Hidden unity in the quantum description of matter

We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity behind seemingly unrelated physical phenomena, thus establishing exact connections between them. This leads to the fundamental concept of {\it universality} of physical phenomena, a general concept not restricted to the domain of critical behavior. Key to our framework is the concept of {\it languages} and the construction of {\it dictionaries} relating them.Comment: 10 pages 2 psfigures. Appeared in Recent Progress in Many-Body Theorie

Ambient noise tomography reveals basalt and sub-basalt velocity structure beneath the Faroe Islands, North Atlantic

© 2017 Elsevier B.V. Ambient noise tomography is applied to seismic data recorded by a portable array of seismographs deployed throughout the Faroe Islands in an effort to illuminate basalt sequences of the North Atlantic Igneous Province, as well as underlying sedimentary layers and Precambrian basement. Rayleigh wave empirical Green's functions between all station pairs are extracted from the data via cross-correlation of long-term recordings, with phase weighted stacking implemented to boost signal-to-noise ratio. Dispersion analysis is applied to extract inter-station group travel-times in the period range 0.5–15 s, followed by inversion for period-dependent group velocity maps. Subsequent inversion for 3-D shear wave velocity reveals the presence of significant lateral heterogeneity (up to 25%) in the crust. Main features of the final model include: (i) a near-surface low velocity layer, interpreted to be the Malinstindur Formation, which comprises subaerial compound lava flows with a weathered upper surface; (ii) a sharp velocity increase at the base of the Malinstindur Formation, which may mark a transition to the underlying Beinisvørð Formation, a thick laterally extensive layer of subaerial basalt sheet lobes; (iii) a low velocity layer at 2.5–7.0 km depth beneath the Beinisvørð Formation, which is consistent with hyaloclastites of the Lopra Formation; (iv) an upper basement layer between depths of 5–9 km and characterized by S wave velocities of approximately 3.2 km/s, consistent with low-grade metamorphosed sedimentary rocks; (v) a high velocity basement, with S wave velocities in excess of 3.6 km/s. This likely reflects the presence of a crystalline mid-lower crust of Archaean continental origin. Compared to previous interpretations of the geological structure beneath the Faroe Islands, our new results point to a more structurally complex and laterally heterogeneous crust, and provide constraints which may help to understand how continental fragments are rifted from the margins of newly forming ocean basins

New insights into North Sea deep crustal structure and extension from transdimensional ambient noise tomography

SUMMARY The deep crustal structure beneath the North Sea is poorly understood since it is constrained by only a few seismic reflection and refraction profiles. However, it is widely acknowledged that the mid to lower crust plays important roles in rift initiation and evolution, particularly when large-scale sutures and/or terrane boundaries are present, since these inherited features can focus strain or act as inhibitors to extensional deformation. Ancient tectonic features are known to exist beneath the iconic failed rift system of the North Sea, making it an ideal location to investigate the complex interplay between pre-existing regional heterogeneity and rifting. To this end, we produce a 3-D shear wave velocity model from transdimensional ambient seismic noise tomography to constrain crustal properties to ∼30 km depth beneath the North Sea and its surrounding landmasses. Major North Sea sedimentary basins appear as low shear wave velocity zones that are a good match to published sediment thickness maps. We constrain relatively thin crust (13–18 km) beneath the Central Graben depocentres that contrasts with crust elsewhere at least 25–30 km thick. Significant variations in crustal structure and rift symmetry are identified along the failed rift system that appears to be related to the locations of Laurentia–Avalonia–Baltica palaeoplate boundaries. We constrain first-order differences in structure between palaeoplates; with strong lateral gradients in crustal velocity related to Laurentia–Avalonia–Baltica plate juxtaposition and reduced lower crustal velocities in the vicinity of the Thor suture, possibly representing the remnants of a Caledonian accretionary complex. Our results provide fresh insight into the pivotal roles that ancient terranes can play in the formation and failure of continental rifts and may help explain the characteristics of other similar continental rifts globally.</jats:p

Statistical distinguishability between unitary operations

The problem of distinguishing two unitary transformations, or quantum gates, is analyzed and a function reflecting their statistical distinguishability is found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there always exists a finite number $N$ such that $U_1^{\otimes N}$ and $U_2^{\otimes N}$ are perfectly distinguishable, although they were not in the single-copy case. This result can be extended to any finite set of unitary transformations. Finally, a fidelity for one-qubit gates, which satisfies many useful properties from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to any finite set of gate

High-Resolution, Wide-Field Imaging of the Galactic Center Region at 330 MHz

We present a wide field, sub-arcminute resolution VLA image of the Galactic Center region at 330 MHz. With a resolution of ~ 7" X 12" and an RMS noise of 1.6 mJy/beam, this image represents a significant increase in resolution and sensitivity over the previously published VLA image at this frequency. The improved sensitivity has more than tripled the census of small diameter sources in the region, has resulted in the detection of two new Non Thermal Filaments (NTFs), 18 NTF candidates, 30 pulsar candidates, reveals previously known extended sources in greater detail, and has resulted in the first detection of Sagittarius A* in this frequency range. A version of this paper containing full resolution images may be found at http://lwa.nrl.navy.mil/nord/AAAB.pdf.Comment: Astronomical Journal, Accepted 62 Pages, 21 Figure

Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.Comment: 5 pages, 4 figure

Random matrix theory, the exceptional Lie groups, and L-functions

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are here extended to non-classical groups. We focus on an explicit example: the exceptional Lie group G_2. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G_2, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the 7-dimensional representation of G_2. The random matrix calculations extend to all exceptional Lie groupsComment: 14 page