Correlation Functions of Quantum Artin System

• Main Authors: Hrachya Babujian, Rubik Poghossian, George Savvidy
• Format: Article
• Language: English
• Published: MDPI AG 2020-06-01
• Series: Universe
• Subjects: artin billiard; chaotic dynamical systems; anosov systems; kolmogorov systems; modular invariance; non-holomorphic automorphic functions
• Online Access: https://www.mdpi.com/2218-1997/6/7/91

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.