High Derivative Theories

2013 ◽  
pp. 81-126
Author(s):  
Jonathan Pearson
Keyword(s):  
High Derivative

Self-Excited Oscillations in Dynamical Systems Possessing Retarded Actions

1942 ◽  
Vol 9 (2) ◽  
pp. A65-A71 ◽  
Author(s):  
Nicholas Minorsky
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Linear Equation ◽  
Finite Order ◽  
Characteristic Equation ◽  
High Derivative ◽  
Time Lags ◽  
Constant Coefficients ◽  
The Subject

Abstract There exists a variety of dynamical systems, possessing retarded actions, which are not entirely describable in terms of differential equations of a finite order. The differential equations of such systems are sometimes designated as hysterodifferential equations. An important particular case of such equations, encountered in practice, is when the original differential equation for unretarded quantities is a linear equation with constant coefficients and the time lags are constant. The characteristic equation, corresponding to the hysterodifferential equation for retarded quantities in such a case, has a series of subsequent high-derivative terms which generally converge. It is possible to develop a simple graphical interpretation for this equation. Such systems with retarded actions are capable of self-excitation. Self-excited oscillations of this character are generally undesirable in practice and it is to this phase of the subject that the present paper is devoted.

scholarly journals Accretion on high derivative asymptotically safe black holes

2020 ◽  
Vol 44 (6) ◽  
pp. 065102 ◽  
Author(s):  
M. Umar Farooq ◽  
Ayyesha K. Ahmed ◽  
Rong-Jia Yang ◽  
Mubasher Jamil
Keyword(s):  
Black Holes ◽  
High Derivative

scholarly journals Nonlocal inflationThis paper was prsented at the Theory CANADA 4 conference, held at the Centre de Recherches Mathématiques at the Université de Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 189-194 ◽  
Author(s):  
Neil Barnaby
Keyword(s):  
Field Theory ◽  
Cosmic Microwave Background ◽  
String Field Theory ◽  
Initial Value Problem ◽  
High Derivative ◽  
Field Theories ◽  
Microwave Background ◽  
Initial Value ◽  
Nonlocal Field

We consider the possibility of realizing inflation in nonlocal field theories containing infinitely many derivatives. Such constructions arise naturally in string field theory and also in a number of toy models, such as the p-adic string. After reviewing the complications (ghosts and instabilities) that arise when working with high-derivative theories, we discuss the the initial value problem and perturbative stability of theories with infinitely many derivatives. Next, we examine the inflationary dynamics and phenomenology of such theories. Nonlocal inflation can proceed even when the potential is naively too steep and generically predicts large non-Gaussianity in the cosmic microwave background.

scholarly journals Some Remarks on High Derivative Quantum Gravity

1997 ◽  
Vol 12 (32) ◽  
pp. 5711-5734 ◽  
Author(s):  
M. Asorey ◽  
J. L. López ◽  
I. L. Shapiro
Keyword(s):  
Quantum Gravity ◽  
High Derivative ◽  
Einstein Gravity ◽  
Low Energy ◽  
Local Action ◽  
Quantum Corrections ◽  
Asymptotic Freedom ◽  
Low Energies ◽  
Gauge Fixing ◽  
High Derivative Gravity

We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a diffeomorphism-invariant local action. In particular, we consider the superrenormalizable case with a large number of metric derivatives in the action. The structure of ultraviolet divergences is analyzed in some detail. We show that they are independent of the gauge-fixing condition and the choice of field reparametrization. The cosmological counterterm is shown to vanish under certain parameter conditions. We elaborate on the unitarity problem of high derivative approaches and the distribution of masses of unphysical ghosts. We also discuss the properties of the low energy regime and explore the possibility of having a multiscale gravity with different scaling regimes compatible with Einstein gravity at low energies. Finally, we show that the ultraviolet scaling of matter theories is not affected by the quantum corrections of high derivative gravity. As a consequence, asymptotic freedom is stable under those quantum gravity corrections.

scholarly journals Holographic p-wave superconductivity from higher derivative theory

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Yan Liu ◽  
Guoyang Fu ◽  
Hai-Li Li ◽  
Jian-Pin Wu ◽  
Xin Zhang
Keyword(s):  
Normal State ◽  
Ac Conductivity ◽  
Energy Gap ◽  
Low Frequency ◽  
High Derivative ◽  
Superconducting Phase ◽  
P Wave ◽  
S Wave ◽  
Higher Derivative ◽  
Superconducting Energy Gap

AbstractWe construct a holographic SU(2) p-wave superconductor model with Weyl corrections. The high derivative (HD) terms do not seem to spoil the generation of the p-wave superconducting phase. We mainly study the properties of AC conductivity, which is absent in holographic SU(2) p-wave superconductor with Weyl corrections. The conductivities in superconducting phase exhibit obvious anisotropic behaviors. Along y direction, the conductivity $$\sigma _{yy}$$ σ yy is similar to that of holographic s-wave superconductor. The superconducting energy gap exhibits a wide extension. For the conductivity $$\sigma _{xx}$$ σ xx along x direction, the behaviors of the real part in the normal state are closely similar to that of $$\sigma _{yy}$$ σ yy . However, the anisotropy of the conductivity obviously shows up in the superconducting phase. A Drude-like peak at low frequency emerges in $$Re\sigma _{xx}$$ R e σ xx once the system enters into the superconducting phase, regardless of the behaviors in normal state.

scholarly journals Lifshitz scaling to Lorentz-violating high derivative operator and gamma-ray bursts

2016 ◽  
Vol 93 (8) ◽  
Author(s):  
E. Passos ◽  
E. M. C. Abreu ◽  
M. A. Anacleto ◽  
F. A. Brito ◽  
C. Wotzasek ◽  
...  
Keyword(s):  
Gamma Ray ◽  
High Derivative ◽  
Gamma Ray Bursts ◽  
Derivative Operator

scholarly journals INFLATION WITH HIGH DERIVATIVE COUPLINGS

2007 ◽  
Vol 22 (25n28) ◽  
pp. 1987-1994 ◽  
Author(s):  
BIN CHEN ◽  
MIAO LI ◽  
TOWER WANG ◽  
YI WANG
Keyword(s):  
Power Spectrum ◽  
Spectral Index ◽  
High Derivative ◽  
Ricci Scalar ◽  
Tensor Mode ◽  
Consistency Relation ◽  
Mode Spectrum

We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general f(φ, R) term. The scalar power spectrum, the spectral index, the running of the spectral index, the tensor mode spectrum and a new consistency relation of the model are calculated.

scholarly journals A note on Kerr/CFT and Wald entropy discrepancy in high derivative gravities

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hai-Shan Liu ◽  
H. Lü
Keyword(s):  
High Derivative ◽  
Einstein Gravity ◽  
Asymptotic Symmetry ◽  
Five Dimensions ◽  
Curvature Invariants ◽  
Symmetry Algebras

Abstract We examine the Kerr/CFT correspondence in Einstein gravity extended with quadratic curvature invariants. We consider two explicit examples in four and five dimensions and compute the central charges of the asymptotic symmetry algebras of the near horizon geometries, using the improved version of the BBC formalism that encompasses the information of the Lagrangian. We find that the resulting Cardy entropy differs from the Wald entropy, caused by the Riemann-squared RμνρσRμνρσ term.

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