scholarly journals Universal flow equations and chaos bound saturation in 2d dilaton gravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
D. Grumiller ◽  
R. McNees
Keyword(s):  
Fixed Point ◽  
Chaotic Behavior ◽  
Broad Class ◽  
Flow Equation ◽  
Two Dimensional ◽  
Maximal Lyapunov Exponent ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Flow Equations ◽  
Universal Properties

Abstract We show that several features of the Jackiw-Teitelboim model are in fact universal properties of two-dimensional Maxwell-dilaton gravity theories with a broad class of asymptotics. These theories satisfy a flow equation with the structure of a dimensionally reduced $$ T\overline{T} $$ T T ¯ deformation, and exhibit chaotic behavior signaled by a maximal Lyapunov exponent. One consequence of our results is a no-go theorem for smooth flows from an asymptotically AdS2 region to a de Sitter fixed point.

scholarly journals Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps

2018 ◽  
Vol 28 (04) ◽  
pp. 1830011
Author(s):  
Mio Kobayashi ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Chaotic Behavior ◽  
Periodic Points ◽  
Two Dimensional ◽  
Stable Fixed Point ◽  
Bifurcation Structure ◽  
Unstable Fixed Point ◽  
Gaussian Map ◽  
Gaussian Maps

A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the [Formula: see text]-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.

scholarly journals Universal entanglement signatures of foliated fracton phases

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Wilbur Shirley ◽  
Kevin Slagle ◽  
Xie Chen
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Topological Phases ◽  
Topological Order ◽  
Two Dimensional ◽  
Adiabatic Evolution ◽  
Universal Properties ◽  
Three Dimensional Models ◽  
Topological Entanglement Entropy

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In , we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

scholarly journals Two-dimensional black holes in the limiting curvature theory of gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Valeri P. Frolov ◽  
Andrei Zelnikov
Keyword(s):  
Black Holes ◽  
Gravity Models ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Curvature Condition ◽  
Curvature Theory ◽  
Theory Of Gravity ◽  
Modified Theory ◽  
Modified Gravity Models

Abstract In this paper we discuss modified gravity models in which growth of the curvature is dynamically restricted. To illustrate interesting features of such models we consider a modification of two-dimensional dilaton gravity theory which satisfies the limiting curvature condition. We show that such a model describes two-dimensional black holes which contain the de Sitter-like core instead of the singularity of the original non-modified theory. In the second part of the paper we study Vaidya type solutions of the model of the limiting curvature theory of gravity and used them to analyse properties of black holes which are created by the collapse of null fluid. We also apply these solutions to study interesting features of a black hole evaporation.

scholarly journals Quasinormal Frequencies of a Two-Dimensional Asymptotically Anti-de Sitter Black Hole of the Dilaton Gravity Theory

2021 ◽  
Vol 8 ◽  
Author(s):  
M. I. Hernández-Velázquez ◽  
A. López-Ortega
Keyword(s):  
Black Hole ◽  
Differential Equations ◽  
Iteration Method ◽  
Gravity Theory ◽  
Asymptotic Iteration Method ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Second Order Differential Equations ◽  
Klein Gordon

We numerically calculate the quasinormal frequencies of the Klein-Gordon and Dirac fields propagating in a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory. For the Klein-Gordon field we use the Horowitz-Hubeny method and the asymptotic iteration method for second order differential equations. For the Dirac field we first exploit the Horowitz-Hubeny method. As a second method, instead of using the asymptotic iteration method for second order differential equations, we propose to take as a basis its formulation for coupled systems of first order differential equations. For the two fields we find that the results that produce the two numerical methods are consistent. Furthermore for both fields we obtain that their quasinormal modes are stable and we compare their quasinormal frequencies to analyze whether their spectra are isospectral. Finally we discuss the main results.

scholarly journals Flow equations for disordered Floquet systems

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Steven Thomson ◽  
Duarte Magano ◽  
Marco Schiro'
Keyword(s):  
Flow Equation ◽  
Two Dimensional ◽  
Many Body ◽  
Integrals Of Motion ◽  
Exact Methods ◽  
New Approach ◽  
Flow Equations ◽  
Periodically Driven ◽  
Floquet Modes ◽  
Many Body Systems

In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.

scholarly journals On thermodynamics of 2D black holes in brane inflationary potentials

2014 ◽  
Vol 11 (05) ◽  
pp. 1450047 ◽  
Author(s):  
A. Belhaj ◽  
M. Chabab ◽  
H. El Moumni ◽  
M. B. Sedra ◽  
A. Segui
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Black Hole Solution ◽  
Brane World ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Asymptotic Behaviors ◽  
Dimensional Black Hole ◽  
Hole Geometry

Inspired from the inflation brane world cosmology, we study the thermodynamics of a black hole solution in two-dimensional dilaton gravity with an arctangent potential background. We first derive the two-dimensional black hole geometry, then we examine its asymptotic behaviors. More precisely, we find that such behaviors exhibit properties appearing in some known cases including the anti-de Sitter and the Schwarzschild black holes. Using the complex path method, we compute the Hawking radiation. The entropy function can be related to the value of the potential at the horizon.

