# Main topic: Nonlocal quantum kinetic theory

 Nonlocal quantum kinetic theory with P. Lipavsky (Charles University Prague) The quantum version of the 130 years-old Boltzmann equation remains still the basis of modern transport theories. Extensions become necessary for transient-time effects like the femtosecond response and for strongly correlated systems. At short time scales higher correlations have no time to develop yet and femto-second laser excitation of collective modes in semiconductors as well as quenches of cold atoms in optical lattices can be described even analytically by fluctuations of the meanfield. For plasma systems exposed to a sudden switching analytical results are available from the time-dependent Fermi’s Golden Rule in good agreement with the results of two-time Greenfunctions solving the Kadanoff and Baym equation. At later times when correlations develop, a kinetic equation of nonlocal and noninstantaneous character is derived which unifies the achievements of the transport in dense quantum gases with the Landau theory of quasiclassical transport in dense Fermi systems. The numerical solution is not more expensive than solving the Boltzmann equation since large cancellations in the off-shell motion appear which are hidden usually in non-Markovian behaviors. The quasiparticle drift of Landau’s equation is connected with a dissipation governed by a nonlocal and non-instant scattering integral in the spirit of Enskog corrections. These corrections are expressed in terms of shifts in space and time that characterize nonlocality of the scattering process. In this way quantum transport is possible to recast into a quasi-classical picture. The balance equations for the density, momentum and energy include quasiparticle contributions and the correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. Damping of giant resonances with Rainer Walke (Rostock), Michale Vogt (Dresden/Zurich) The giant resonances in symmetric and asymmetric nuclear matter [1] are described using a conserving relaxation time approximation to include collision effects and compared with experimental data of hot resonances. The isovector and isoscalar modes are coupled due to asymmetric nuclear meanfield acting on neutrons and protons differently. A further coupling is observed caused by collisional correlations. The latter one leads to the appearance of a third mode [2]. We had suggested that this mode might be observable in neutron rich systems like 11Be while in proton rich isobars this mode should appear with strong damping which was observed later as Pygmy resonances. Using a pseudoparticle simulation technique we simulate large amplitude isoscalar octupole excitations in a finite nuclear system [3]. Dependent on the initialization we can either observe clear octupole modes or overdamped octupole modes which decay immediately into quadrupole ones. Octupole modes should be present in central asymmetric collisions of heavy ions with mass relation 3:7. The contribution of surface scattering is compared with the contribution from the interparticle collisions. A unified response function is derived which includes surface damping via the Lyapunov exponent [4] as well as collisional damping. The former one is calculated for different shape deformations of quadrupole and octupole type [5]. The surface as well as the collisional contribution each reproduce the experimental value, therefore we propose a proper weighting between both contributions related to their relative occurrence due to collision frequency between particles and of particles with the surface. We find that for low and high temperatures the collisional contribution dominates whereas the surface damping is dominant around temperatures of a third of the centroid energy [5]. Nonlocal kinetic theory and simulation of heavy ion collisions with P. Lipavsky (Charles University Prague) With the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium a consistent treatment is reached of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and the results are compared with the former theory and recent experimental data. movie: Ta +Au at 33 MeV movie: central collisions movie: Au+Au (40-150 MeV, 0-12 fm impact) Dynamical constraints on phase transitions with J. Normand, D. Cussol, J. Colin, B. Tamain (LPC Caen), P. Lipavsky (Charles University Prague) The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of central heavy ion reactions are parametrized in terms of time-dependent thermodynamical variables in the Fermi liquid sense. This allows one to discuss dynamical trajectories in phase space. The nonequilibrium state is characterized by nonisobaric, nonisochoric, etc., conditions, shortly called isonothing conditions. Therefore a com- bination of thermodynamical observables is constructed which allows one to locate instabilities and points of possible phase transition in a dynamical sense. We find two different mechanisms of instability, a short time surface-dominated instability and later a spinodal-dominated volume instability. The latter one occurs only if the incident energies do not exceed significantly the Fermi energy and might be attributed to spinodal decomposition. In contrast the fast surface explosion occurs far outside the spinodal region and pertains also in the cases where the system develops too fast to suffer a spinodal decomposition and where the system approaches equilibrium outside the spinodal region. Mid-rapidity charge distribution with