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PaRDeS, the journal of the German Association for Jewish Studies, aims at exploring the fruitful and multifarious cultures of Judaism as well as their relations to their environment within diverse areas of research. In addition, the journal promotes Jewish Studies within academic discourse and reflects on its historic and social responsibilities.
Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements-the principles of relativity and light speed invariance-are used to derive the mathematical structure of Minkowski space-time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.
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.
We establish a link between unitary relaxation dynamics after a quench in closed many-body systems and the entanglement in the energy eigenbasis. We find that even if reduced states equilibrate, they can have memory on the initial conditions even in certain models that are far from integrable. We show that in such situations the equilibrium states are still described by a maximum entropy or generalized Gibbs ensemble, regardless of whether a model is integrable or not, thereby contributing to a recent debate. In addition, we discuss individual aspects of the thermalization process, comment on the role of Anderson localization, and collect and compare different notions of integrability.
The sediment profile from Lake Goscia(z) over dot in central Poland comprises a continuous, seasonally resolved and exceptionally well-preserved archive of the Younger Dryas (YD) climate variation. This provides a unique opportunity for detailed investigation of lake system responses during periods of rapid climate cooling (YD onset) and warming (YD termination). The new varve record of Lake Goscia(z) over dot presented here spans 1662 years from the late Allerod (AL) to the early Preboreal (PB). Microscopic varve counting provides an independent chronology with a YD duration of 1149+14/-22 years, which confirms previous results of 1140 +/- 40 years. We link stable oxygen isotopes and chironomid-based air temperature reconstructions with the response of various geochemical and varve microfacies proxies especially focusing on the onset and termination of the YD. Cooling at the YD onset lasted similar to 180 years, which is about a century longer than the terminal warming that was completed in similar to 70 years. During the AL/YD transition, environmental proxy data lagged the onset of cooling by similar to 90 years and revealed an increase of lake productivity and internal lake re-suspension as well as slightly higher detrital sediment input. In contrast, rapid warming and environmental changes during the YD/PB transition occurred simultaneously. However, initial changes such as declining diatom deposition and detrital input occurred already a few centuries before the rapid warming at the YD/PB transition. These environmental changes likely reflect a gradual increase in summer air temperatures already during the YD. Our data indicate complex and differing environmental responses to the major climate changes related to the YD, which involve different proxy sensitivities and threshold processes.
The performance of grating interferometers coming up now for imaging interfaces within materials depends on the efficiency (visibility) of their main component, namely the phase grating. Therefore, experiments with monochromatic synchrotron radiation and corresponding simulations are carried out. The visibility of a phase grating is optimized by different photon energies, varying detector to grating distances and continuous rotation of the phase grating about the grid lines. Such kind of rotation changes the projected grating shapes, and thereby the distribution profiles of phase shifts. This yields higher visibilities than derived from ideal rectangular shapes. By continuous grating rotation and variation of the propagation distance, we achieve 2D visibility maps. Such maps provide the visibility for a certain combination of grating orientation and detector position. Optimum visibilities occur at considerably smaller distances than in the standard setup.
The sediment profile from Lake Goscia(z) over dot in central Poland comprises a continuous, seasonally resolved and exceptionally well-preserved archive of the Younger Dryas (YD) climate variation. This provides a unique opportunity for detailed investigation of lake system responses during periods of rapid climate cooling (YD onset) and warming (YD termination). The new varve record of Lake Goscia(z) over dot presented here spans 1662 years from the late Allerod (AL) to the early Preboreal (PB). Microscopic varve counting provides an independent chronology with a YD duration of 1149+14/-22 years, which confirms previous results of 1140 +/- 40 years. We link stable oxygen isotopes and chironomid-based air temperature reconstructions with the response of various geochemical and varve microfacies proxies especially focusing on the onset and termination of the YD. Cooling at the YD onset lasted similar to 180 years, which is about a century longer than the terminal warming that was completed in similar to 70 years. During the AL/YD transition, environmental proxy data lagged the onset of cooling by similar to 90 years and revealed an increase of lake productivity and internal lake re-suspension as well as slightly higher detrital sediment input. In contrast, rapid warming and environmental changes during the YD/PB transition occurred simultaneously. However, initial changes such as declining diatom deposition and detrital input occurred already a few centuries before the rapid warming at the YD/PB transition. These environmental changes likely reflect a gradual increase in summer air temperatures already during the YD. Our data indicate complex and differing environmental responses to the major climate changes related to the YD, which involve different proxy sensitivities and threshold processes.