Symplectic geometry of entanglement

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In particular, using Kostant-Sternberg theorem, we show that separable states form a unique Kaehler orbit, whereas orbits of entanglement states are characterized by different degrees of degeneracy of the canonical symplectic form on the complex projective space. The degree of degeneracy may be thus used as a new geometric measure of entanglement and we show how to calculate it for various multiparticle systems providing also simple criteria of separability. The presented method is general and can be applied also under different additional symmetry conditions stemming, eg. from the indistinguishability of particles.Comment: LaTex, 31 pages, typos correcte

Small bound for birational automorphism groups of algebraic varieties (with an Appendix by Yujiro Kawamata)

We give an effective upper bound of |Bir(X)| for the birational automorphism group of an irregular n-fold (with n = 3) of general type in terms of the volume V = V(X) under an ''albanese smoothness and simplicity'' condition. To be precise, |Bir(X)| < d_3 V^{10}. An optimum linear bound |Bir(X)|-1 < (1/3)(42)^3 V is obtained for those 3-folds with non-maximal albanese dimension. For all n > 2, a bound |Bir(X)| < d_n V^{10} is obtained when alb_X is generically finite, alb(X) is smooth and Alb(X) is simple.Comment: Mathematische Annalen, to appea

Derivation of determinantal structures for random matrix ensembles in a new way

There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a new approach to calculate averages over ratios of characteristic polynomials. At first sight paradoxically, one can coin our approach "supersymmetry without supersymmetry" because we use structures from supersymmetry without actually mapping onto superspaces. We address two kinds of integrals which cover a wide range of applications for random matrix ensembles. For probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way. As a new application we derive an expression for the k-point correlation function of an arbitrary rotation invariant probability density over the Hermitian matrices in the presence of an external field.Comment: 36 pages; 2 table

Surficial geology of the Wittmann and Hieroglyphic Mountains Southwest 7.5' Quadrangles, northern Maricopa County, Arizona

Most of southern and western Arizona lie within the Basin and Range physiographic province, a region characterized by broad valleys and linear mountain ranges. The valleys are deeply filled with alluvium that has eroded from adjacent mountains during the last 10 My 1. This aggradation has been driven by tectonism and climate change, although regional tectonic stability within the last 5 My suggests that climate change is the more recent dominant driving force (Morrison, 1985). Climatic fluctuations between relatively wet and dry conditions have resulted in pulses of aggradation producing a mosaic of different aged alluvial deposits in piedmont areas. Urban development on piedmonts, especially in the Phoenix Basin, has created a need to better understand the distribution and nature of these deposits. Surficial geologic maps characterize and distinguish different piedmont deposits on the basis of age and genesis. Such information provides baseline data for evaluating geologic hazards potential (e.g., Pearthree, 1991), locating possible source areas for industrial minerals (e.g., Wellendorf et aI., 1986), and determining locations favorable for groundwater recharge (e.g., Huckleberry, 1994). Moreover, these maps are also useful for assessing the potential for buried cultural resources and providing insight into local geologic history and landscape evolution. This report presents the results of surficial geologic mapping in the Wittmann and Hieroglyphic Mountains SW 7.5' quadrangles located northwest of metropolitan Phoenix (Figure 1). The project area includes segments of U.S. Highway 60, State Route 79, and the Central Arizona Project Canal, and is contiguous to the south with the White Tanks Mountain piedmont area previously mapped by Field and Pearthree (1991). (24 pages; 2 map sheets, map scale 1:24,000)Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]

Geomorphology and Surficial Geology of Garden Canyon, Huachuca Mountains, Arizona

Increasing destruction of natural habitat in the United States due to growing population has resulted in a series of laws, policies, and guidelines designed to protect and better manage natural resources. Garden Canyon, located in the pine and oak-covered Huachuca Mountains in the southern part of the Fort Huachuca Military Reservation (Figure 1), contains many plant and animal species that are federally listed or are candidates for listing as threatened or endangered. The geomorphology and surficial geology of Garden Canyon were assessed through interpretation of aerial photographs and soil maps and extensive fieldwork. Color aerial photography (1:23,000 scale) and Soil Conservation Service soil maps were used to distinguish geologic surfaces. Geomorphic surfaces of different ages and landform type were distinguished and mapped using criteria such as topographic position, degree of stream dissection, degree of surface clast weathering, and soil development (see Bull, 1991). Map unit boundaries and surface correlations were then field checked. Age estimates for the different surfaces are based on correlations to surfaces with similar weathering and soil characteristics that have radiometric age control and are located in the lower Colorado River Valley (Bull, 1991) and middle Rio Grande Valley (Gile et al., 1983).Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]

