-cleaning, since protons diffuse into the bulk. The final product of the insertion process would be H_1.6MoO₃, the properties of which have been studied in detail elsewhere. The model which is summarized above is very different from that which would result from the classical views on the so-called hydrogen spillover process since the Pt surface producing the H atoms spilling over the surface would operate only during the activation step.     

Der Einflu\ unipolarer elektrischer Ladungen auf die Beweglichkeit von natürlichem Aerosol

The size distribution of natural occuring aerosol particles with radii from 10^?6 to 10^?5 cm was measured by investigation of the distribution of thoron decay products on the mobility spectrum. In addition we used an artifical ionization of the particles traversing a corona discharge. Thus the efficiency of the mobility spectrometer could be increased by a factor of four (as a function of corona current). The electrical charge distribution on the particles having passed the corona is out of equilibrium. Therefore the mobility spectrum can be reduced to a size spectrum only by means of an experimentally determined calibration function.     

Inelastic hadron-nucleus interactions at 20 and 37 GeV/c

The experiment studies charged particle production for π^?, K^?, and $\text{p}$ interactions on nuclei at 20 and 37 GeV/c at the CERN SPS. A non-magnetic detector, consisting of CsI(Tl) scintillation and lucite ?erenkov counters, distinguishes between fast particles, mainly pions, and slow particles, mainly nucleons, with a cut at velocity β ≈ 0.7. Angular distributions, multiplicity distributions and correlations of slow and fast particles were analysed. It is shown that the measurement of the correlations can provide a critical test for different theoretical models of the hadron-nucleus interaction. At the energies studied so far a systematic deviation from KNO scaling is observed. This gives further support to the “standard picture” of the hadron-nucleus interaction and it contrasts with predictions of the coherent-tube model. The regularity observed for the angular distribution of fast secondaries as a function of the number of slow particles can only be explained by combining features predicted by different models.     

Structure of complexes responsible for radiation-stimulated softening of silicon single crystals

The rate of the radiation-stimulated change in the microhardness of silicon single crystals exposed to irradiation with a low-intensity flux of beta particles (10⁵ < I < 2.9 × 10⁶ cm^?2 s^?1) is studied as a function of the radiation intensity. The temperature is determined at which the microhardness H = H _τ reached in a time τ under low-intensity beta irradiation regains its initial value H ₀. The results obtained indicate that complexes containing two vacancies play a dominant role in the radiation-stimulated softening of silicon single crystal     

Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within “small size” phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to t≈10⁶) by a q-Gaussian (1<q<3) distribution and tend to a Gaussian (q=1) for longer times, as the orbits eventually enter into “large size” chaotic domains. However, in agreement with other studies, we find in certain cases that the q-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called “crossover” function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these q-Gaussian distributions to identify two energy regimes of “weak chaos”—one where the system melts and one where it transforms from liquid to a gas state-by observing where the q-index of the distribution increases significantly above the q=1 value of strong chaos.     

Production and two-photon decay of the MSSM scalar Higgs bosons at the LHC

We consider the production and two-photon decay of theCP-even Higgs bosons (h ⁰ andH ⁰) of the Minimal Supersymmetric Standard Model (MSSM) at the Large Hadron Collider. We study in detail the dependence of the cross section on various parameters of the MSSM, especially the dependence on the mixing effects in the squark sector due to the Higgs bilinear parameterμ and the soft supersymmetry breaking parameterA. We find that the cross section for the production of these Higgs bosons has a significant dependence on the parameters which determine the chiral mixing in the squark sector. The cross section times the two-photon branching ratio ofh ⁰ is of the order of 15–25 fb in much of the parameter space that remains after imposing the present experimental constraints. For theH ⁰ the two-photon branching ratio is only significant if theH ⁰ is light, but then the cross section times the branching ratio may exceed 200 fb. The QCD corrections due to quark loop contributions are known to increase the cross section by 50%. We find the dependence of the cross section on the gluon distribution function used to be rather insignificant.     

Left-flat spaces and their associated space-times

It is already known that for an asymptotically flat space-time the metric coefficients and the other Newman-Penrose variables (in a suitable frame) can be constructed, in principle, by specifying certain initial data at conformal null infinity (and one further function on another null hypersurface), integrating the Newman-Penrose equations in the conformally rescaled “unphysical” space, and then transforming the results back to the physical space-time. If this is done approximately near ?⁺, for vacuum, the well-known Newman-Unti expansion is obtained. In this paper, after complexifying null infinity ?⁺ we generate, in a similar fashion, a left-flat spaceH using as much of the initial data of a given asymptotically flat space-timeM as possible, and show that the left-flat spaceH thus constructed is, in fact, the H-space corresponding toM. The advantage of our method is that it allows a reversal of procedure. Under suitable conditions we can generate from a given left-flat spaceH a class of physical space-times whose H-space is precisely the given left-flat spaceH. We shall see that the formal procedure requires only the local but not the global properties of ?⁺.     

