Zeitschrift fur Naturforschung a

Considering a periodically oscillating harmonic potential, we explored the dynamic properties of bright solitons in a Bose-Einstein condensate by using Darboux transformation. It is found that the soliton movement exhibits a nonperiodic oscillation under a slow oscillating potential, while it is hardly affected under a fast oscillating potential. Furthermore, the head-on and/or ‘chase’ collisions of two solitons have been obtained, which could be controlled by the oscillation frequency of the potential.

The electronic and magnetic properties of the graphene/Eu/Ni(111) intercalation-like system are studied in the framework of the GGA+U approach with dispersive interactions taken into account. Intercalation of monoatomic Eu layer underneath graphene on Ni(111) leads to the drastic changes of the electronic structure of graphene compared to free-standing graphene as well as graphene/Ni(111). The strong influence of the spin-polarised Eu 4f states, crossing the graphene-derived π states, on magnetic properties of graphene and on spin-filtering properties of the graphene/Eu/Ni(111) trilayer is discussed.

The paper considers the use of a static mass spectrometer modified by installation of a Baur-Signer ion source and an ion-counting system to detect xenon from single grains from inclusions in the C3 meteorite Allende. The inferred iodine concentrations increased from pentlandite to melilite, but vary widely from one grain to another, indicating that the iodine resides in a minor phase which is included 'spottily' in the bulk phases. It is likely that the detectability for excess Xe achieved here could be improved; about 23,000 of fissiogenic Xe-132 was detected in the largest melelite sample analyzed, but it cannot be determined from this study whether the PU-244 is 'spotty' like I-129 or is uniformly distributed in the melilite.

In 1948, Koppe formulated an almost complete recipe for statistical-thermal models including particle production, formation and decay of resonances, temporal and thermal evolution of the interacting system, statistical approaches and equilibrium condition in final state of the nuclear interaction. As the rate of particle production was one of the basic assumptions, recalling Koppe's work would be an essential input to be involved in the statistical prediction of non-equilibrium particle production in recent and future ultra-relativistic collisions.

We study the level spacing distribution $P(S)$ of 2D real random matrices both symmetric as well as general, non-symmetric. In the general case we restrict ourselves to Gaussian distributed matrix elements, but different widths of the various matrix elements are admitted. The following results are obtained: An explicit exact formula for $P(S)$ is derived and its behaviour close to S=0 is studied analytically, showing that there is linear level repulsion, unless there are additional constraints for the probability distribution of the matrix elements. The constraint of having only positive or only negative but otherwise arbitrary non-diagonal elements leads to quadratic level repulsion with logarithmic corrections. These findings detail and extend our previous results already published in a preceding paper. For the {\em symmetric} real 2D matrices also other, non-Gaussian statistical distributions are considered. In this case we show for arbitrary statistical distribution of the diagonal and non-diagonal elements that the level repulsion exponent $\rho$ is always $\rho = 1$, provided the distribution function of the matrix elements is regular at zero value. If the distribution function of the matrix elements is a singular (but still integrable) power law near zero value of $S$, the level spacing distribution $P(S)$ is a fractional exponent pawer law at small $S$. The tail of $P(S)$ depends on further details of the matrix element statistics. We explicitly work out four cases: the constant (box) distribution, the Cauchy-Lorentz distribution, the exponential distribution and, as an example for a singular distribution, the power law distribution for $P(S)$ near zero value times an exponential tail.

Data is examined for volatile/mobile Ag, As, Au, Bi, Cd, Co, Cs, Cu, Ga, In, Rb, Sb, Se, Te, Tl and Zn in exterior and/or interior samples of four Antarctic meteorites from the Allan Hills (ALH): A77005 (unique achondrite); A77257 (ureilite); A77278 (L3); A77299 (H3). Exterior samples reflect contamination and/or leaching by weathering but trace element (ppm-ppt) contents in interior samples seem reasonable for representatives of these rare meteoritic types. The A77005 achondrite is shown to be related to shergottites; other samples extend compositional ranges previously known for their groups or types. With suitable precautions, Antarctic meteorite finds yield trace element data as reliable as those obtained from previously known falls.

The symmetry of vacuum is characterized by the Lorentz group with the parameter $c$. Physical space inside the homogeneous optical medium should be described by the Lorentz group with the parameter $c/n$, where $n$ is the refractive index of the medium. Violation of a one-parameter phenomenological symmetry in the discrete medium, such as gas, creates the opportunity for the experimental detecting the motion of the optical medium relative to luminiferous aether.

The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).

