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

A random matrix approach to decoherence

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems. We introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find no significant differences except for very low-dimensional spaces.Comment: 11 pages, 5 eps-figure

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

Nonperiodic echoes from mushroom billiard hats

Mushroom billiards have the remarkable property to show one or more clear cut integrable islands in one or several chaotic seas, without any fractal boundaries. The islands correspond to orbits confined to the hats of the mushrooms, which they share with the chaotic orbits. It is thus interesting to ask how long a chaotic orbit will remain in the hat before returning to the stem. This question is equivalent to the inquiry about delay times for scattering from the hat of the mushroom into an opening where the stem should be. For fixed angular momentum we find that no more than three different delay times are possible. This induces striking nonperiodic structures in the delay times that may be of importance for mesoscopic devices and should be accessible to microwave experiments.Comment: Submitted to Phys. Rev. E without the appendi

Intruder States and their Local Effect on Spectral Statistics

The effect on spectral statistics and on the revival probability of intruder states in a random background is analysed numerically and with perturbative methods. For random coupling the intruder does not affect the GOE spectral statistics of the background significantly, while a constant coupling causes very strong correlations at short range with a fourth power dependence of the spectral two-point function at the origin.The revival probability is significantly depressed for constant coupling as compared to random coupling.Comment: 18 pages, 10 Postscript figure

Correlations between spectra with different symmetry: any chance to be observed?

A standard assumption in quantum chaology is the absence of correlation between spectra pertaining to different symmetries. Doubts were raised about this statement for several reasons, in particular, because in semiclassics spectra of different symmetry are expressed in terms of the same set of periodic orbits. We reexamine this question and find absence of correlation in the universal regime. In the case of continuous symmetry the problem is reduced to parametric correlation, and we expect correlations to be present up to a certain time which is essentially classical but larger than the ballistic time

Loschmidt echoes in two-body random matrix ensembles

Fidelity decay is studied for quantum many-body systems with a dominant independent particle Hamiltonian resulting e.g. from a mean field theory with a weak two-body interaction. The diagonal terms of the interaction are included in the unperturbed Hamiltonian, while the off-diagonal terms constitute the perturbation that distorts the echo. We give the linear response solution for this problem in a random matrix framework. While the ensemble average shows no surprising behavior, we find that the typical ensemble member as represented by the median displays a very slow fidelity decay known as ``freeze''. Numerical calculations confirm this result and show, that the ground state even on average displays the freeze. This may contribute to explanation of the ``unreasonable'' success of mean field theories.Comment: 9 pages, 5 figures (6 eps files), RevTex; v2: slight modifications following referees' suggestion

Ancient Egypt 1916 Part 2

Part 2 of the 1916 Ancient Egypt books. Contents include the Gorringe collection, an early figure of Taurt, Egypt in the Grail Romance, and the queenly title, XXIInd dynasty.https://knowledge.e.southern.edu/kweeks_coll/1006/thumbnail.jp