scholarly journals Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions

2020 ◽  
Vol 152 (20) ◽  
pp. 204101 ◽  
Author(s):  
Tatsushi Ikeda ◽  
Gregory D. Scholes
Keyword(s):  
Correlation Functions ◽  
Equations Of Motion

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

Correlation Structure and Time Scale of Simple Hydrologic Systems

1977 ◽  
Vol 8 (3) ◽  
pp. 129-140 ◽  
Author(s):  
Lars Gottschalk
Keyword(s):  
River Runoff ◽  
Groundwater Level ◽  
Correlation Functions ◽  
Time Scale ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Correlation Structure ◽  
Linearized Equations ◽  
Hydrologic Systems ◽  
Meteorological Input

Correlation structure of river runoff is a complicated set of different persistence phenomena in the watershed itself and in the meteorological input to the watershed. Correlation functions and time scale of isolated processes in a watershed (groundwater level and river runoff) are derived analytically from the linearized equations of motion for these processes. Nonlinear effects on the correlation functions are shown for river runoff and for the watershed as a whole.

scholarly journals CFT in AdS and boundary RG flows

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Simone Giombi ◽  
Himanshu Khanchandani
Keyword(s):  
Free Energy ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Flat Space ◽  
De Sitter ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Epsilon Expansion ◽  
Boundary Operators ◽  
Renormalization Group Flows

Abstract Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O(N) model in general dimension d, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

SOME DYNAMICAL PROPERTIES OF THE ISING FERROMAGNET

1967 ◽  
Vol 45 (6) ◽  
pp. 2091-2111 ◽  
Author(s):  
Noboru Matsudaira
Keyword(s):  
Correlation Functions ◽  
Equations Of Motion ◽  
Pair Correlation ◽  
Linear Chain ◽  
Heat Bath ◽  
Spin Correlation ◽  
Square Lattice ◽  
Two Dimensional ◽  
The Many ◽  
Sums Of Products

Time-dependent statistics of the Ising model proposed by Glauber for the one-dimensional chain are extended to the example of a two-dimensional square lattice. Each spin is assumed to change its state through the interaction with a heat bath. The equations of motion for both the single spin and the spin correlation functions are solved approximately by using a decoupling procedure where the many-body correlation functions are taken as sums of products of pair correlation functions. As a special case, our theory allows the approximate calculation of the equilibrium properties of the system and it turns out that, in this case, our result is an improvement over the Bethe approximation. Both the frequency-dependent magnetic susceptibility and the decay of the magnetic moment to the equilibrium state are calculated above and below the Curie temperature. The fluctuation–dissipation theorem developed by Glauber for the linear chain is shown to hold in the two-dimensional case also.

scholarly journals On Equations of Motion in Twist-Four Evolution

2015 ◽  
Vol 37 ◽  
pp. 1560051
Author(s):  
Yao Ji ◽  
A.V. Belitsky
Keyword(s):  
Correlation Functions ◽  
Evolution Equations ◽  
Equations Of Motion ◽  
High Twist ◽  
Loop Order ◽  
Gauge Invariant ◽  
Feynman Graphs ◽  
Explicit Analysis ◽  
Main Complication

Explicit diagrammatic calculation of evolution equations for high-twist correlation functions is a challenge already at one-loop order in QCD coupling. The main complication being quite involved mixing pattern of the so-called non-quasipartonic operators. Recently, this task was completed in the literature for twist-four nonsinglet sector. Presently, we elaborate on a particular component of renormalization corresponding to the mixing of gauge-invariant operators with QCD equations of motion. These provide an intrinsic contribution to evolution equations yielding total result in agreement with earlier computations that bypassed explicit analysis of Feynman graphs.

scholarly journals Comments on contact terms and conformal manifolds in the AdS/CFT correspondence

2020 ◽  
Author(s):  
Tadakatsu Sakai ◽  
Masashi Zenkai
Keyword(s):  
Fixed Point ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Mathematical Structure ◽  
Regularization Scheme ◽  
Anomalous Dimensions ◽  
Geometrical Data ◽  
Conformal Manifolds ◽  
General Setup ◽  
Marginal Deformation

Abstract We study the contact terms that appear in the correlation functions of exactly marginal operators using the AdS/CFT correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms is crucial for a consistency of with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ holographic RG to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP-Witten prescription, and show that they match with the expected results precisely. It is pointed out that The cut-off surface prescription in the bulk provides us with a regularization scheme for performing a conformal perturbation. serves as a regularization scheme for conformal perturbation theory in the boundary CFT. around a fixed point is regularized by putting a cut-off surface in the bulk. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.

scholarly journals Reciprocal Relations for the Open Hydrodynamic Steady States (OHSS)

2019 ◽  
Vol 64 (2) ◽  
pp. 126
Author(s):  
V. P. Lesnikov
Keyword(s):  
Steady State ◽  
Correlation Functions ◽  
Continuous Medium ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Reciprocal Relation ◽  
Reciprocal Relations ◽  
Mutual Correlation ◽  
Time Symmetry ◽  
Macroscopic Equations

Based on Onsager’s regressive hypothesis and a local equilibrium in hydrodynamics, the time symmetry of the mutual correlation functions of fluctuations is analyzed directly from the macroscopic equations of motion for the open steady state of a continuous medium. It is shown that, in OHSS, the flux violates the symmetry of correlation functions and Onsager’s reciprocal relation, which take place near the equilibrium steady state. The reciprocal relations for OHSS are found. Examples of their use are considered.

LOOP EQUATIONS AND NON-PERTURBATIVE EFFECTS IN TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 05 (13) ◽  
pp. 1019-1029 ◽  
Author(s):  
F. DAVID
Keyword(s):  
Quantum Gravity ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Painlevé Equation ◽  
Two Dimensional ◽  
Real Solutions ◽  
Painleve Equation

We present the loop equations of motion which define the correlation functions for loop operators in two-dimensional quantum gravity. We show that non-perturbative correlation functions constructed from real solutions of the Painlevé equation of the first kind violate these equations by non-perturbative terms.

scholarly journals Spatial Correlation of Hydrologic and Physiographic Elements

1978 ◽  
Vol 9 (5) ◽  
pp. 267-276 ◽  
Author(s):  
Lars Gottschalk
Keyword(s):  
Spatial Correlation ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Time Correlation ◽  
Space Correlation ◽  
Linearized Equations ◽  
Hydrologic Processes ◽  
Analytical Expressions

In an earlier paper (Gottschalk 1977) analytical expressions were given for the time correlation of hydrologic processes from the linearized equations of motion for these processes. In this paper space correlation is similarly treated. Comparison is made with empirical space correlation functions of hydrologic and physiographic elements.

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