Spectral analysis of finite-time correlation matrices near equilibrium phase transitions

We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be derived from the spatial correlations. In practice time series are short in the sense that they are either not stationary over long time intervals or not available over long time intervals. Also we usually do not have time series for all variables available. We shall make numerical simulations on a two-dimensional Ising model with the usual Metropolis algorithm as time evolution. Using all spins on a grid with periodic boundary conditions we find a power law, that is, for large grids, compatible with the analytic result. We still find a power law even if we choose a fairly small subset of grid points at random. The exponents of the power laws will be smaller under such circumstances. For very short time series leading to singular correlation matrices we use a recently developed technique to lift the degeneracy at zero in the spectrum and find a significant signature of critical behavior even in this case as compared to high temperature results which tend to those of random matrix models.Comment: 4 pages, 5 figure

Individualism as Principle: Its Emergence, Institutionalization, and Contradictions, political philosophy

Symposium: Law and Civil Societ

Parabolic manifolds in the scattering map and direct quantum processes

International audienceWe analyse the quantum effects of parabolic manifolds in Jung's iterated scattering map. For this purpose we consider the classical map proposed previously to be the exact classical analogue of Rydberg molecules calculated with the approximations relevant to the multichannel quantum defect theory for energies above the ionization threshold. The part corresponding to positive electron energies can be viewed as a Jung scattering map without the trivial direct processes. This map contains a parabolic manifold of fixed points which gives rise to a regular series of quantum states which behave very much like eigenchannels that miss the target

Unified theory of bound and scattering molecular Rydberg states as quantum maps

Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map

Microwave fidelity studies by varying antenna coupling

The fidelity decay in a microwave billiard is considered, where the coupling to an attached antenna is varied. The resulting quantity, coupling fidelity, is experimentally studied for three different terminators of the varied antenna: a hard wall reflection, an open wall reflection, and a 50 Ohm load, corresponding to a totally open channel. The model description in terms of an effective Hamiltonian with a complex coupling constant is given. Quantitative agreement is found with the theory obtained from a modified VWZ approach [Verbaarschot et al, Phys. Rep. 129, 367 (1985)].Comment: 9 pages 5 figur

Happiness Drives Performance

The article of record as published may be found at https://markets.businessinsider.com/news/stocks/happiness-drives-performance-103120049

Multi-cyclic and isotopically diverse silicic magma generation in an arc volcano : Gorely Eruptive Center, Kamchatka, Russia

The Kamchatka Peninsula is home to some of the most frequent and prolific subduction-related volcanic activity in the world, with the largest number of caldera-forming eruptions per length of the volcanic arc. Among those, Gorely volcano has a topographically prominent Late Pleistocene caldera (13 km × 12 km, estimated to have produced >100 km3 of magma), which is now almost completely filled by a central cone. We report new 40Ar/39Ar ages and geochemical and isotopic data for newly recognized Mid-Pleistocene ignimbrite units of large but unknown volume sourced from the Gorely eruptive center, most of which were deposited in marginal glacial conditions. These ignimbrites have crystallinities of 9–24% and most are quartz-, amphibole-, and zircon-undersaturated. Additionally, we studied 32 eruptive units, including stratigraphically constrained Holocene tephra, and pre- and post-caldera lava sequences, to understand the petrogenetic and temporal evolution of this long-lived, multi-cyclic, arc volcano. Material erupted prior to the formation of the modern Gorely edifice, including the voluminous ignimbrites and eruptions of the ‘pra-Gorely’ stage, consist primarily of dacite and andesite, whereas sequences of the modern Gorely edifice are represented by basalt to basaltic andesite. MELTS and EC-AFC modeling shows that it is possible to obtain silicic compositions near those of the evolved ignimbrite compositions through 60–75% fractional crystallization at 1 kbar and nickel–nickel oxide (NNO) oxygen fugacity. However, our newly compiled major and trace element data for Gorely yield two separate bimodal peaks in a SiO2–frequency diagram, showing a prominent Daly Gap, with a deficiency in andesite. Trace element concentrations define two separate trends, one for more silicic and another for more mafic sequences. Additionally, δ18Omelt values reconstructed from coexisting plagioclase and clinopyroxene phenocrysts range from a low value of 4·85‰ to a normal value of 6·22‰. The low δ18O values range throughout the known lifespan of Gorely, with the lowest value being from the first known ignimbrite to erupt, indicating episodic but temporally decreasing crustal assimilation of previously hydrothermally altered material. 87Sr/86Sr and 143Nd/144Nd ratios show wide ranges from 0·70328 to 0·70351 and from 0·51303 to 0·51309 respectively, also suggesting incorporation of surrounding crust, although there are less clear trends throughout the lifespan of Gorely. The combination of light and diverse δ18O values with elevated 87Sr/86Sr and low 143Nd/144Nd ratios suggests contamination by older and isotopically diverse, low-δ18O country-rocks, such as the neighboring 11 Ma Akhomten granitic massif, which shows ranges in δ18O, 87Sr/86Sr, and 144Nd/143Nd values overlapping with the Gorely magmas. In addition, the presence of glomerocrysts and mafic enclaves in the majority of Gorely dacites indicates a period of crystal settling and subsequent intrusion of hot, primitive basalt that probably triggered eruption. Finally, elevated Nb concentrations relative to other Kamchatkan volcanoes suggest that Gorely magmas may involve an enriched component, probably caused by delamination of a lower crustal root. Our results argue for an incremental view of silicic magma generation at so-called ‘long-term eruptive centers’, in Kamchatka and worldwide, consisting of alternating episodes of magmatic and hydrothermal activity, and glacial advances and retreats. We demonstrate that large-volume, isotopically distinct, silicic magma can be generated rapidly between cone-building phases of volcanic activity through a combination of fractional crystallization, assimilation of older country rocks, and shallow assimilation of hydrothermally altered but otherwise petrochemically similar older intracaldera tuffs and intrusions. These transient shallow silicic magma chambers empty nearly completely in ignimbrite-forming eruptions after 103–105 years of assembly, partially triggered by glacial surface dynamics