J. Normand, D. Cussol, J. Colin, B. Tamain (LPC Caen), P. Lipavsky (Charles University Prague) The experimental finding of enhancement of midrapidity matter shows the necessity to include correlations beyond Boltzmann-Uehling-Uhlenbeck (BUU) which was performed in the framework of nonlocal kinetic theory. Different theoretical improvements are discussed. While the in-medium cross section changes the number of collisions, it leaves the transferred energy almost unchanged. In contrast the nonlocal scenario changes the energy transferred during collisions and leads to an enhancement of midrapidity matter. The renormalization of quasiparticle energies can be included in nonlocal scenarios and leads to a further enhancement of midrapidity matter distribution. This renormalization is accompanied by a dynamical softening of the equation of state seen in longer oscillation periods of the excited compressional collective mode. We propose to include quasiparticle renormalization by using the Pauli-rejected collisions which circumvent the problem of backflows in Landau theory. Using the maximum relative velocity of projectile and targetlike fragments we associate experimental events with impact parameters of the simulations. For peripheral collisions we find reasonable agreement between experiment and theory. For more central collisions, the velocity damping is higher in one-body simulations than observed experimentally, because of missing cluster formations in the kinetic theory used. Asymmetric Bethe-Salpeter equation for pairing and condensation with P. Lipavsky (Charles University Prague) The Martin-Schwinger hierarchy of correlations are reexamined and the three-part icle correlations are investigated under various partial summations. Besides the known approximations of screened, ladder and maximally crossed diagrams the pair-pair correlations are considered. It is shown that the recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical repeated collisions is derived as a result of the hierarchical dependencies of correlations. Exceeding the parquet approximation we show that an asymmetry appears in the selfconsistent propagators. This form is superior over the symmetric selfconsistent one since it provides the Nambu-Gorkov equations and gap equation for fermions and the Beliaev equations for bosons while from the symmetric form no gap equation results. The selfenergy diagrams which account for the subtraction of unphysical repeated collisions are derived from the pair-pair correlation in the three-particle Greenfunction. It is suggested to di stinguish between two types of selfconsistency, the channel-dressed propagators and the completely dressed propagators, with the help of which the asymmetric ex pansion completes the Ward identity and is phi-derivable. The resulting T-matrix theory provides a consistent approach to superconductivity above and below the critical temprature. Bose condensation of squeezed light Light with a chemical potential and no mass is shown to possess a general phase-transition curve to Bose-Einstein condensation. This limiting density and temperature range is found by the diverging in-medium potential range of effective interaction. The inverse expansion series of the effective interaction from Bethe-Salpeter equation is employed exceeding the ladder approximation. While usually the absorption and emission with Dye molecules is considered, here it is proposed that squeezing can create also such a mean interaction leading to a chemical potential. The equivalence of squeezed light with a complex Bogoliubov transformation of interacting Bose system with finite lifetime is established with the help of which an effective gap is deduced where the squeezing parameter is related to an equivalent gap by $|\Delta(\omega)|={\hbar \omega/( \coth {2|z(\omega)|}-1)}$. This gap phase creates a finite condensate in agreement with the general limiting density and temperature range. In this sense it is shown that squeezing induces the same effect on light as an interaction leading to possible condensation. The phase diagram for condensation is presented due to squeezing and the appearance of two gaps is discussed. Birth of quasiparticles - Femtosecond formation of collective modes with P. Lipavsky (Charles University Prague) Starting from a quantum kinetic equation including the mean field and a conserving relaxation-time approximation we derive an analytic formula which describes the time dependence of the dielectric function in a plasma created by a short intense laser pulse. This formula reproduces universal features of the formation of collective modes seen in recent experimental data of femtosecond spectroscopy. The presented formula offers a tremendous simplification for the description of the formation of quasiparticle features in interacting systems. Numerical demanding treatments can now be focused on effects beyond these gross features found here to be describable analytically. with V, Ashokan, K.\ N.\ Pathak (Punjab India), N.\ D.