Propagation and spectral properties of quantum walks in electric fields

We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\Phi$, e.g., on whether $\Phi/(2\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.Comment: 7 pages, 4 figure

Chemical Geodynamics Insights From a Machine Learning Approach

The radiogenic isotope heterogeneity of oceanic basalts is often assessed using 2D isotope ratio diagrams. But because the underlying data are at least six dimensional (87Sr/86Sr, 143Nd/144Nd, 176Hf/177Hf, and 208,207,206Pb/204Pb), it is important to examine isotopic affinities in multi‐dimensional data space. Here, we apply t‐distributed stochastic neighbor embedding (t‐SNE), a multi‐variate statistical data analysis technique, to a recent compilation of radiogenic isotope data of mid ocean ridge (MORB) and ocean island basalts (OIB). The t‐SNE results show that the apparent overlap of MORB‐OIB data trends in 2‐3D isotope ratios diagrams does not exist in multi‐dimensional isotope data space, revealing that there is no discrete “component” that is common to most MORB‐OIB mantle sources on a global scale. Rather, MORB‐OIB sample stochastically distributed small‐scale isotopic heterogeneities. Yet, oceanic basalts with the same isotopic affinity, as identified by t‐SNE, delineate several globally distributed regional domains. In the regional geodynamic context, the isotopic affinity of MORB and OIB is caused by capturing of actively upwelling mantle by adjacent ridges, and thus melting of mantle with similar origin in on, near, and off‐ridge settings. Moreover, within a given isotopic domain, subsidiary upwellings rising from a common deep mantle root often feed OIB volcanism over large surface areas. Overall, the t‐SNE results define a fundamentally new basis for relating isotopic variations in oceanic basalts to mantle geodynamics, and may launch a 21st century era of “chemical geodynamics.”Plain Language Summary: The isotopic heterogeneity of basalts erupted at mid ocean ridges (MORB) and ocean islands (OIB) reflects the chemical evolution of Earth's mantle. The visual inspection of various 2D isotope ratio diagrams has fueled a four decade‐long discussion whether basalt heterogeneity reflects melting of only a small number of mantle components, and in particular, whether the apparent overlap of local data trends in global 2D isotope ratio diagrams indicates that melting of a common mantle component contributes to most MORB‐OIB. Here, we use multi‐variate statistical data analysis to show that the apparent overlap of MORB‐OIB data trends in 2D isotope ratio diagrams does not exist in multi‐dimensional isotope data space. Our finding invalidates any inference made for mantle compositional evolution based on the previously proposed existence of a common mantle component, its potential nature or distribution within the mantle. Rather, global MORB‐OIB sample small‐scale isotopic heterogeneities that are distributed stochastically in the Earth's mantle. Yet, MORB‐OIB with the same isotopic affinity, as identified by our multi‐variate data analysis, delineate several globally distributed regional domains. Within the regional geodynamic context, this discovery forms a fundamentally new basis for relating isotopic variations in MORB‐OIB to mantle geodynamics.Key Points: Multi‐variate statistical data analysis (t‐distributed stochastic neighbor embedding) identifies global Sr‐Nd‐Hf‐Pb isotopic affinities of oceanic basalts. There is no “common mantle component;” rather, global mid ocean ridge‐ocean island basalts sample stochastically distributed small‐scale isotopic heterogeneities. Globally distributed regional domains of isotopically alike oceanic lavas define a new basis for relating isotopic variations to geodynamics.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung http://dx.doi.org/10.13039/501100001711DAAD, German Academic Exchange Servicehttps://doi.org/10.25625/0SVW6Shttps://doi.org/10.25625/BQENG

Ubiquitous ultra-depleted domains in Earth’s mantle

Partial melting of Earth’s mantle generates oceanic crust and leaves behind a chemically depleted residual mantle. The time-integrated composition of this chemically depleted mantle is generally inferred from basalts produced at mid-ocean ridges. However, isotopic differences between oceanic mantle rocks and mid-ocean ridge basalts suggest that mantle and basalt composition could differ. Here we measure neodymium isotope ratios in olivine-hosted melt inclusions from lavas of the Azores mantle plume. We find neodymium isotope ratios that include the highest values measured in basalts, and suggest that melts from ultra-depleted mantle contribute to the isotopic diversity of the erupted lavas. Ultra-depleted melts have exceedingly low preservation potential during magma extraction and evolution due to progressive mixing with melts that are enriched in incompatible elements. A notable contribution of ultra-depleted melts to the Azores mantle plume therefore implies that variably depleted mantle is the volumetrically dominant component of the Azores plume. We argue that variably depleted mantle, sometimes ranging to ultra-depleted compositions, may be a ubiquitous part of most ocean island and mid-ocean ridge basalt sources. If so, Earth’s mantle may be more depleted than previously thought, which has important implications for the rate of mass exchange between crust and mantle, plume dynamics and compositional stratification of Earth’s mantle

