Institut für Physik und Astronomie
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We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-1/2 chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.
We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an arbitrary fixed product basis. We show that linear growth of separability entropy provides a stricter criterion of complexity than Kolmogorov-Sinai entropy, namely it requires that the dynamics be exponentially unstable, nonlinear, and non-Markovian.
The discovery of a plume of water vapour and ice particles emerging from warm fractures ('tiger stripes') in Saturn's small, icy moon Enceladus(1-6) raised the question of whether the plume emerges from a subsurface liquid source(6-8) or from the decomposition of ice(9-12). Previous compositional analyses of particles injected by the plume into Saturn's diffuse E ring have already indicated the presence of liquid water(8), but the mechanisms driving the plume emission are still debated(13). Here we report an analysis of the composition of freshly ejected particles close to the sources. Salt-rich ice particles are found to dominate the total mass flux of ejected solids (more than 99 per cent) but they are depleted in the population escaping into Saturn's E ring. Ice grains containing organic compounds are found to be more abundant in dense parts of the plume. Whereas previous Cassini observations were compatible with a variety of plume formation mechanisms, these data eliminate or severely constrain non-liquid models and strongly imply that a salt-water reservoir with a large evaporating surface(7,8) provides nearly all of the matter in the plume.
Resonant soft x-ray diffraction (RSXD) with femtosecond (fs) time resolution is a powerful tool for disentangling the interplay between different degrees of freedom in strongly correlated electron materials. It allows addressing the coupling of particular degrees of freedom upon an external selective perturbation, e. g., by an optical or infrared laser pulse. Here, we report a time-resolved RSXD experiment from the prototypical correlated electron material magnetite using soft x-ray pulses from the free-electron laser FLASH in Hamburg. We observe ultrafast melting of the charge-orbital order leading to the formation of a transient phase, which has not been observed in equilibrium.
We study the propagation of ultra-high-energy cosmic rays (UHECRs) in the Galaxy, concentrating on the energy range below the ankle in the spectrum at 4 EeV. A Monte Carlo method, based on analytical solutions to the time-dependent diffusion problem, is used to account for intermittency by placing sources at random locations. Assuming a source population that scales with baryon mass density or star formation (e.g., long GRB), we derive constraints arising from intermittency and the observational limits on the composition and anisotropy. It is shown that the composition and anisotropy at 10(18) eV are difficult to reproduce and require that either (1) the particle mean free path is much smaller than a gyroradius, implying the escape time is very long, (2) the composition is heavier than suggested by recent Auger data, (3) the ultra-high-energy sub-ankle component is mostly extragalactic, or (4) we are living in a rare lull in the UHECR production, and the current UHECR intensity is far below the Galactic time average. We therefore recommend a strong observational focus on determining the UHECR composition around 10(18) eV.
We consider general heterogeneous ensembles of phase oscillators, sine coupled to arbitrary external fields. Starting with the infinitely large ensembles, we extend the Watanabe-Strogatz theory, valid for identical oscillators, to cover the case of an arbitrary parameter distribution. The obtained equations yield the description of the ensemble dynamics in terms of collective variables and constants of motion. As a particular case of the general setup we consider hierarchically organized ensembles, consisting of a finite number of subpopulations, whereas the number of elements in a subpopulation can be both finite or infinite. Next, we link the Watanabe-Strogatz and Ott-Antonsen theories and demonstrate that the latter one corresponds to a particular choice of constants of motion. The approach is applied to the standard Kuramoto-Sakaguchi model, to its extension for the case of nonlinear coupling, and to the description of two interacting subpopulations, exhibiting a chimera state. With these examples we illustrate that, although the asymptotic dynamics can be found within the framework of the Ott-Antonsen theory, the transients depend on the constants of motion. The most dramatic effect is the dependence of the basins of attraction of different synchronous regimes on the initial configuration of phases.
We study the discrete nonlinear Schrodinger equation with a random potential in one dimension. It is characterized by the length, the strength of the random potential, and the field density that determines the effect of nonlinearity. Following the time evolution of the field and calculating the largest Lyapunov exponent, the probability of the system to be regular is established numerically and found to be a scaling function of the parameters. This property is used to calculate the asymptotic properties of the system in regimes beyond our computational power.