\ Drummond (Lancaster) We study the ground-state properties of ferromagnetic quasi-quantum wire using the quantum Monte Carlo (QMC) method. The correlation energy, pair-correlation function, static structure factor, and momentum density are calculated for various wire widths at high-density. It is observed that the peak in the static-structure factor at twice Fermi momentum grows sub-linearly as the wire width decreases. We also obtain the exact ground-state properties of finite thickness wire theoretically using first-order RPA with exchange and self-energy contributions in the high-density limit. The correlation between electrons of different quantum wires is expected to affect the quantum properties of the whole system. Specifically, the ground-state energy, the correlation energy, the interaction energy, the pair-correlation function (PCF), the static structure factor (SSF), and the momentum distribution (MD) function is calculated. The PCF shows an oscillatory behavior at all densities considered here. As two parallel wires approach each other, inter-wire correlations increase while intra-wire correlations decrease. The SSF shows a peak at twice Fermi momentum at higher densities. The values of TL parameters are found in agreement with that of a single wire for large separation between the two wires. MD of the EEBW at various values Universal short-time response and formation of correlations after quantum quenches The short-time evolution of two distinct systems, the pump and probe experiments with semiconductor and the sudden quench of cold atoms in an optical lattice, is found to be described by the same universal response function. This analytic formula at short time scales is derived from the quantum kinetic theory approach observing that correlations need time to be formed. The influence of finite trapping potential is derived and discussed as well as Singwi-Sjølander local field corrections. The quantum kinetic equation allows to understand how two-particle correlations are formed and the screening and collective modes are build up. Spin dependent transport in quantum dot systems Fabricio Macedo de Souza (Univeristy Uberlandia) Spin-dependent transport in quantum dots is a subject of intense study nowdays due to its relevance to the new generation of proposed spintronic devices that encompasses, for instance, the Datta-Das transistor, memory devices and as an ultimate goal quantum computers. In particular, the recent progress in the coherent control of electron spins in quantum dots has stimulated even further the research in this field, for possible applications in quantum computation and quantum information processing. In addition to these fascinating technological applications, quantum dots constitute a unique well-controllable system to study fundamental physical aspects of transport in the strong Coulomb-correlated regime, and its interplay with spin-dependent effects. Our group deals with both ac and dc transport of charge and spin in quantum dots coupled to nonmagnetic of ferromagnetic leads. Terahertz out-of-plane resonances due to spin-orbit coupling A microscopic kinetic theory is developed which allows to investigate non-Abelian SU(2) systems interacting with mean fields and spin-orbit coupling under magnetic fields in one, two, and three dimensions. The coupled kinetic equations for the scalar and spin components are presented and linearized with respect to an external electric field. The dynamical classical and quantum Hall effect are described in this way as well as the anomalous Hall effect for which a new symmetric dynamical contribution to the conductivity is presented. The coupled density and spin response functions to an electric field are derived including arbitrary magnetic fields. The magnetic field induces a staircase structure at frequencies of the Landau levels. It is found that for linear Dresselhaus and Rashba spin-orbit coupling a dynamical out-of-plane spin response appears at these Landau level frequencies establishing terahertz resonances. Spin and density response with magentic fields and spin-orbit coupling with J. Kailasvuori (MPIPKS Dresden) The quantum kinetic equation for SU(2) symmetric systems is derived with special consideration of spin-orbit coupling in magnetic and electric fields. The theory is applicable for linear and nonlinear intrinsic and extrinsic spin-orbit coupling as well as graphene. The RPA response functions to an electric field are derived for arbitrary magnetic fields and spin-orbit coupling. The coupled density and spin response functions allow to describe dynamical classical, quantum, and anomalous Hall effect as well as spin-Hall effects and its inverse. The collective modes show a splitting due to polarization and/or spin-orbit coupling for neutral impurity scattering. The long-range Coulomb potential of charged impurities are considered and the spin-orbit coupling leads to characteristic modifications of the screening parameter. New high-frequency modes out-of-plane are found. Explicit expressions for the dynamical response and conductivity for relativistic Fermions, Dirac particles and graphene are presented. Regularization-free transport properties of graphene Based on the quantum kinetic equations for systems with SU(2) symmetry, the density and spin currents are calculated in graphene realized here as the infinite mass-limit of electrons with quadratic dispersion and a proper spin-orbit coupling. Correspondingly the currents possess no quasiparticle part but only anomalous parts. The intraband and interband conductivities are discussed with respect to magnetic fields and magnetic domain puddles. It is found that the magnetic field and meanfield of domains can be represented by an effective Zeeman field. For large Zeeman fields the dynamical conductivities become independent of the density and are universal in this sense. The different limits of vanishing density, relaxation, frequency, and