Interpretation of photo-polarimetric observations of comet 17P/Holmes

We present multispectral photo-polarimetric observations of comet 17P/Holmes taken at three different dates. These observations show the evolution of the negative polarization branch (NPB) as a function of time and wavelength. We perform discrete-dipole approximation (DDA) simulations on agglomerated debris particles of various sizes and refractive indices. Our simulations show that the observations are consistent with the cloud being composed of agglomerated debris particles having refractive indices of approximately m=1.5-1.6+0.1i. Our results are also consistent with the particles obeying a power-law size distribution r^-a and having a lower particle-radius cut-off of approximately 0.6 μm, where the index a∼3.5 for the early observations and shrinks to a∼1.5 for the later observations. This is consistent with the smaller, more accelerated particles in the distribution being propelled out of the field of view.     

Heavy SUSY Higgs bosons at e + e − linear colliders

The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future e ⁺ e ^? colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass m₀, gaugino mass m_1/2 and trilinear coupling A, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low tan β solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high tan β case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into b and τ pairs. The main production mechanisms for the heavy Higgs particles are the associated AH production and H ⁺H^? pair production with cross sections of the order of a few fb.     

Anisotropy dispersion in (CoCrPt)1−x(SiO2)x perpendicular recording media

The distribution of easy axis orientation in perpendicular media is of technological importance because it affects the value of S^* (see Fig. 1), which quantifies the switching field distribution (SFD) and hence partially determines the data density achievable on a given medium. The distribution is controlled by the crystallographic orientation of grains and factors such as intergranular exchange and dipolar coupling. Due to strong demagnetising fields in the perpendicular orientation, traditional measurements of remanence as a function of angle are difficult to interpret and have required the use of large-scale computational models. In this work we have utilised the variation of coercivity H_C with angle, which has the advantage that at H_C the global demagnetising field is zero. Additionally, since such materials follow essentially the Stoner–Wohlfarth mode of reversal, the variation of H_C with angle, H_C(θ), is much greater than that for the remanence. We find that for (CoCrPt)_1−x(SiO₂)_x, where the level of exchange coupling is controlled, the distribution of magnetic easy axes is narrower when the exchange coupling is reduced, but dipolar coupling between the grains is strong and affects the magnetisation reversal significantly.     

Non-equilibrium statistical mechanics in the general theory of relativity: II. Linear fields in a kinetic approximation

The first paper in this series introduced a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. The object of this second paper is to apply that formalism to the evolution of a collection of particles that interact via linear fields in a fixed curved background spacetime. Given the viewpoint adopted here, the fundamental objects of the theory are a many-particle distribution function, which lives in a many-particle phase space, and a many-particle conservation equation which this distribution satisfies. By viewing a composite N-particle system as interacting one- and (N ? 1)-particle subsystems, one can derive exact coupled equations for appropriately defined reduced one- and (N ? 1)-particle distribution functions. Alternatively, by treating all the particles on an identical footing, one can extract an exact closed equation involving only the one-particle distribution. The implementation of plausible assumptions, which constitute straightforward generalizations of standard non-relativistic “kinetic approximations”, then permits the formulation of an approximate kinetic equation for the one-particle distribution function. In the obvious non-relativistic limit, one recovers the well-known Vlasov-Landau equation. The explicit form for the relativistic expression is obtained for three concrete examples, namely, interactions via an electromagnetic field, a massive scalar field, and a symmetric second rank tensor field. For a large class of interactions, of which these three examples are representative, the kinetic equation will admit a relativistic Maxwellian distribution as an exact stationary solution; and, for these interactions, an H-theorem may be proved.     

Modeling and computation of two phase geometric biomembranes using surface finite elements

Biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions. The modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces. This leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints. In this paper we propose a new computational tool for computing equilibria based on an L² relaxation flow for the total energy in which the line energy is approximated by a surface Ginzburg–Landau phase field functional. The relaxation dynamics couple a nonlinear fourth order geometric evolution equation of Willmore flow type for the membrane with a surface Allen–Cahn equation describing the lateral decomposition. A novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface, the mean curvature vector and the surface phase field function. The resulting variational formulation uses H¹ spaces, and we employ triangulated surfaces and H¹ conforming quadratic surface finite elements for approximating solutions. Together with a semi-implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only. Numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells, discocytes and starfishes with lateral phase separation.     

