We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For systems with fourfold rotation symmetry, we show that in the presence of ...disclination lines with a total Frank angle, which is an integer multiple of 2 π , there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines. This results in disclination-induced non-Hermitian skin effects. By doubling a non-Hermitian Hamiltonian to a Hermitian three-dimensional chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the effective surface Dirac fermion(s) in the presence of a pseudomagnetic flux induced by disclinations. Furthermore, we find that our results have a field theoretic description, and the corresponding geometric response actions (e.g., the Euclidean Wen-Zee action) enrich the topological field theory of non-Hermitian systems.
The First CHIME/FRB Fast Radio Burst Catalog Amiri, Mandana; Andersen, Bridget C.; Bandura, Kevin ...
The Astrophysical journal. Supplement series,
12/2021, Volume:
257, Issue:
2
Journal Article
Peer reviewed
Open access
Abstract
We present a catalog of 536 fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) Project between 400 and 800 MHz from 2018 ...July 25 to 2019 July 1, including 62 bursts from 18 previously reported repeating sources. The catalog represents the first large sample, including bursts from repeaters and nonrepeaters, observed in a single survey with uniform selection effects. This facilitates comparative and absolute studies of the FRB population. We show that repeaters and apparent nonrepeaters have sky locations and dispersion measures (DMs) that are consistent with being drawn from the same distribution. However, bursts from repeating sources differ from apparent nonrepeaters in intrinsic temporal width and spectral bandwidth. Through injection of simulated events into our detection pipeline, we perform an absolute calibration of selection effects to account for systematic biases. We find evidence for a population of FRBs—composing a large fraction of the overall population—with a scattering time at 600 MHz in excess of 10 ms, of which only a small fraction are observed by CHIME/FRB. We infer a power-law index for the cumulative fluence distribution of
α
=
−
1.40
±
0.11
(
stat.
)
−
0.09
+
0.06
(
sys.
)
, consistent with the −3/2 expectation for a nonevolving population in Euclidean space. We find that
α
is steeper for high-DM events and shallower for low-DM events, which is what would be expected when DM is correlated with distance. We infer a sky rate of
820
±
60
(
stat.
)
−
200
+
220
(
sys.
)
/
sky
/
day
above a fluence of 5 Jy ms at 600 MHz, with a scattering time at 600 MHz under 10 ms and DM above 100 pc cm
−3
.
A mechanism to construct asymptotically flat, isolated, stationary black hole (BH) spacetimes with no Z2 (NoZ) isometry is described. In particular, the horizon geometry of such NoZ BHs does not have ...the usual north-south (reflection) symmetry. We discuss two explicit families of models wherein NoZ BHs arise. In one of these families, we exhibit the intrinsic horizon geometry of an illustrative example by isometrically embedding it in Euclidean 3-space, resulting in an “egg-like” shaped horizon. This asymmetry leaves an imprint in the NoZ BH phenomenology, for instance in its lensing of light; but it needs not be manifest in the BH shadow, which in some cases can be analytically shown to retain a Z2 symmetry. Light absorption and scattering due to an isotropic source surrounding a NoZ BH endows it with a non-zero momentum, producing an asymmetry triggered BH rocket effect.
Realizing the no-boundary proposal of Hartle and Hawking as a consistent gravitational path integral has been a long-standing puzzle. In particular, it was demonstrated by Feldbrugge, Lehners, and ...Turok that the sum over all universes starting from a zero size results in an unstable saddle point geometry. Here we show that, in the context of gravity with a positive cosmological constant, path integrals with a specific family of Robin boundary conditions overcome this problem. These path integrals are manifestly convergent and are approximated by stable Hartle-Hawking saddle point geometries. The price to pay is that the off-shell geometries do not start at a zero size. The Robin boundary conditions may be interpreted as an initial state with Euclidean momentum, with the quantum uncertainty shared between the initial size and momentum.
SummaryWe give two formulas for finding the volumes of solids of revolution in hyperbolic geometry. We also prove each formula. These formulas and their proofs are analogous to the ones in Euclidean ...geometry. We also provide several examples of their use. These formulas may be useful in college geometry courses that include a section on hyperbolic geometry.
Recently, dealing the Non-Euclidean data and its characterization is considered as one of the major issues by researchers. The first problem arises while distinction of among Euclidean and ...non-Euclidean geometry. The second problem arises with dealing the Non-Euclidean geometry in true, false and uncertain regions. The third problem arises while investigating some pattern in Non-Euclidean data sets. This paper focused on tackling these issues with some real life examples.
Free energy from replica wormholes Engelhardt, Netta; Fischetti, Sebastian; Maloney, Alexander
Physical review. D,
02/2021, Volume:
103, Issue:
4
Journal Article
Peer reviewed
Open access
Euclidean wormholes-geometries which connect disconnected boundaries-present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the ...gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies and appears in the computation of any extensive quantity. We argue that both JT gravity and a simplified version of CGHS admit a regime where the contribution of connected replica wormholes to the free energy is larger than that of disconnected topologies. In both theories we find evidence of replica symmetry breaking, which is reminiscent of the behavior of certain spin glasses. We discuss possible insights about ensemble averaging in gravity from this perspective.
Loops in Anti-de Sitter Space Bertan, Igor; Sachs, Ivo
Physical review letters,
2018-Sep-07, Volume:
121, Issue:
10
Journal Article
Peer reviewed
Open access
We obtain analytic results for the four-point amplitude, at one loop, of an interacting scalar field theory in four-dimensional, Euclidean anti-de Sitter space without exerting any conformal field ...theory knowledge. For the two-point function, we provide analytic expressions up to two loops. In addition, we argue that the critical exponents of correlation functions near the conformal boundary of anti-de Sitter space provide the necessary data for the renormalization conditions, thus replacing the usual on-shell condition.
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or ...classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a probabilistic, distance-based, iterative method for clustering data in very high-dimensional space, using the ℓ1-metric that is less sensitive to high dimensionality than the Euclidean distance. For K clusters in ℝn, the problem decomposes to K problems coupled by probabilities, and an iteration reduces to finding Kn weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.
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