Zeeman field are not interchangeable. The optical conductivity agrees well with the experimental values using screened impurity scattering and an effective Zeeman field. The universal value of Hall conductivity is shown to be modified due to the Zeeman field. The spin current shows a subtlety in that a quasiparticle part appears though it vanishes for particle currents. The density and spin response functions to an external electric field are calculated and the dielectric function is discussed with respect to collective excitations. A frequency and wave-vector range is identified where the dielectric function changes sign and the repulsive Coulomb potential becomes effectively attractive allowing Cooper pairing. Real optical conductivity versus frequency for different applied voltages compared with the experimental data (dashed).} Weyl systems: anomalous transport normally explained The chiral kinetic theory is derived from exact spinor mean field equations without symmetry-breaking terms for large classes of SU(2) systems with spin-orbit coupling. As special limit, Weyl systems are considered. The anomalous term $\sim\V E\V B$ in the balance of the chiral density appears consequently by an underlying conserving theory. The experimental observation of this term and the anomalous magneto-transport in solid-sate physics which are described by chiral kinetic theory are therefore neither a unique signal for mixed axial-gravitational or triangle anomaly nor a signal for the breaking of Lorentz-invariance. Here it is shown that the chiral kinetic theory which describes the experiments can be derived without fictitious vector fields or other symmetry-breaking assumptions in the underlying field theory. The source of the anomalous term is by two thirds the divergence of Berry curvature at zero momentum which can be seen as Dirac monopole and by one third the Dirac sea at infinite momentum. During the derivation of the chiral kinetic theory this source by the Dirac sea is transferred exclusively to the Dirac monopole due to the projection of the spinor Wigner functions to the chiral basis. The dynamical result is shown to suppress the anomalous term by two thirds. Transport and noise in organic field effect devices with L. M. Eng (IaPP Dresden), S. Gemming (HFZD Dresden-Rossendorf), T. Kunze (HFZD Dresden Rossendorf), P. Lipavsky (Charles University Prague), R. Luschtinetz (TU Dresden), P. Milde (IaPP Dresden), G. Seifert (TU Dresden) The goal to develop low cost storage and microelectronic devices has triggered an enormous activity in the research of organic field effect transistors (OFETs) based on different polymers. It is desireable that the molecular material possesses a high structural ordering to reach high charge carrier mobilities and low resistive losses. One of the most promising materials are Oligothiophenes and their derivatives. In general, the charge transport is largest in the direction perpendicular to the plane of the thiophene rings. This suggest to construct devices with parallely ordered molecular rings. Just recently an OFET structure has been built from ultra-thin self-assembly films made up from oligothiophenes, which are arranged in a high-order lamellar stacking perpendicular to the substrate surface. The transport properties are calculated with the help of surface Green functions. movies: shuttling transport of molecules(red +, green -,grey 0 charged) Metal-insulator transition in heterojunctions with E. Nakhmedov (TU Chemnitz), C. Olbricht (TU Chemnitz) The conductivity in quasi two-dimensional systems is calculated using the quantu m kinetic equation as well as molecular dynamical simulations. The system of qua si two-dimensional electrons in hetero-junctions which interact with charged and neutral impurities and the low temperature correction to the conductivity is ca lculated analytically. It turns out that the dynamical screening due to charged impurities leads to a linear temperature dependence, while the scattering from n eutral impurities leads to the usual Fermi-liquid behavior. The experimental met al-insulator transition at low temperatures are reproduced. The effective ma ss of quasiparticle excitations in quasi two-dimensional systems is calculated analytically. It is shown that the effective mass increases sharply when the density approaches the critical one of metal-insulator transition. This suggests a Mott-type of transition rather than an Anderson-like transition. Anomalous 0.7 conductance and analogs in 1D systems with Marcelo Rosenau da Costa (Uberlandia) We analyze the fractional quantization of the ballistic conductance associated with the light and heavy hole bands in Si, Ge, and GaAs systems. It is shown that the formation of a localized hole state in the region of the quantum point contact connecting two quasi-one-dimensional hole leads drastically modifies the conductance pattern. The exchange interaction between localized and propagating holes results in fractional quantization of the ballistic conductance unlike that in electronic systems. The value of the conductance at the additional plateaus depends on the offset between the bands of the light and heavy holes and the sign of the exchange interaction constant. Equation of state for interacting Bose/Fermi systems and the BCS-BEC transition with P. Lipavsky (Charles University Prague), M. Männel (FH Münster) Near Feshbach resonances it is possible to tune the interaction in ultra-cold Fermi and Bose gases. One