In this study, using the analytical and recurrence relations suggested by the authors in previous works, the new efficient and reliable program procedure for the overlap integrals over Slater type orbitals (STOs) is presented. The proposed procedure guarantees a highly accurate evaluation of the overlap integrals with arbitrary values of quantum numbers, screening constants and internuclear distances. It is demonstrated that the computational accuracy of the proposed procedure is not only dependent on the efficiency of formulas, as has been discussed previously, but also on a number of other factors including the used program language package and solvent properties. The numerical results obtained using the algorithm described in the present work are in a complete agreement with those obtained using the alternative evaluation procedure. We notice that the program works without any restrictions and in all range of integral parameters.

An exhaustive analysis of wave motion in a compressible isothermal medium under the influence of gravity is presented. The dispersion relation governing the wave propagation is derived from the linearized equations of fluid dynamics and thermodynamics, and it is arranged in a nondimensional form. Penetration depths, frequency cutoffs, and particle orbits are calculated under the assumption of an ideal gas. With the nondimensional form of the dispersion relation these data can be expressed in a form independent of the constants describing a particular atmosphere. The results can be conventiently displayed on a number of diagrams valid for monatomic and diatomic gases. Dissipative effects arising from viscosity and heat conduction are neglected.

In the framework of the quantum-mechanical theory of elementary act of non-adiabatic electrochemical reactions, it is carried out the calculation of the discharge current of ions at the semiconductor--electrolyte solution interface using the model of isotropic spherically symmetric band. It is shown that our results generalize the well-known formulae for the current density obtained by R.R. Dogonadze, A.M. Kuznetsov, and Yu.A. Chizmadzhev [R.R. Dogonadze, A.M. Kuznetsov, and Yu.A. Chizmadzhev, The kinetics of some heterogeneous reactions at semiconductor--electrolyte interface, Zhur. Fiz. Khim. 38 (1964) 1195--1202]. The average densities of states in the valence band and the conduction band of the semiconductor electrode in the heterogeneous charge transfer are found.

We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator.

The classical and quantum mechanics of isolated, nonlinear resonances in integrable systems with N>=2 degrees of freedom is discussed in terms of geometry in the space of action variables. Energy surfaces and frequencies are calculated and graphically presented for invariant tori inside and outside the resonance zone. The quantum mechanical eigenvalues, computed in the semiclassical WKB approximation, show a regular pattern when transformed into the action space of the associated symmetry reduced system: eigenvalues inside the resonance zone are arranged on N-dimensional cubic lattices, whereas those outside are, in general, non-periodically distributed. However, N-dimensional triclinic (skewed) lattices exist locally. Both kinds of lattices are joined smoothly across the classical separatrix surface. The statements are illustrated with the help of two and three coupled rotors.

Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential to examine the minimum energy gap between the ground level and the next one through the evolution. In this letter, we show a way of speedup in quantum adiabatic evolution algorithm, using the extended Hamiltonian. We present the exact relation between the energy gap and the elements of the extended Hamiltonian, which provides the new point of view to reduce the running time.

Resistance measurements of five different portions of uncoated and partially SiO-overcoated aluminum stripes are reported. In specimens of both types the resistance increases at the cathode when the stripe is subjected to high current densities. In partially coated specimens the resistance decreases at the anode whereas it remains constant in the uncoated sample. The difference in behavior at the anode between coated and uncoated specimens is interpreted as being due to differences of ion accumulation: In the uncoated films hillocks are formed whereas in the specimen with partial overcoat the ions accumulate more evenly. Scanning-electron micrographs are shown to support this interpretation.

We propose a method to reach the antiferromagnetic state of two-dimensional Fermi gases trapped in optical lattices: Independent subsystems are prepared in suitable initial states and then connected by a sudden or slow quench of the tunneling between the subsystems. Examples of suitable low-entropy subsystems are double wells or plaquettes, which can be experimentally realized in Mott insulating shells using optical super-lattices. We estimate the effective temperature T* of the system after the quench by calculating the distribution of excitations created using the spin wave approximation in a Heisenberg model. We investigate the effect of an initial staggered magnetic field and find that for an optimal polarization of the initial state the effective temperature can be significantly reduced from T* approximately T_c at zero polarization to T*<0.65 T_c, where T_c is the crossover temperature to the antiferromagnetic state. The temperature can be further reduced by using a finite quench time. We also show that T* decreases logarithmically with the linear size of the subsystem.

For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\'e II, Painlev\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutions can be obtained by solving linear ordinary differential equations.