Chemical Geodynamics Insights From a Machine Learning Approach

Abstract The radiogenic isotope heterogeneity of oceanic basalts is often assessed using 2D isotope ratio diagrams. But because the underlying data are at least six dimensional (87Sr/86Sr, 143Nd/144Nd, 176Hf/177Hf, and 208,207,206Pb/204Pb), it is important to examine isotopic affinities in multi‐dimensional data space. Here, we apply t‐distributed stochastic neighbor embedding (t‐SNE), a multi‐variate statistical data analysis technique, to a recent compilation of radiogenic isotope data of mid ocean ridge (MORB) and ocean island basalts (OIB). The t‐SNE results show that the apparent overlap of MORB‐OIB data trends in 2‐3D isotope ratios diagrams does not exist in multi‐dimensional isotope data space, revealing that there is no discrete “component” that is common to most MORB‐OIB mantle sources on a global scale. Rather, MORB‐OIB sample stochastically distributed small‐scale isotopic heterogeneities. Yet, oceanic basalts with the same isotopic affinity, as identified by t‐SNE, delineate several globally distributed regional domains. In the regional geodynamic context, the isotopic affinity of MORB and OIB is caused by capturing of actively upwelling mantle by adjacent ridges, and thus melting of mantle with similar origin in on, near, and off‐ridge settings. Moreover, within a given isotopic domain, subsidiary upwellings rising from a common deep mantle root often feed OIB volcanism over large surface areas. Overall, the t‐SNE results define a fundamentally new basis for relating isotopic variations in oceanic basalts to mantle geodynamics, and may launch a 21st century era of “chemical geodynamics.

O isotopes in the Azores : mantle melting versus AFC

The Azores archipelago in the central North Atlantic has been studied wideley over the last few decades, one reason being its formation history that is related to a slow-upwelling mantle plume. The plume sources identified in these ocean islands are predominantly inferred from Sr-Nd-Pb-(Hf) radiogenic isotope data along with major and trace element geochemistry. Contrastingly, few studies have dealt with the variability in stable isotopic composition. Here, we present a detailed isotopic study of oxygen isotope ratios (¹⁸O/¹⁶O) in olivines, clinopyroxenes and plagioclases that allow to infer on the quantiative and qualitativey involvement of altered oceanic crust (AOC) during ascent of the magmas. This is particularly important when aiming to place constraints on the primary O isotopic composition of the mantle plume source. Furthermore, such estimates can be combined with other newly availabe isotope data of boron (B) and Lithium (Li) of the Azores lavas. We provide a comprehensive data set of phenocryst O isotope data obtained by laser fluorination along with their individual mineral chemistry measured by electron microprobe on the same grain. The phenocrysts originate from lavas from the entire archipelago, namely Faial and Pico (central Azores) and Sao Miguel (east Azores), and, for the first time, include data for the two islands west of the mid-Atlantic ridge (MAR), Flores and Corvo. The samples were selected from geochemically well characterised host lavas such that the newly obtained O data are placed in a tight geochemical and petrological background. Our data indicate that the eastern Azores lavas are characterized by O ratios (i.e. δ¹⁸O₍ₒ₁₎ 4.7-5.2‰) slightly lighter than the primitive mantle range (δ¹⁸O₍ₒ₁₎ approximately 5.2±0.2‰), while the western lavas fall within the latter range. However, we find that decreasing forsterite contents in olivines are tightly correlated with decreasing δ¹⁸O₍ₒ₁₎. Such systematic is also observed in Hawaii', which is explained by assimilation of hydrothermally altered material during the crystallization-differentiation process. We test whether assimilation fractional crystallization (AFC) models sufficiently describe the δ¹⁸O₍ₒ₁₎ systematic of the Azores lavas, and if the highest forsterite olivines can be used to distinguish the δ¹⁸O₍ₒ₁₎ signal of the plume source. Our data are also compared with those of the MAR to better evaluate the nature and distribution of enriched components in the north Atlantic mantle.1 page(s

Plume-ridge interaction : constraints on melting dynamics from the Azores and Iceland