The motions of hydrogen impurities in α-Palladium-hydride

The intensity distribution of inelastically scattered thermal and hot neutrons on hydrogen impurities in α-palladium hydride has been studied as a function of concentration, temperature, momentum transfer and different annealing procedures. In up-scattering experiments the first and second harmonics appear at E₁^H = (66 ± 4) me V and E₂^H = (135 ± 15) meV respectively, and the hydrogen band modes have a frequency distribution as expected from measured dispersion curves for pure palladium. For deuterium the first harmonic appears at E₁^D = (48 ± 4) meV. The width of the hydrogen local mode E₁^H changes from 30 to 20 me V and its position from 63 to 66 meV, when the hydrogen concentration is altered from 2.7 to 0.2 at.%. After an extended annealing procedure and at the lowest concentration of 0.2 at.%, the local mode appears in down-scattering experiments at E₁^H = (68.5 ± 2) meV with a full width at half height ΔE₁^H = 4 meV, which is purely instrumental. For higher concentrations and insufficient annealing of the sample, cluster of hydrogen atoms are formed even in the α-phase, as indicated by the increasing width of the local mode. The peak intensity of the E₁^H mode decreases upon changing the temperature from 423 to 673°K. Upon changing the direction of the k-vector from the [1,0,0]- to the [1,1,0]-direction, the peak intensity of the local mode decreases by a factor of ten. These observations indicate the existence of anhannonic effects along the [l,l,0]-direction.     

Study of the Cumulative Number Distribution of Charged Particles Produced in d<Superscript>12</Superscript>C-Interactions at 4.2 A GeV/c

In this paper the behavior of the cumulative number and also with maximum values of cumulative number distribution of protons, π⁺ and π^?-mesons, have been studied, produced in d¹²C-interctions at 4.2 A GeV/c. The experimental data has been compared with ones coming from the Dubna version of the cascade model. In the analysis we have observed; four different regions in the cumulative number distributions for all charged particle and protons and the last region is corresponding to values of cumulative number greater than 1; for pions number of regions decreased to 2 for π^±-mesons but cumulative area is absent for both mesons. Cascade cannot describe satisfactorily the distributions of the cumulative protons and cumulative π^?+-mesons, it gives less number for the all produced particles. In case of particles with maximum values of cumulative number cascade can describe the behavior of cumulative number distribution well. There exist some events with two cumulative particles which could not describe by the cascade dynamics. May be collective nucleon effect could be reasons of the observation two cumulative particles events.     

Probability of ionization of sputtered particles as a function of their energy: Part I: Negative Si ions

In this study we have investigated how the probability of ionization of sputtered Si atoms to form negative ions depends on the energy of the atoms. We have determined the ionization probability from experimental SIMS energy distributions using a special experimental technique, which included de-convolution of the energy distribution with an instrumental transmission function, found by separate measurements.We found that the ionization probability increases as a power law ∼E^0.677 for particles sputtered with energies of 0-10 eV, then becomes a constant value (within the limits of experimental error) for particles sputtered with energies of 30-100 eV. The energy distributions of Si⁻ ions, measured under argon and cesium ion sputtering, confirmed this radical difference between the yields from low and high-energy ions.To explain these results we have considered ionization mechanisms that are different for the low energy atoms (<10 eV) and for the atoms emitted with higher energy (>30 eV).     

Switching field distribution of magnetic fine particles

In the magnetic recording media the switching field distribution (SFD) is an important micromagnetic characteristic curve. However, in general case, methods of assessing SFD have not presented a reasonable relation between the macroscopic measurements and the microscopic properties of the system. The degree of alignment of particles easy axis in a texture and the angular dependence of switching field are two fundamental factors for the distribution function. A technique for determining the switching field distribution curve due to these factors is reported. This technique is performed for textured iron fine particles and samples of CrO₂ and γFe₂O₃ commercial tapes. The distribution differs from a gaussian function. However, the width and the mean switching field equal to twice of the width of dM_r/dH curve and the remanent coercivity, respectively. Furthermore, it is shown that the width of the switching field distribution decreases with increasing the degree of easy axis orientation.