Relativistic entanglement of two massive particles

We describe the spin and momentum degrees of freedom of a system of two massive spin--$\tfrac{1}{2}$ particles as a 4 qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alice's and Bob's subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin- with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the 4 qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.Comment: 17 pages, 4 figure

Accretion geometry of the black-hole binary Cygnus X-1 from X-ray polarimetry

Black-hole binary (BHB) systems comprise a stellar-mass black hole and a closely orbiting companion star. Matter is transferred from the companion to the black hole, forming an accretion disk, corona and jet structures. The resulting release of gravitational energy leads to emission of X-rays. The radiation is affected by special/general relativistic effects, and can serve as a probe of the properties of the black hole and surrounding environment, if the accretion geometry is properly identified. Two competing models describe the disk-corona geometry for the hard spectral state of BHBs, based on spectral and timing measurements. Measuring the polarization of hard X-rays reflected from the disk allows the geometry to be determined. The extent of the corona differs between the two models, affecting the strength of relativistic effects (e.g., enhancement of polarization fraction and rotation of polarization angle). Here, we report observational results on linear polarization of hard X-ray (19-181 keV) emission from a BHB, Cygnus X-1, in the hard state. The low polarization fraction, <8.6% (upper limit at 90% confidence level), and the alignment of the polarization angle with the jet axis show that the dominant emission is not influenced by strong gravity. When considered together with existing spectral and timing data, our result reveals that the accretion corona is either an extended structure, or is located far from the black hole in the hard state of Cygnus X-1.Comment: 44 pages, 15 figures, 1 tabl

Topology and Phases in Fermionic Systems

There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of exponentially localized Wannier functions. We show that by taking two copies of a gapped, free fermionic system with complex conjugate Hamiltonians, it is always possible to overcome these obstructions. This allows us to write the ground state in matrix product form using Grassman-valued bond variables, and show insensitivity of the ground state density matrix to boundary conditions.Comment: 4 pages, see also arxiv:0710.329

Shedding new light on the Crab with polarized X-rays

Strong magnetic fields, synchrotron emission, and Compton scattering are omnipresent in compact celestial X-ray sources. Emissions in the X-ray energy band are consequently expected to be linearly polarized. X-ray polarimetry provides a unique diagnostic to study the location and fundamental mechanisms behind emission processes. The polarization of emissions from a bright celestial X-ray source, the Crab, is reported here for the first time in the hard X-ray band (~20-160 keV). The Crab is a complex system consisting of a central pulsar, a diffuse pulsar wind nebula, as well as structures in the inner nebula including a jet and torus. Measurements are made by a purpose-built and calibrated polarimeter, PoGO+. The polarization vector is found to be aligned with the spin axis of the pulsar for a polarization fraction, PF = (20.9 $\pm$ 5.0)%. This is higher than that of the optical diffuse nebula, implying a more compact emission site, though not as compact as, e.g., the synchrotron knot. Contrary to measurements at higher energies, no significant temporal evolution of phase-integrated polarisation parameters is observed. The polarization parameters for the pulsar itself are measured for the first time in the X-ray energy band and are consistent with observations at optical wavelengths.Comment: Accepted for publication in Scientific Reports, www.nature.com/sre

Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting

Relativistic quantum clocks

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for "Workshop on Time in Physics" Zurich 201