The present theory is closely related to Dirac's equation of the electron, but not to his magnetic monopole theory, except for his relation between electric and magnetic charge. The theory is based on the fact, that the massless Dirac equation admits a second electromagnetic coupling, deduced from a pseudo-scalar gauge invariance. The equation thus obtained has the symmetry laws of a massless leptonic, magnetic monopole, able to interact weakly. We give a more precise form of the Dirac relation between electric and magnetic charges and a quantum form of the Poincare first integral. In the Weyl representation our equation splits into P-conjugated monopole and antimonopole equations with the correct electromagnetic coupling and opposite chiralities, predicted by P. Curie. Charge-conjugated monopoles are symmetric in space and not in time (contrary to the electric particles), an important fact for the vacuum polarization. Our monopoles are magnetically excited neutrinos, which leads to experimental consequences. These monopoles are assumed to be produced by electromagnetic pulses or arcs, leading to nuclear transmutations and, for beta radioactive elements, a shortening of the life time and the emission of monopoles instead of neutrinos in a magnetic field. A corresponding discussion is given.

A calculation is made of the cumulative effect of numerous small orbital perturbations caused by gravitational and collisional deflections of meteorites by other bodies in the asteroid belt. It is found that in a time equal to the age of the solar system the mean change in perihelion distance caused by gravitational perturbation is of the order of 10 This phenomenon is consequently of negligible importance in removing meteorites from the asteroid belt. This conclusion is in disagreement with a result reported in the recent literature. The calculated mean change in perihelion distance caused by multiple collisional scattering is somewhat higher, about 10

Since the 1930s, astronomical observations have accumulated evidence that our understanding of the dynamics of galaxies and groups of galaxies is grossly incomplete: assuming the validity of Newton's law of gravity on astronomical scales, the observed mass (stored in stars and interstellar gas) of stellar systems can account only for roughly 10% of the dynamical (gravitating) mass required to explain the high velocities of stars in those systems. The standard approach to this "missing mass problem" has been the postulate of "dark matter", meaning an additional, electromagnetically dark, matter component that provides the missing mass. However, direct observational evidence for dark matter has not been found to date. More importantly, astronomical observations obtained during the last decade indicate that dark matter cannot explain the kinematics of galaxies. Multiple observations show that the discrepancy between observed and dynamical mass is a function of gravitational acceleration (or field strength) but not of other parameters (size, rotation speed, etc.) of a galaxy; the mass discrepancy appears below a characteristic and universal acceleration ("Milgrom's constant"). Consequently, the idea of a modified law of gravity, specifically the ansatz of Modified Newtonian Dynamics (MOND), is becoming increasingly important in astrophysics. MOND has successfully predicted various important empirical relations of galaxy dynamics, including the famous Tully-Fisher and Faber-Jackson relations. MOND is found to be consistent with stellar dynamics from binary stars to clusters of galaxies, thus covering stellar systems spanning eight orders of magnitude in size and 14 orders of magnitude in mass. These developments have the potential to initiate a paradigm shift from dark matter to a modified law of gravity as the physical mechanism behind the missing mass problem.

The properties of warm symmetric and asymmetric nuclear matter are investigated in the frame of the Thomas-Fermi approximation using a recent modern parametrization of the effective nucleon-nucleon interaction of Myers and Swiatecki. Special attention is paid to the liquid-gas phase transition, which is of special interest in modern nuclear physics. We have determined the critical temperature, critical density and the so-called flash temperature. Furthermore the equation of state for cold neutron star matter was calculated.

The formation of colored silicon compounds under nonequilibrium conditions is discussed with reference to the composition of the Jupiter atmosphere. It is shown that many of these reactions produce strongly colored intermediates that are relatively stable and similar in appearance to those observed on Jupiter. It is suggested that the silicon compounds could substantially contribute to the colors observed on Jupiter. The colored intermediates may be the result of relatively rapid amorphous silicon monoxide formation in vertical atmospheric currents in the region near the red spot and in the red spot itself.

Calculation of the intensity of two of the emissions produced during the dissociative excitation of carbon dioxide in the upper atmosphere of Mars by solar ultraviolet radiation. The calculation tangential column emission rates of the atomic oxygen 2972-A line and the carbon monoxide Cameron bands produced by the photodissociative mechanism are found to be factors of 3 and 10, respectively, smaller than the emission rates observed by Mariner ultraviolet spectrometers.

A quantum system being observed evolves more slowly. This `'quantum Zeno effect'' is reviewed with respect to a previous attempt of demonstration, and to subsequent criticism of the significance of the findings. A recent experiment on an {\it individual} cold trapped ion has been capable of revealing the micro-state of this quantum system, such that the effect of measurement is indeed discriminated from dephasing of the quantum state by either the meter or the environment.

Recent experiments to test Bell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted and observing a violation of Bell's inequality is the only way to test whether a scheme works with a high precision or not.