can therefore vary the interaction in a Bose-Einstein condensate (BEC) or drive a Fermi gas through a transition from Cooper pairs in a BCS state to two-particle bound states which can also form a BEC. The main interest lies on the conditions for the formation of bound states, Cooper pairs or a BEC. Especially the dependence of these conditions on the interaction is investigated. Calculations are done mainly analytically with a many-body Green functions technique for idealized potentials. Therefore also medium effects such as Bose enhancement and Pauli repulsion can be included. Enhancement of pairing in correlated electron systems with nanostructures with P. Lipavsky (Charles University Prague), M. Männel (TU Chemnitz), M. Schreiber (TU Chemnitz) A correlated fermion system is considered surrounding a finite cavity with virtual levels. The pairing properties are calculated and the influence of the cavity is demonstrated. To this end the Gell-Mann and Goldberger formula is generalized to many-body systems. We find a possible enhancement of pairing temperature if the Fermi momentum times the cavity radius fulfills a certain resonance condition which suggests an experimental realization. Bernoulli potential at superconducting surfaces and deformation with E. H. Brandt (MPI Stuttgart), J. Kolacek (Charles University Prague), P. Lipavsky (Charles University Prague) In superconductors penetrated by Abrikosov vortices the magnetic pressure and the inhomogeneous condensate density induce a deformation of the ionic lattice. Forces evoked by vortices create a tension which modifies the total volume of the sample and which was observed as magnetostriction. The force which holds electrons inward naturally pulls the oppositely charged ions outwards and also corrugates the surface. The general relation between the surface dipole and the surface tension with the contribution of the superconducting condensate has been worked out for anisotropic materials. movie: direction dependent effective vortex mass of YBCO The NMR and NQR spectra of 63Cu in the CuO2 plane of YBa2Cu3O7 in the superconducting state are discussed in terms of a phenomenological theory of Ginzburg-Landau type extended to lower temperatures. We show that the observed spectra, can be explained by a standard theory of the Bernoulli potential with the charge transfer between CuO2 planes and CuO chains assumed. Huddling of penguins as collective motion due to far-field cor relations with F. Morawetz (Kreuzgymnasium Dresden), D. Zitterbart (University of Erlangen-Nuremberg) Emperor penguins (Aptenodytes forsteri) have developed a specific tactics to sur vive the Antarctic winter where they breed during 3 months basically living on t heir reserves. They stand together so tightly that the temperature is more than 20 degrees higher than surrounding. At the same time the huddle is in continuous move allowing a reshuffling of the outer and inner positions. Within an observe d time of 30-60 seconds, all penguins make small steps that travel as a wave thr ough the entire huddle. We simulate the huddling behavior by a cellular automate and show that nearest neighbor interactions are not sufficient to create this c ollective behavior. Instead the next nearest neighbor interaction is necessary t o describe basic properties of the collective motion, the rotation and mixing as well as regular outbursts. movie: Simulation of 113 pinguins, individuals colored, periodic boundaries, start as cluster movie: Simulation of 1239 pinguins, individuals colored, periodic boundaries, start as random movie: Simulation of 709 pinguins, individuals colored, with panic between times 10-20, 310-320, 610, 620 Formation of brine channels in sea ice with Bernd Kutschan (FH Münster), Silke Thoms (AWI Bremerhafen), Sibylle Gemming (HFZD Dresden-Rossendorf) Sea ice is a very variable biotope with respect to extension,thickness, porosity or texture. Therefore the basic understanding of brine channel formation in sea ice is important for the interplay between the microbial colonization and their natural habitat. The early phase of brine channel formation in sea ice is considered. The first structures emerging during sea-ice formation are determined by the phase instability of the ice-water system in the presence of salt. We apply a Ginzburg-Landau type approach to describe the phase separation in the two-component system (ice, salt). The free energy density involves two order parameters: one for the hexagonal ice phase with low salinity, and one for the liquid water with high salinity. A gradient dynamics minimizes the free energy with respect to the conservation of the salinity. The resulting model equations are solved numerically in one and two dimensions. The numerical solution shows a short-time behavior of structure formation where the freezing is assumed and a large-time broadening of the structure. A stability analysis provides the phase diagram where brine channels can be formed. In thermodynamics the parameters determine the supercooling or superheating region and the specific heat respectively. The size of the brine channels depends on the salinity and the temperature. With the help of realistic parameters the brine channel distribution is calculated and found in agreement with the measured samples. Turing vs phase field structure Dynamical mechanism of antifreeze proteins with Bernd Kutschan (FH Münster), Silke Thoms (AWI Bremerhafen), Sibylle Gemming (HFZD Dresden-Rossendorf) The