scholarly journals Holographic scalar and vector exchange in OTOCs and pole-skipping phenomena

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Keun-Young Kim ◽  
Mitsuhiro Nishida ◽  
Kyung-Sun Lee
Keyword(s):  
Vector Fields ◽  
Equations Of Motion ◽  
Computational Method ◽  
Dual Operator ◽  
Exchange Effect ◽  
Time Order ◽  
Vector Exchange

Abstract We study scalar and vector exchange terms in out-of-time-order correlators (OTOCs) holographically. By applying a computational method in graviton exchange, we analyze exponential behaviors in scalar and vector exchange terms at late times. We show that their exponential behaviors in simple holographic models are related to pole-skipping points obtained from the near-horizon equations of motion of scalar and the vector fields. Our results are generalizations of the relation between the graviton exchange effect in OTOCs and the pole-skipping phenomena of the dual operator, to scalar and the vector fields.

Recursive Linearization of Multibody Dynamics and Application to Control Design

1990 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

Abstract The non-linear equations of motion in multi-body dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

OBSERVATIONS ON A U(1) × U(1) VECTOR THEORY

2002 ◽  
Vol 17 (16) ◽  
pp. 2211-2217
Author(s):  
D. G. C. MCKEON
Keyword(s):  
Vector Fields ◽  
Equations Of Motion ◽  
Quantization Condition ◽  
Constraint Condition ◽  
Supersymmetric Version ◽  
Dirac Quantization ◽  
Covariant Gauge ◽  
Vector Theory ◽  
Two Sectors ◽  
Conserved Currents

The symmetry between two sectors of a model containing two U(1) vector fields (related by a constraint condition) and two conserved currents is examined. The equations of motion for the vector fields, once the constraint condition is applied, is similar in form to the Maxwell equations in the presence of both electric and magnetic charge. The Dirac quantization condition need not be applied. The propagators for the vector fields are computed in a covariant gauge, demonstrating that the model is unitary and renormalizable. A supersymmetric version of the model is presented.

scholarly journals ISRAEL–WILSON–PERJÉS SOLUTIONS IN HETEROTIC STRING THEORY

1999 ◽  
Vol 14 (09) ◽  
pp. 1345-1356 ◽  
Author(s):  
ALFREDO HERRERA-AGUILAR ◽  
OLEG KECHKIN
Keyword(s):  
String Theory ◽  
Vector Fields ◽  
Equations Of Motion ◽  
Simple Algorithm ◽  
Heterotic String ◽  
Three Dimensions ◽  
Heterotic String Theory ◽  
The Matrix ◽  
Em Theory ◽  
Bosonic Part

We present a simple algorithm to obtain solutions that generalize the Israel–Wilson–Perjés class for the low energy limit of heterotic string theory toroidally compactified from D=d+3 to three dimensions. A remarkable map existing between the Einstein–Maxwell (EM) theory and the theory under consideration allows us to solve directly the equations of motion making use of the matrix Ernst potentials connected with the coset matrix of heterotic string theory.1 For the particular case d=1 (if we put n=6, the resulting theory can be considered as the bosonic part of the action of D=4, N=4 supergravity) we obtain explicitly a dyonic solution in terms of one real 2×2-matrix harmonic function and 2n real constants (n being the number of Abelian vector fields). By studying the asymptotic behavior of the field configurations we define the charges of the system. They satisfy the Bogomol'nyi–Prasad–Sommerfield (BPS) bound.

BOUNDARY CONDITIONS IN THE MECHANICS OF FIELDS

1952 ◽  
Vol 30 (6) ◽  
pp. 684-698
Author(s):  
S. M. Neamtan ◽  
E. Vogt
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Vector Fields ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Second Order ◽  
Dirac Field ◽  
Energy Tensor ◽  
Complex Scalar ◽  
Set Up

A variational principle has been set up for the description of relativistic fields with the aid of Lagrangians involving second order derivatives of the field functions. This constitutes a generalization of the usual formulation in that, besides the boundary conditions usually imposed, it admits also linear homogeneous boundary conditions. The formulation has been developed for the complex scalar and complex vector fields. The variational principle then yields not only the wave equations but also the allowed boundary conditions. A Hamiltonian and equations of motion in canonical form can be set up. A symmetric stress–energy tensor and a charge–current vector are defined, yielding the usual conservation equations. For the vector field, π4 is not identically zero; also the Lorentz condition arises out of the variational principle and does not have to be separately imposed. For the Dirac field an extension to Lagrangians with second order derivatives is not possible, but for this field also the variational principle yields the allowed boundary conditions.

DEVELOPMENT OF AN OPTIMAL OIL BOOM IN WAVES

1995 ◽  
Vol 1995 (1) ◽  
pp. 869-871 ◽  
Author(s):  
Il-Hyoung Cho ◽  
Byung-W. Cho
Keyword(s):  
Equations Of Motion ◽  
Optimal Shape ◽  
Computational Method ◽  
Vertical Position ◽  
Parameter Study ◽  
Linear Potential ◽  
Oil Boom ◽  
Dimensional Approximation ◽  
Motion Characteristics ◽  
Linear Potential Theory

ABSTRACT The performance of an air-inflated oil boom, recently developed by the authors, is investigated for the purpose of designing an optimal shape. Well-designed oil booms should be able to follow the water surface closely and also maintain a vertical position in waves. A numerical method based on a linear potential theory is developed to predict the motion characteristics of oil boom in waves; the optimal configuration of the boom is determined based on numerical studies. Hamilton's principle is employed to derive the equations of motion of the float and the skirt. The equations of motion are formulated for the case in which the float and the skirt are connected by a hinge. The computational method is limited to a two-dimensional approximation. Through the parameter study of physical properties (draft, shape of boom, weight of chain, water plane area), we can decide the optimal shape of oil boom to produce minimum relative heave response in waves.

