Spatial Localization and Relativistic Transformation of Quantum Spins

The purity of a reduced state for spins that is pure in the rest frame will most likely appear to degrade because spin and momentum become mixed when viewed by a moving observer. We show that such a boost-induced decrease in spin purity observed in a moving reference frame is intrinsically related to the spatial localization properties of the wave package observed in the rest frame. Furthermore, we prove that, for any localized pure state with separable spin and momentum in the rest frame, its reduced density matrix for spins inevitably appears to be mixed whenever viewed from a moving reference frame.Comment: 5 pages, 1 figur

Simultaneous Border-Collision and Period-Doubling Bifurcations

We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely classified; in particular, we give conditions that ensure chaos.Comment: 22 pages; 5 figure

Constraints on QCD Sum-rules from the H\"older Inequalities

A new technique based on H\"older's integral inequality is applied to QCD sum-rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum-rules are to consistently describe integrated physical cross-sections, but these constraints do not require any experimental data and therefore can be applied to any hadronic spectral function. As an illustration of this technique the Laplace sum-rules of the light-quark correlation function for the vector and the axial-vector currents are examined in detail. We find examples of inconsistency between the inequalities and sum-rule parameters used in some previous analyses of the vector and axial-vector channels.Comment: 13 pages, RevTeX, 4 figures available upon request, to appear in Phys. Lett

An early Little Ice Age brackish water invasion along the south coast of the Caspian Sea (sediment of Langarud wetland) and its wider impacts on environment and people

Caspian Sea level has undergone significant changes through time with major impacts not only on the surrounding coasts, but also offshore. This study reports a brackish water invasion on the southern coast of the Caspian Sea constructed from a multi-proxy analysis of sediment retrieved from the Langarud wetland. The ground surface level of wetland is >6 m higher than the current Caspian Sea level (at -27.41 m in 2014) and located >11 km far from the coast. A sequence covering the last millennium was dated by three radiocarbon dates. The results from this new study suggest that Caspian Sea level rose up to at least -21.44 m (i.e. >6 m above the present water level) during the early Little Ice Age. Although previous studies in the southern coast of the Caspian Sea have detected a high-stand during the Little Ice Age period, this study presents the first evidence that this high-stand reached so far inland and at such a high altitude. Moreover, it confirms one of the very few earlier estimates of a high-stand at -21 m for the second half of the 14th century. The effects of this large-scale brackish water invasion on soil properties would have caused severe disruption to regional agriculture, thereby destabilizing local dynasties and facilitating a rapid Turko-Mongol expansion of Tamerlane’s armies from the east.N Ghasemi (INIOAS), V Jahani (Gilan Province Cultural Heritage and Tourism Organisation) and A Naqinezhad (University of Mazandaran), INQUA QuickLakeH project (no. 1227) and to the European project Marie Curie, CLIMSEAS-PIRSES-GA-2009-24751

Active faulting within a megacity: the geometry and slip rate of the Pardisan thrust in central Tehran, Iran

Tehran, the capital city of Iran with a population of over 12 million, is one of the largest urban centres within the seismically active Alpine–Himalayan orogenic belt. Although several historic earthquakes have affected Tehran, their relation to individual faults is ambiguous for most. This ambiguity is partly due to a lack of knowledge about the locations, geometries and seismic potential of structures that have been obscured by dramatic urban growth over the past three decades, and which have covered most of the young geomorphic markers and natural exposures. Here we use aerial photographs from 1956, combined with an ~1 m DEM derived from stereo Pleiades satellite imagery to investigate the geomorphology of a growing anticline above a thrust fault—the Pardisan thrust—within central Tehran. The topography across the ridge is consistent with a steep ramp extending from close to the surface to a depth of ~2 km, where it presumably connects with a shallow-dipping detachment. No primary fault is visible at the surface, and it is possible that the faulting dissipates in the near surface as distributed shearing. We use optically stimulated luminescence to date remnants of uplifted and warped alluvial deposits that are offset vertically across the Pardisan fault, providing minimum uplift and slip-rates of at least 1 mm yr$^{−1}$. Our study shows that the faults within the Tehran urban region have relatively rapid rates of slip, are important in the regional tectonics, and have a great impact on earthquake hazard assessment of the city and surrounding region.Geological Survey of Iran, Christ Church College Oxford, Natural Environment Research Council, Economic and Social Research Counci