Selection and application of a one-dimensional non-Darcy flow equation for two-dimensional flow through rockfill embankments

1995 ◽  
Vol 32 (2) ◽  
pp. 223-232 ◽  
Author(s):  
David Hansen ◽  
Vinod K. Garga ◽  
D. Ronald Townsend
Keyword(s):  
Packed Column ◽  
Flow Equation ◽  
Hydraulic Gradient ◽  
Darcy Flow ◽  
Two Dimensional ◽  
Rating Curve ◽  
One Dimensional ◽  
Flow Equations ◽  
Flow Through ◽  
Hydraulics Laboratory

Porous embankments comprised of relatively homogeneous coarse rockfill can be used to reduce the amount of spillage at downstream hydro dams or to control the outflow from stormwater detention basins. The stage-discharge rating curve is important in the design of such applications. In general, the coarseness of the material causes the flow to be non-Darcy; that is, characterized by a nonlinear relationship between bulk velocity and hydraulic gradient. Six one-dimensional (1D) non-Darcy flow equations, appearing in the literature, are presented. A limited comparison between computed and experimental results is then made on the basis of 1D packed-column tests performed in the hydraulics laboratory of the University of Ottawa. The question as to how such 1D closed-conduit equations might be used to estimate the quantity of flow through a porous embankment is then addressed, considering that the latter has a free surface and is a two-dimensional (2D) flow. The problem is successfully dealt with using the concept of "effective hydraulic gradient," a concept reminiscent of the method of sections used to analyze confined 2D seepage problems. A general equation is presented in which the effective hydraulic gradient is shown to be a function of two factors: (1) the shape of the embankment and (2) the upstream depth, relative to the height of the dam. The development and verification of the equation for the effective hydraulic gradient is described, together with its use in obtaining a rating curve for a hypothetical flowthrough dam composed of rock material 0.25 m in diameter. Key words : non-Darcy flow, flowthrough rockfill, effective hydraulic gradient, stage-discharge rating curve.

scholarly journals THE AdS/CFT CORRESPONDENCE IN TWO DIMENSIONS

2001 ◽  
Vol 16 (04n06) ◽  
pp. 171-178 ◽  
Author(s):  
MARIANO CADONI ◽  
PAOLO CARTA
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Recent Progress ◽  
Two Dimensions ◽  
Gravity Theory ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Conformal Field

We review recent progress in understanding the anti-de Sitter/conformal field theory correspondence in the context of two-dimensional (2D) dilaton gravity theory.

scholarly journals Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

2021 ◽  
Author(s):  
Alexander Mielke
Keyword(s):  
Gradient Flow ◽  
Careful Analysis ◽  
Flow Equation ◽  
Uniqueness Result ◽  
Gradient System ◽  
Independent System ◽  
Exact Relation ◽  
Flow Equations ◽  
Total Variation Flow ◽  
Energetic Solutions

AbstractWe consider a non-negative and one-homogeneous energy functional $${{\mathcal {J}}}$$ J on a Hilbert space. The paper provides an exact relation between the solutions of the associated gradient-flow equations and the energetic solutions generated via the rate-independent system given in terms of the time-dependent functional $${{\mathcal {E}}}(t,u)= t {{\mathcal {J}}}(u)$$ E ( t , u ) = t J ( u ) and the norm as a dissipation distance. The relation between the two flows is given via a solution-dependent reparametrization of time that can be guessed from the homogeneities of energy and dissipations in the two equations. We provide several examples including the total-variation flow and show that equivalence of the two systems through a solution dependent reparametrization of the time. Making the relation mathematically rigorous includes a careful analysis of the jumps in energetic solutions which correspond to constant-speed intervals for the solutions of the gradient-flow equation. As a major result we obtain a non-trivial existence and uniqueness result for the energetic rate-independent system.

scholarly journals Bra-ket wormholes in gravitationally prepared states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yiming Chen ◽  
Victor Gorbenko ◽  
Juan Maldacena
Keyword(s):  
Hyperbolic Space ◽  
Path Integral ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
De Sitter ◽  
Euclidean Case ◽  
Fine Grained ◽  
Entropy Formula ◽  
First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

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