Multi-Cyclic and Isotopically Diverse Silicic Magma Generation in an Arc Volcano: Gorely Eruptive Center, Kamchatka, Russia

The Kamchatka Peninsula is home to some of the most frequent and prolific subduction-related volcanic activity in the world, with the largest number of caldera-forming eruptions per length of the volcanic arc. Among those, Gorely volcano has a topographically prominent Late Pleistocene caldera (13 km × 12 km, estimated to have produced >100 km3 of magma), which is now almost completely filled by a central cone. We report new 40Ar/39Ar ages and geochemical and isotopic data for newly recognized Mid-Pleistocene ignimbrite units of large but unknown volume sourced from the Gorely eruptive center, most of which were deposited in marginal glacial conditions. These ignimbrites have crystallinities of 9-24% and most are quartz-, amphibole-, and zircon-undersaturated. Additionally, we studied 32 eruptive units, including stratigraphically constrained Holocene tephra, and pre- and post-caldera lava sequences, to understand the petrogenetic and temporal evolution of this long-lived, multi-cyclic, arc volcano. Material erupted prior to the formation of the modern Gorely edifice, including the voluminous ignimbrites and eruptions of the ‘pra-Gorely' stage, consist primarily of dacite and andesite, whereas sequences of the modern Gorely edifice are represented by basalt to basaltic andesite. MELTS and EC-AFC modeling shows that it is possible to obtain silicic compositions near those of the evolved ignimbrite compositions through 60-75% fractional crystallization at 1 kbar and nickel-nickel oxide (NNO) oxygen fugacity. However, our newly compiled major and trace element data for Gorely yield two separate bimodal peaks in a SiO2-frequency diagram, showing a prominent Daly Gap, with a deficiency in andesite. Trace element concentrations define two separate trends, one for more silicic and another for more mafic sequences. Additionally, δ18Omelt values reconstructed from coexisting plagioclase and clinopyroxene phenocrysts range from a low value of 4·85‰ to a normal value of 6·22‰. The low δ18O values range throughout the known lifespan of Gorely, with the lowest value being from the first known ignimbrite to erupt, indicating episodic but temporally decreasing crustal assimilation of previously hydrothermally altered material. 87Sr/86Sr and 143Nd/144Nd ratios show wide ranges from 0·70328 to 0·70351 and from 0·51303 to 0·51309 respectively, also suggesting incorporation of surrounding crust, although there are less clear trends throughout the lifespan of Gorely. The combination of light and diverse δ18O values with elevated 87Sr/86Sr and low 143Nd/144Nd ratios suggests contamination by older and isotopically diverse, low-δ18O country-rocks, such as the neighboring 11 Ma Akhomten granitic massif, which shows ranges in δ18O, 87Sr/86Sr, and 144Nd/143Nd values overlapping with the Gorely magmas. In addition, the presence of glomerocrysts and mafic enclaves in the majority of Gorely dacites indicates a period of crystal settling and subsequent intrusion of hot, primitive basalt that probably triggered eruption. Finally, elevated Nb concentrations relative to other Kamchatkan volcanoes suggest that Gorely magmas may involve an enriched component, probably caused by delamination of a lower crustal root. Our results argue for an incremental view of silicic magma generation at so-called ‘long-term eruptive centers', in Kamchatka and worldwide, consisting of alternating episodes of magmatic and hydrothermal activity, and glacial advances and retreats. We demonstrate that large-volume, isotopically distinct, silicic magma can be generated rapidly between cone-building phases of volcanic activity through a combination of fractional crystallization, assimilation of older country rocks, and shallow assimilation of hydrothermally altered but otherwise petrochemically similar older intracaldera tuffs and intrusions. These transient shallow silicic magma chambers empty nearly completely in ignimbrite-forming eruptions after 103-105 years of assembly, partially triggered by glacial surface dynamic