scholarly journals Semiclassical torus blocks in the t-channel

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Juan Ramos Cabezas
Keyword(s):  
Geodesic Length

Abstract We explicitly demonstrate the relation between the 2-point t-channel torus block in the large-c regime and the geodesic length of a specific geodesic diagram stretched in the thermal AdS3 spacetime.

scholarly journals Complexity growth in integrable and chaotic models

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Matthew DeCross ◽  
Arjun Kar ◽  
Yue Li ◽  
Onkar Parrikar
Keyword(s):  
Time Evolution ◽  
Evolution Operator ◽  
Linear Growth ◽  
Conjugate Points ◽  
Majorana Fermions ◽  
Time Evolution Operator ◽  
Free Theory ◽  
Group Manifold ◽  
Geodesic Length ◽  
Evolution Trajectory

Abstract We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($$ \sqrt{N} $$ N ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

scholarly journals Holographic Formulation of 3D Metric Gravity with Finite Boundaries

Universe ◽  
2019 ◽  
Vol 5 (8) ◽  
pp. 181 ◽  
Author(s):  
Seth Asante ◽  
Bianca Dittrich ◽  
Florian Hopfmueller
Keyword(s):  
Effective Action ◽  
Boundary Point ◽  
Ricci Scalar ◽  
General Family ◽  
Geodesic Length ◽  
Geometric Boundary ◽  
3D Gravity

In this work we construct holographic boundary theories for linearized 3D gravity, for a general family of finite or quasi-local boundaries. These boundary theories are directly derived from the dynamics of 3D gravity by computing the effective action for a geometric boundary observable, which measures the geodesic length from a given boundary point to some center in the bulk manifold. We identify the general form for these boundary theories and find that these are Liouville-like with a coupling to the boundary Ricci scalar. This is illustrated with various examples, which each offer interesting insights into the structure of holographic boundary theories.

EEG channel interpolation using ellipsoid geodesic length

2016 ◽  
Author(s):  
Hristos S. Courellis ◽  
John R. Iversen ◽  
Howard Poizner ◽  
Gert Cauwenberghs
Keyword(s):  
Geodesic Length

scholarly journals Holographic van der Waals Phase Transition for a Hairy Black Hole

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Xiao-Xiong Zeng ◽  
Yi-Wen Han
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Order Phase Transition ◽  
Phase Structure ◽  
Van Der Waals ◽  
Thermal Entropy ◽  
First Order Phase Transition ◽  
Geodesic Length ◽  
First Order Phase ◽  
Hairy Black Hole

The van der Waals (VdW) phase transition in a hairy black hole is investigated by analogizing its charge, temperature, and entropy as the temperature, pressure, and volume in the fluid, respectively. The two-point correlation function (TCF), which is dual to the geodesic length, is employed to probe this phase transition. We find the phase structure in the temperature-thermal entropy plane besides the scale of the horizontal coordinate (geodesic length plane resembles that in the temperature). In addition, we find the equal area law (EAL) for the first-order phase transition and critical exponent of the heat capacity for the second-order phase transition in the temperature-thermal entropy plane (geodesic length plane is consistent with that in temperature), which implies that the TCF is a good probe to probe the phase structure of the back hole.

scholarly journals Optimal Surveillance of Covert Networks by Minimizing Inverse Geodesic Length

2019 ◽  
Vol 33 ◽  
pp. 533-540
Author(s):  
Serge Gaspers ◽  
Kamran Najeebullah
Keyword(s):  
Network Performance ◽  
Vertex Cover ◽  
Quadratic Program ◽  
Edge Deletion ◽  
Fixed Parameter Tractable ◽  
Fpt Algorithms ◽  
Neighborhood Diversity ◽  
Geodesic Length ◽  
Split Graphs ◽  
Covert Networks

The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In network analysis, IGL of a network is often used to assess and evaluate how well heuristics perform in strengthening or weakening a network. We consider the edge-deletion problem MINIGLED. Formally, given a graph G, a budget k, and a target inverse geodesic length T, the question is whether there exists a subset of edges X with |X| ≤ ck, such that the inverse geodesic length of G − X is at most T.In this paper, we design algorithms and study the complexity of MINIGL-ED. We show that it is NP-complete and cannot be solved in subexponential time even when restricted to bipartite or split graphs assuming the Exponential Time Hypothesis. In terms of parameterized complexity, we consider the problem with respect to various parameters. We show that MINIGL-ED is fixed-parameter tractable for parameter T and vertex cover by modeling the problem as an integer quadratic program. We also provide FPT algorithms parameterized by twin cover and neighborhood diversity combined with the deletion budget k. On the negative side we show that MINIGL-ED is W[1]-hard for parameter tree-width.

scholarly journals Holographic renormalization group flow effect on quantum correlations

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Chanyong Park ◽  
Jung Hun Lee
Keyword(s):  
Entanglement Entropy ◽  
Finite Size ◽  
Quantum Correlations ◽  
Scaling Effects ◽  
Point Function ◽  
Holographic Renormalization ◽  
Geodesic Length ◽  
Local Operators ◽  
The One ◽  
Group Flow

Abstract We holographically study the finite-size scaling effects on macroscopic and microscopic quantum correlations deformed by excitation and condensation. The excitation (condensation) increases (decreases) the entanglement entropy of the system. We also investigate the two-point correlation function of local operators by calculating the geodesic length connecting two local operators. As opposed to the entanglement entropy case, the excitation (condensation) decreases (increases) the two-point function. This is because the screening effect becomes strong in the background with the large entanglement entropy. We further show that the holographic renormalization leads to the qualitatively same two-point function as the one obtained from the geodesic length.

scholarly journals Quasi-Closeness: A Toolkit for Social Network Applications Involving Indirect Connections

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Yugang Yin ◽  
Yahui Liu
Keyword(s):  
Social Network ◽  
Exponential Decay ◽  
Sample Space ◽  
Optimal Route ◽  
Dijkstra Algorithm ◽  
Attenuation Effect ◽  
Network Applications ◽  
Centrality Index ◽  
Geodesic Length ◽  
To Come

We come up with a punishment in the form of exponential decay for the number of vertices that a path passes through, which is able to reconcile the contradictory effects of geodesic length and edge weights. This core thought is the key to handling three typical applications; that is, given an information demander, he may be faced with the following problems: choosing optimal route to contact the single supplier, picking out the best supplier between multiple candidates, and calculating his point centrality, which involves indirect connections. Accordingly, three concrete solutions in one logic thread are proposed. Firstly, by adding a constraint to Dijkstra algorithm, we limit our candidates for optimal route to the sample space of geodesics. Secondly, we come up with a unified standard for the comparison between adjacent and nonadjacent vertices. Through punishment in the form of exponential decay, the attenuation effect caused by the number of vertices that a path passes through has been offset. Then the adjacent vertices and punished nonadjacent vertices can be compared directly. At last, an unprecedented centrality index, quasi-closeness, is ready to come out, with direct and indirect connections being summed up.

Sign in / Sign up

Export Citation Format

Share Document