Recursive Linearization of Multibody Dynamics and Application to Control Design

1994 ◽  
Vol 116 (2) ◽  
pp. 445-451 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
General Purpose ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

The nonlinear equations of motion in multibody dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

scholarly journals Some minisuperspace model for the Faddeev formulation of gravity

2014 ◽  
Vol 29 (27) ◽  
pp. 1450141 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Distinctive Feature ◽  
Vector Fields ◽  
Measure Zero ◽  
Equations Of Motion ◽  
Zero Set ◽  
Constant Vector ◽  
Field Equations ◽  
Piecewise Constant ◽  
The Continuum

We consider Faddeev formulation of General Relativity (GR) in which the metric is composed of ten vector fields or a 4 ×10 tetrad. This formulation reduces to the usual GR upon partial use of the field equations. A distinctive feature of the Faddeev action is its finiteness on the discontinuous fields. This allows to introduce its minisuperspace formulation where the vector fields are constant everywhere on ℝ4 with exception of a measure zero set (the piecewise constant fields). The fields are parametrized by their constant values independently chosen in, e.g. the 4-simplices or, say, parallelepipeds into which ℝ4 can be decomposed. The form of the action for the vector fields of this type is found. We also consider the piecewise constant vector fields approximating the fixed smooth ones. We check that if the regions in which the vector fields are constant are made arbitrarily small, the minisuperspace action and equations of motion tend to the continuum Faddeev ones.

scholarly journals Reconstruction of Nonlinear Flows from Noisy Time Series

2021 ◽  
Author(s):  
Juanjuan Wang ◽  
zishuo Yan ◽  
Lili Gui ◽  
Kun Xu ◽  
Yueheng Lan
Keyword(s):  
Time Series ◽  
Vector Fields ◽  
Partial Information ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Local Approximation ◽  
Unknown Parameters ◽  
Lorenz Equation ◽  
Noise Interference ◽  
Time Translation

Abstract Nonlinear dynamics is a rapidly developing subject across all disciplines involving spatial or temporal evolution. The reconstruction of the equations of motion for a nonlinear system from observed time series has been a hot topic for a long time. Nevertheless, in practice only partial information is available for many systems which are very likely contaminated with noise. Here, based on the invariance of the evolution equation during time translation, a globally valid local approximation of the trajectory is determined, which could be reliably used for the reconstruction of the vector fields with unknown parameters or functional forms, even with partial information of the state evolution. The global consideration very effectively alleviates noise interference and bestows exceptional robustness to the technique, which asks only for solution of linear equations and thus is very efficient. The new scheme is nicely demonstrated in the Lorenz equation in different conditions, while an FHN neural network model is used to show its strength in high-dimensions.

scholarly journals Spin-Valued Four Bosons Electrodynamics

2021 ◽  
Vol 19 ◽  
pp. 93-133
Author(s):  
R. Doria ◽  
I. Soares
Keyword(s):  
Lie Algebra ◽  
Electric Charge ◽  
Lorentz Group ◽  
Vector Fields ◽  
Magnetic Moments ◽  
Equations Of Motion ◽  
Spin Coupling ◽  
Abelian Gauge ◽  
Spin Effects ◽  
Massive Photon

Electromagnetism is based on electric charge and spin. The study here corresponds to understand on spin effects at a vectorial electrodynamics. Its scenario is a non-linear abelian electromagnetism where the electric charge is transmitted through a four bosons quadruplet, constituted by the usual photon, massive photon and charged massive photons. These four bosons intermediate the charge exchange ΔQ = 0, ±1.The spin is introduced at first principles. A spintronics Lagrangian for four vector fields is performed. Considering that spin is a space-time physical entity derived from Lorentz Group, these vector fields are associated to Lorentz Group, as Lie algebra valued. Similarly to non-abelian gauge theories where Aμ≡ Aμ,ata, one introduces the relationship Aμ≡ Aμ,κλΣκλ where (Σκλ)αβ is the Lorentz Group generator. Thus, based on three fundamentals which are light invariance, electric charge conservation law and vector fields Lie algebra valued through Lorentz Group generators, one derives a spin-valued four vectorial electrodynamics. It is given by the fields quadruplet Aμ1 ≡ {Aμ, Uμ, Vμ±}  where Aμ means the usual photon, Uμ a massive photon and Vμ± massive charged photons. Two novelties appear. The first one is that, new terms are developed into usual four bosons electromagnetism. They contribute to Lagrangian, equations of motion, Noether theorem. The second one is that the equations of motion derive a renormalizable spin coupling with the electric and magnetic fields.There is a spin-1 electrodynamics to be investigated. A neutral electromagnetism is mandatory to be analyzed. Something beyond dipole, quadrupole and so on. Understand the role of spin in the electrical and magnetic properties of particles. A spin vectorial expression S-->  is obtained. It adds EM interactions not depending on electric charge and with spin interactions through electric dipole and magnetic moments.

scholarly journals The Electromagnetic and Proca Fields Revisited: A Unified Quantization

1997 ◽  
Vol 12 (20) ◽  
pp. 3609-3623 ◽  
Author(s):  
Víctor Aldaya ◽  
Manuel Calixto ◽  
Miguel Navarro
Keyword(s):  
Gauge Transformation ◽  
Vector Fields ◽  
Mass Shell ◽  
Local Group ◽  
Equations Of Motion ◽  
Generalized Equations ◽  
Photon Mass ◽  
New Approach ◽  
Gauge Transformations ◽  
Group Law

Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μ φ (x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U (1)(x,t), acquire dynamical content outside the photon mass shell, a fact which also allows a unified quantization of both the electromagnetic and Proca fields.

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