Historical channel changes on the San Pedro River, southeastern Arizona

The San Pedro River in southeast Arizona is by no means a major watercourse in the Southwest, but yet it is probably one of the most-studied rivers in the region. In particular, the upper San Pedro River has been the topic of study by geologists, geographers, hydrologists, and ecologists interested in environmental change (see Bahr, 1991 and Cooke and Reeves, 1976 for an overview). Since 1870, inhabitants of the San Pedro River Valley have witnessed substantial vegetation change (Bahr, 1991; Henderson and MinkIey, 1986; Hastings, 1959; Hastings and Turner, 1965; Leopold, 1951) as well as changes in the geometry and hydrologic regime of the river (Cooke and Reeves, 1976; Hereford, 1993; Hereford and Betancourt, 1993). After decades of multidisciplinary research, the chronology of historic channel changes, at least on the upper San Pedro River, is well defined, although the reasons why the channel has changed are still debated (i.e., natural vs. anthropogenic forces). What the physical characteristics of the San Pedro River were in 1912 is the topic of this report. Because the State of Arizona's claim to ownership of river channels within its boundaries hinges on their navigability at time of statehood, this report is designed to provide baseline information on the historical physical characteristics of the San Pedro River channel and how they have changed through time. It is clear that the San Pedro River was experiencing changes in channel geometry in 1912, but unfortunately there are few descriptions of the channel during that year. The physical characteristics of the river thus must be interpolated from descriptions made before and after 1912. Understanding the geomorphic properties of the river helps to refine the interpolation. ( 35 pages)Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]

Rates of Holocene Soil Formation in South-Central Arizona

Establishment of chronology is essential to historical sciences like geology and archaeology. In geology, it is the starting point for understanding biological and landscape evolution. In archaeology, it is the framework for attaining the more important goal of understanding cultural change through time. One of the tools geologists and archaeologists use to assess chronology is stratigraphy. Both specialists employ the principle of superposition to define a relative chronology based on vertical stratigraphic relationships, i.e., in undisturbed strata, younger deposits overlie older deposits. Determining the relative ages of landforms is more problematic, because seldom is it possible to trace strata between non-contemporaneous surfaces. Consequently, geologists and archaeologists have turned to soils to help assess relative ages of landforms and associated cultural deposits (Birkeland, 1984; Holliday, 1990) In most situations, soils provide relative chronologies for landforms and cultural deposits. If, however, soils of different age are independently dated over a given area, then calibrated ages (Colman et aI., 1987) can be derived for landforms and cultural deposits based on soil development.Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]

Surficial geology of the Lower Agua Fria River, Lake Pleasant to Sun City, Maricopa County, Arizona

Surficial Geology of the Lower Agua Fria River, Lake Pleasant to Sun City, Maricopa County, Arizona. One report and two map sheets, scale 1:24,000.Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]

Surficial geology of the Superstition Mountain Piedmont Area, northern Pinal and eastern Maricopa Counties, Arizona

One of the fastest growing areas of Arizona is the eastern part of the Phoenix Basin near the communities of Chandler, Gilbert, Mesa, and Apache Junction. Much of this development has occurred on the piedmont near the base of the mountains where little of the surficial geology has ever been mapped. Because this area of the Phoenix Basin will continue to grow in the future, there is a need to understand the nature and distribution of surficial deposits. Surficial geologic mapping provides a spatial data base for assessing potential geologic hazards (pearthree, 1991), for defining important groundwater recharge zones, and for analyzing the physical characteristics of surface deposits for excavation purposes. Such mapping is also valuable to earth scientists who are interested in defining the links between landscape evolution and climate change (Bull, 1991). This report presents the results of surficial geologic mapping in the eastern margins of the Phoenix Basin including the Superstition Mountain piedmont and Queen Creek alluvial fan (Figure 1). The region mapped is contained within the Florence Junction, Florence NE, Goldfield, Magma, and Superstition Mountains SW quadrangles (1:24,000), and part of the Weavers Needle quadrangle (1:24,000). This area contains a variety of landscape elements including steep mountain slopes, pediments, and alluvial fans. Included within this report is a discussion of the origins of pediments and an analysis of streamflow processes on the Queen Creek fan. (33 pages; 6 map sheets, map scale 1:24,000)Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]

Surficial Geology of the Eastern Gila River Indian Community Area, Western Pinal County, Arizona

Geologic maps have traditionally emphasized bedrock rather than unconsolidated sediments, the latter usually being lumped into the generic category of "Tertiary and/or Quaternary alluvium". This tradition has left many areas, especially those within the Basin and Range physiographic province, incompletely mapped. Recently, however, there have been systematic efforts to map unconsolidated surficial deposits at small (1:500,000), intermediate (1:100,000), and large (1:24,000) scales (Demsey, 1989; Field and Pearthree, 1992; Hunt, 1978; Jackson, 1990). The impetus for surficial geologic mapping lies in the fact that humans have a vested interest in knowing the distribution and nature of late Cenozoic geological deposits and landforms. Most of the Southwest's urban areas including Albuquerque, El Paso, Las Vegas, Phoenix, and Tucson lie on basin fill. Consequently, there is an interest in the physical properties of the substrata, the distribution of industrial minerals, and the potential for flooding and other geologic hazards. These types of information can be obtained from surficial geologic mapping (Pearthree, 1991). In addition to engineering concerns, other research-oriented information can be gained as well. Because surficial geologic mapping is based on temporally discrete geomorphic surfaces, it provides insight into climatic and tectonic mechanisms of landscape evolution (Bull, 1991). Also, surficial geologic maps can be used to assess subsurface archaeological potential (Davidson, 1985) and serve as a guide for avoiding archaeologically sensitive areas.Documents in the AZGS Document Repository collection are made available by the Arizona Geological Survey (AZGS) and the University Libraries at the University of Arizona. For more information about items in this collection, please contact [email protected]