Neumark Operators and Sharp Reconstructions, the finite dimensional case

A commutative POV measure $F$ with real spectrum is characterized by the existence of a PV measure $E$ (the sharp reconstruction of $F$) with real spectrum such that $F$ can be interpreted as a randomization of $E$. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of $F$ and the sharp reconstruction of $F$. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.Comment: 37 page

Spatio-temporal evolution of intraplate strike-slip faulting: the Neogene-Quaternary Kuh-e-Faghan Fault, Central Iran

Central Iran provides an ideal region to study the long-term morphotectonic response to the nucleation and propagation of intraplate faulting. In this study, a multidisciplinary approach that integrates structural and stratigraphic field investigations with apatite (U+Th)/He (AHe) thermochronometry is used to reconstruct the spatio-temporal evolution of the Kuh-e-Faghan Fault (KFF) in northeastern Central Iran. The KFF is a narrow, ca. 80 km long, deformation zone that consists of three main broadly left stepping, E-W trending, dextral fault strands that cut through the Mesozoic-Paleozoic substratum and the Neogene-Quaternary sedimentary cover. The AHe thermochronometry results indicate that the intra-fault blocks along the KFF experienced two major episodes of fault-related exhumation at ~18 Ma and ~4 Ma. The ~18 Ma faulting/exhumation episode is chiefly recorded by the structure and depositional architecture of the Neogene deposits along the KFF. A source-to-sink scenario can be reconstructed for this time frame, where topographic growth caused the synchronous erosion/exhumation of the pre-Neogene units and deposition of the eroded material in the surrounding fault-bounded continental depocenters. Successively, the KFF gradually entered a period of relative tectonic quiescence and, probably, of regional subsidence during which a thick pile of fine-grained onlapping sediments were deposited. This may have caused resetting of the He ages of apatite in the pre-Neogene and the basal Neogene successions. The ~4 Ma faulting episode caused the final exhumation of the fault system, resulting in the current fault zone and topography. The two fault-related exhumation episodes fit with the regional early Miocene collision-enhanced uplift/exhumation, and the late Miocene–early Pliocene widespread tectonic reorganization of the Iranian plateau. The reconstructed long term, spatially and temporally punctuated fault system evolution in intraplate Central Iran during Neogene-Quaternary times may reflect states of far-field stress changes at the collisional boundaries

Barycentric decomposition of quantum measurements in finite dimensions

We analyze the convex structure of the set of positive operator valued measures (POVMs) representing quantum measurements on a given finite dimensional quantum system, with outcomes in a given locally compact Hausdorff space. The extreme points of the convex set are operator valued measures concentrated on a finite set of k \le d^2 points of the outcome space, d< \infty being the dimension of the Hilbert space. We prove that for second countable outcome spaces any POVM admits a Choquet representation as the barycenter of the set of extreme points with respect to a suitable probability measure. In the general case, Krein-Milman theorem is invoked to represent POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points of the outcome space.Comment: !5 pages, no figure

Spreading of a Macroscopic Lattice Gas

We present a simple mechanical model for dynamic wetting phenomena. Metallic balls spread along a periodically corrugated surface simulating molecules of liquid advancing along a solid substrate. A vertical stack of balls mimics a liquid droplet. Stochastic motion of the balls, driven by mechanical vibration of the corrugated surface, induces diffusional motion. Simple theoretical estimates are introduced and agree with the results of the analog experiments, with numerical simulation, and with experimental data for microscopic spreading dynamics.Comment: 19 pages, LaTeX, 9 Postscript figures, to be published in Phy. Rev. E (September,1966