Ocean Island Basalts (OIB) erupted in the vincinity of Mid-Ocean Ridges (MOR) provide important information on melting processes, melt movement and composition of the Earth's mantle. In particular the major element, trace element and Sr-Nd-Pb isotope ratios allow for constraints on the distinct melting behaviour of enriched and depleted mantle sources, their along and across axis distribution and potential changes in melting depth and melting temperatures. While the flow of melts into the Mid-Atlantic Ridge (MAR) in the Azores and Iceland has been the subject of several studies, both plumes exhibit active volcanism on the western side of the Mid-Atlantic Ridge away from the proposed plume locality. Such off-axis volcanism beneath the North-American plate is comparable for the two OIB settings in terms of trace element and isotopic source composition relative to the main plume centre. Incompatible trace element ratios of Nb/Zr, Ta/Hf and La/Sm are elevated by similar factors in the off-axis (western) lavas when compared to the lavas from the plume centre. We compare the melting dynamics (i.e. P-T conditions of basalt generation) underneath the Snaefelsness peninsula (Iceland) with those underneath Flores and Corvo islands (Azores); both examples of unusual off-axis and "off-plume" magmatism. We demonstrate that Iceland and the Azores exhibit comparable excess temperatures, but that melting underneath the western Azores islands is initiated deeper. The sources in the Azores are more enriched and degrees of partial melting are slightly lower than compared to Snaefellsness. This implies that for both cases melting dynamics are largely controlled by the geochemical composition of the source and possibly lithosphere thickness rather than upwelling rate. The differences between eastern and western (i.e. plume related vs. "off-plume") sources may reflect different proportions of enriched melts during binary mixing with depleted MORB mantle (DMM) sources.1 page(s

Magmatic Evidence for Carbonate Metasomatism in the Lithospheric Mantle underneath the Ohre (Eger) Rift

Magmas erupted in intracontinental rifts typically form from melting of variable proportions of asthenospheric or lithospheric mantle sources and ascend through thick continental lithosphere. This ascent of magma is accompanied by differentiation and assimilation processes. Understanding the composition of rift-related intracontinental volcanism is important, particularly in densely populated active rift zones such as the Ohre (Eger) Rift in Central Europe. We have sampled and analysed nephelinites from Zelezna hurka (Eisenbuhl), the youngest (<300 ka) Quaternary volcano related to the Ohre Rift where frequent earthquake swarms indicate continuing magmatic activity in the crust. This nephelinite volcano is part of a larger eruptive centre (Mytina Maar) representing a single locality of recurrent volcanism in the Ohre Rift. We present a detailed petrographic, mineralogical and geochemical study (major and trace elements and Sr-Nd-Hf-O isotopes) of Zelezna' hurka to further resolve the magmatic history and mantle source of the erupted melt. We find evidence for a highly complex evolution of the nephelinitic melts during their ascent to the surface. Most importantly, mixing of melts derived from different sources and of strong chemical contrast controls the composition of the erupted volcanic products. These diverse parental melts originate from a highly metasomatized subcontinental lithospheric mantle (SCLM) source. We use a combined approach based on mineral, glass and whole-rock compositions to show that the mantle underneath the western Ohre Rift is metasomatized dominantly by carbonatitic melts. The nephelinites of Zelezna hurka formed by interaction between a carbonatitic melt and residual mantle peridotite, partial crystallization in the lithospheric mantle and minor assimilation of upper continental crust. Thermobarometric estimates indicate that the stagnation levels of the youngest volcanism in this part of the Ohre Rift were deeper than the focal depths of recent earthquake swarms, indicating that those are not directly linked to magma ascent. Furthermore, close mineralogical and geochemical similarities between the Zelezna 'hurka nephelinite and fresh kimberlites may point towards a genetic link between kimberlites, melilitites and nephelinites

Oxygen isotopes in the Azores islands : crustal assimilation recorded in olivine

Oxygen isotope ratios of olivine have become a widely used tool for the study of magmatic systems, especially in the interpretation of source heterogeneities in mantle plume-derived ocean island basalts. The underlying assumption is that fresh minerals provide a better guide to magma δ¹⁸O than bulk rock analyses and that olivine is also likely to be a major phenocryst phase in primitive magmas. However, distinctions between source compositions and the effects of subsequent magma evolution have not always been thoroughly scrutinized. For the Azores samples investigated here, we can demonstrate that the δ¹⁸O variation (+4.84‰ to +5.25‰ Vienna standard mean ocean water) observed in the olivine phenocryst population is closely linked to evolution in the host magmas during ascent to the surface. We observe a linear, positive correlation between forsterite (Fo) content and δ¹⁸O in all of the individual island lava suites. This forces us to conclude that the low oxygen isotope ratios result from combined assimilation and fractional crystallization processes, the assimilant being hydrothermally (temperature > 250°C) altered, lower oceanic crust. Linear regression of the measured δ¹⁸O olivine values to Fo₈₉ suggests a homogeneous mantle source with δ¹⁸O = +5.2‰ ± 0.1‰.4 page(s