Resonant inelastic soft x-ray scattering (RIXS) spectra excited at the 1 sigma(g) -> 3 sigma(u) resonance in gas-phase O-2 show excitations due to the nuclear degrees of freedom with up to 35 well-resolved discrete vibronic states and a continuum due to the kinetic energy distribution of the separated atoms. The RIXS profile demonstrates spatial quantum beats caused by two interfering wave packets with different momenta as the atoms separate. Thomson scattering strongly affects both the spectral profile and the scattering anisotropy.
We present a comprehensive study of X-ray emission by, and wind properties of, massive magnetic early B-type stars. Dedicated XMM-Newton observations were obtained for three early-type B-type stars, xi(1) CMa, V2052 Oph and zeta Cas, with recently discovered magnetic fields. We report the first detection of X-ray emission from V2052 Oph and zeta Cas. The latter is one the softest X-ray sources among the early-type stars, while the former is one of the X-ray faintest. The observations show that the X-ray spectra of our programme stars are quite soft with the bulk of X-ray emitting material having a temperature of about 1 MK. We compile the complete sample of early B-type stars with detected magnetic fields to date and existing X-ray measurements, in order to study whether the X-ray emission can be used as a general proxy for stellar magnetism. We find that the X-ray properties of early massive B-type magnetic stars are diverse, and that hard and strong X-ray emission does not necessarily correlate with the presence of a magnetic field, corroborating similar conclusions reached earlier for the classical chemically peculiar magnetic Bp-Ap stars.
We analyse the ultraviolet (UV) spectra of five non-supergiant B stars with magnetic fields (tau Sco, beta Cep, xi(1) CMa, V2052 Oph and zeta Cas) by means of non-local thermodynamic equilibrium (non-LTE) iron-blanketed model atmospheres. The latter are calculated with the Potsdam Wolf-Rayet (PoWR) code, which treats the photosphere as well as the wind, and also accounts for X-rays. With the exception of t Sco, this is the first analysis of these stars by means of stellar wind models. Our models accurately fit the stellar photospheric spectra in the optical and the UV. The parameters of X-ray emission, temperature and flux are included in the model in accordance with observations. We confirm the earlier findings that the filling factors of X-ray emitting material are very high.
Our analysis reveals that the magnetic early-type B stars studied here have weak winds with velocities not significantly exceeding upsilon(esc). The mass-loss rates inferred from the analysis of UV lines are significantly lower than predicted by hydrodynamically consistent models. We find that, although the X-rays strongly affect the ionization structure of the wind, this effect is not sufficient in reducing the total radiative acceleration. When the X-rays are accounted for at the intensity and temperatures observed, there is still sufficient radiative acceleration to drive a stronger mass-loss than we empirically infer from the UV spectral lines.
We investigate the connections between the magnetic fields and the X-ray emission from massive stars. Our study shows that the X-ray properties of known strongly magnetic stars are diverse: while some comply to the predictions of the magnetically confined wind model, others do not. We conclude that strong, hard, and variable X-ray emission may be a sufficient attribute of magnetic massive stars, but it is not a necessary one. We address the general properties of X-ray emission from "normal" massive stars, especially the long standing mystery about the correlations between the parameters of X-ray emission and fundamental stellar properties. The recent development in stellar structure modeling shows that small-scale surface magnetic fields may be common. We suggest a "hybrid" scenario which could explain the X-ray emission from massive stars by a combination of magnetic mechanisms on the surface and shocks in the stellar wind. The magnetic mechanisms and the wind shocks are triggered by convective motions in sub-photospheric layers. This scenario opens the door for a natural explanation of the well established correlation between bolometric and X-ray luminosities.
We implemented an experimental scheme for ultrafast x-ray diffraction at storage rings based on a laser-driven Bragg-switch that shortens the x-ray pulses emitted from an undulator. The increased time-resolution is demonstrated by observing changes of intensity, position and width of the diffraction peaks of a La(0.7)Sr(0.3)MnO(3)/SrTiO(3) superlattice sample after optical excitation, i.e., by quantitatively measuring the propagation of an expansion wave through the sample. These experimental transients with timescales of 35 to 60 ps evidence a reduction of the x-ray pulse duration by a factor of two.