fascinating ability of algae, insects and fishes to survive at temperatures below normal freezing is realized by antifreeze proteins (AFPs). Antifreeze proteins (AFPs) are surface-active molecules and interact with the diffusive water/ice interface preventing a complete solidification. A new dynamical mechanism is proposed how these proteins inhibit the freezing of water. We apply a Ginzburg-Landau type approach to describe the phase separation in the two-component system (ice, AFP). The free energy density involves two fields: one for the ice phase with low AFP concentration, and one for the liquid water with high AFP concentration. The time evolution of the ice reveals microstructures as a result of phase separation in the presence of AFPs. We observe a faster clustering of pre-ice structure connected with a locking of grain size by the action of AFP which is an essentially dynamical process. The adsorption of additional water molecules are inhibited and the further growth of ice grains are stopped. The interfacial energy between ice and water is lowered by which the AFPs allow only smaller critical ice nucleus to be formed. Analogously to hysteresis in magnetic materials we observe a thermodynamic hysteresis leading to a nonlinear density dependence of the freezing point depression [1] in agreement with the experiments [2]. The freezing temperature depression of four different classes of AFP structures and insects with the fits compared to the experimental data (points) of [2]. Theory of water and charged liquid bridges The phenomenon of liquid bridge formation due to an applied electric field is investigated. A solution of a charged catenary is presented, which allows one to determine the static and dynamical stability conditions where charged liquid bridges are possible. The creeping height, the bridge radius and length, as well as the shape of the bridge are calculated showing an asymmetric profile, in agreement with observations. The flow profile is calculated from the Navier-Stokes equation leading to a mean velocity, which combines charge transport with neutral mass flow and which describes recent experiments on water bridges. movie: Experiment by Woisetschläger, Fuchs,..(http://www.youtube.com/ElmarCFuchs) Interplay of viscosity and surface tension for ripple formation by laser melting with S. Trinschek, E. L. Gurevich, (M\"unster) A model for ripple formation on liquid surfaces exposed to an external laser or particle beam and a variable ground is developed. The external incident beam is hereby mechanically coupled to the liquid surface due to surface roughness. Starting from the Navier Stokes equation the coupled equations for the velocity potential and the surface height are derived in a shallow-water approximation with special attention to viscosity. The resulting equations obey conservation laws for volume and momentum where characteristic potentials for gravitation and surface tension are identified analogously to conservative forces. The approximate solutions are discussed in the context of ripple formation in laser materials processing involving melting of a surface by a laser beam. Linear stability analysis provides the formation of a damped wave modified by an interplay between the external beam, the viscosity, and the surface tension. The limit of small viscosity leads to damped gravitational and the limit of high viscosity to capillary waves. The resulting wavelengths are in the order of the ripples occurring in laser welding experiments hinting to the involvement of hydrodynamic processes in their origin. By discussing the response of the system to external periodic excitations with the help of Floquet multipliers, we show that the ripple formation could be triggered by a a periodically modulated external beam, e.g. appropriate repetition rates of an incident laser beam. The weak nonlinear stability analysis provides ranges where hexagonal or stripe structures can appear. The orientation of stripe structures and ripples are shown to be dependent on the incident angle of the laser or particle beam where a minimal angle is reported. Numerical simulations confirm the findings and allow to describe the influence of variable grounds. The contours of Floquet multipliers Consistent solution of Einstein-Cartan equations with torsion outside matter The Einstein-Cartan equations in first-order action of torsion are considered. From Belinfante-Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion is given by the spin which leads to an extended Oppenhaimer-Volkov equation. Outside matter a second solution is found besides the torsion-free Schwarzschild one with the torsion completely determined by the metric and vice-versa. This solution is shown to be of non-spherical origin and its uniqueness with respect to the consistence is demonstrated. Unusual properties are discussed in different coordinate systems where the cosmological constant assumes the role of the Friedman parameter in Friedman-Lama\^itre-Robertson-Walker cosmoses. Parameters are specified where wormholes are possible. Transformations are presented to explore and map regions of expanding and contracting universes to the form of static metrics. The autoparallel equations are solved exactly and compared with geodesic motion. The Weyl tensor reveals that the here found solution is of Petrov-D type. The 3D embedding diagram of the solution with torsion and different cosmological constants with the case of a finite throat

Klaus Morawetz