scholarly journals Power-law out of time order correlation functions in the SYK model

2017 ◽  
Vol 921 ◽  
pp. 727-752 ◽  
Author(s):  
Dmitry Bagrets ◽  
Alexander Altland ◽  
Alex Kamenev
Keyword(s):  
Power Law ◽  
Correlation Functions ◽  
Time Order

Addendum to ‘Isotropic correlation functions on d-dimensional balls’

2000 ◽  
Vol 32 (4) ◽  
pp. 960-961
Author(s):  
Tilmann Gneiting
Keyword(s):  
Power Law ◽  
Correlation Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bounded Domains ◽  
Unpublished Work ◽  
Polynomial Models ◽  
Necessary And Sufficient

We discuss necessary and sufficient conditions for power-law and polynomial models to be correlation functions on bounded domains. These results date back to unpublished work by Matheron (1974) and generalize the findings of Gneiting (1999).

Power-law correlations and other models with long-range dependence on a lattice

2003 ◽  
Vol 40 (3) ◽  
pp. 690-703 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Long Range ◽  
Power Law ◽  
Correlation Functions ◽  
Short Range ◽  
Long Range Dependence ◽  
Correlation Model ◽  
Double Sequences ◽  
Exact Power ◽  
Stationary Random Field ◽  
Dependent Correlation

This paper introduces long-range dependence for a stationary random field on a plane lattice, derives an exact power-law correlation model and other models with long-range dependence on the lattice, and explores the close connection between short-range dependent correlation functions and absolutely summable double sequences.

scholarly journals Correlation Functions of Quantum Artin System

Universe ◽  
2020 ◽  
Vol 6 (7) ◽  
pp. 91
Author(s):  
Hrachya Babujian ◽  
Rubik Poghossian ◽  
George Savvidy
Keyword(s):  
Dynamical System ◽  
Correlation Functions ◽  
Modular Group ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Temperature Dependent ◽  
Chaotic Dynamical System ◽  
Classical Chaos ◽  
Time Order ◽  
Point Correlation

It was conjectured by Maldacena, Shenker and Stanford that the classical chaos can be diagnosed in thermal quantum systems by using an out-of-time-order correlation function. The Artin dynamical system defined on the fundamental region of the modular group SL(2,Z) represents a well defined example of a highly chaotic dynamical system in its classical regime. We investigated the influence of the classical chaotic behaviour on the quantum–mechanical properties of the Artin system calculating the corresponding out-of-time-order thermal quantum–mechanical correlation functions. We demonstrated that the two- and four-point correlation functions of the Liouiville-like operators decay exponentially with temperature dependent exponents and that the square of the commutator of the Liouiville-like operators separated in time grows exponentially.

Power-law correlations and other models with long-range dependence on a lattice

2003 ◽  
Vol 40 (03) ◽  
pp. 690-703 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Long Range ◽  
Power Law ◽  
Correlation Functions ◽  
Short Range ◽  
Long Range Dependence ◽  
Correlation Model ◽  
Double Sequences ◽  
Exact Power ◽  
Stationary Random Field ◽  
Dependent Correlation

This paper introduces long-range dependence for a stationary random field on a plane lattice, derives an exact power-law correlation model and other models with long-range dependence on the lattice, and explores the close connection between short-range dependent correlation functions and absolutely summable double sequences.

scholarly journals CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1047-1059 ◽  
Author(s):  
S. GURUSWAMY ◽  
P. VITALE
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Radius Of Curvature ◽  
Nonlinear Sigma Model ◽  
Long Distance ◽  
Point Correlation ◽  
Point Correlation Function

We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

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