Atom chips are a promising candidate for a scalable architecture for quantum information processing provided a universal set of gates can be implemented with high fidelity. The difficult part in achieving universality is the entangling two-qubit gate. We consider a Rydberg phase gate for two atoms trapped on a chip and employ optimal control theory to find the shortest gate that still yields a reasonable gate error. Our parameters correspond to a situation where the Rydberg blockade regime is not yet reached. We discuss the role of spontaneous emission and the effect of noise from the chip surface on the atoms in the Rydberg state.
Given some observable H on a finite-dimensional quantum system, we investigate the typical properties of random state vectors vertical bar psi >> that have a fixed expectation value < psi vertical bar H vertical bar psi > = E with respect to H. Under some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We discuss the implications of our results as new proof tools in quantum information theory and to study phenomena in quantum statistical mechanics. As a by-product, we derive a method to sample the resulting distribution numerically, which generalizes the well-known Gaussian method to draw random states from the sphere.
The inspiral and merger of two black holes is among the most exciting and extreme events in our universe. Being one of the loudest sources of gravitational waves, they provide a unique dynamical probe of strong-field general relativity and a fertile ground for the observation of fundamental physics. While the detection of gravitational waves alone will allow us to observe our universe through an entirely new window, combining the information obtained from both gravitational wave and electro-magnetic observations will allow us to gain even greater insight in some of the most exciting astrophysical phenomena. In addition, binary black-hole mergers serve as an intriguing tool to study the geometry of space-time itself. In this dissertation we study the merger process of binary black-holes in a variety of conditions. Our results show that asymmetries in the curvature distribution on the common apparent horizon are correlated to the linear momentum acquired by the merger remnant. We propose useful tools for the analysis of black holes in the dynamical and isolated horizon frameworks and shed light on how the final merger of apparent horizons proceeds after a common horizon has already formed. We connect mathematical theorems with data obtained from numerical simulations and provide a first glimpse on the behavior of these surfaces in situations not accessible to analytical tools. We study electro-magnetic counterparts of super-massive binary black-hole mergers with fully 3D general relativistic simulations of binary black-holes immersed both in a uniform magnetic field in vacuum and in a tenuous plasma. We find that while a direct detection of merger signatures with current electro-magnetic telescopes is unlikely, secondary emission, either by altering the accretion rate of the circumbinary disk or by synchrotron radiation from accelerated charges, may be detectable. We propose a novel approach to measure the electro-magnetic radiation in these simulations and find a non-collimated emission that dominates over the collimated one appearing in the form of dual jets associated with each of the black holes. Finally, we provide an optimized gravitational wave detection pipeline using phenomenological waveforms for signals from compact binary coalescence and show that by including spin effects in the waveform templates, the detection efficiency is drastically improved as well as the bias on recovered source parameters reduced. On the whole, this disseration provides evidence that a multi-messenger approach to binary black-hole merger observations provides an exciting prospect to understand these sources and, ultimately, our universe.
We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.
To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation, we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law.
The dynamics of the North Atlantic subpolar gyre (SPG) are assessed under present and glacial boundary conditions by investigating the SPG sensitivity to surface wind-stress changes in a coupled climate model. To this end, the gyre transport is decomposed in Ekman, thermohaline, and bottom transports. Surface wind-stress variations are found to play an important indirect role in SPG dynamics through their effect on water-mass densities. Our results suggest the existence of two dynamically distinct regimes of the SPG, depending on the absence or presence of deep water formation (DWF) in the Nordic Seas and a vigorous Greenland-Scotland ridge (GSR) overflow. In the first regime, the GSR overflow is weak and the SPG strength increases with wind-stress as a result of enhanced outcropping of isopycnals in the centre of the SPG. As soon as a vigorous GSR overflow is established, its associated positive density anomalies on the southern GSR slope reduce the SPG strength. This has implications for past glacial abrupt climate changes, insofar as these can be explained through latitudinal shifts in North Atlantic DWF sites and strengthening of the North Atlantic current. Regardless of the ultimate trigger, an abrupt shift of DWF into the Nordic Seas could result both in a drastic reduction of the SPG strength and a sudden reversal in its sensitivity to wind-stress variations. Our results could provide insight into changes in the horizontal ocean circulation during abrupt glacial climate changes, which have been largely neglected up to now in model studies.