Abstract
In this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time scale. We also provide a strict model independent bound on the measure of quantum chaos, −1/N (1 − 1/π) ≤ SFF ≤ 0 and 0 ≤ SFF ≤ 1/πN, valid for thermal systems with large and small number of degrees of freedom respectively. We have studied both the early and late behaviour of SFF to check the validity and applicability of our derived bound. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos. Finally, we provide an example of integrability from GUE based RMT from Toda Lattice model to explicitly show the application of our derived bound on SFF to quantify chaos.
Highlights
Where by the parenthesis symbol · · · we represent the thermal average or expectation of a physical observable associated with the physical system under consideration
In this article, using the principles of Random Matrix Theory (RMT) with Gaussian Unitary Ensemble (GUE), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time scale
We briefly review about the construction of two and four point OTOC from GUE based RMT. [7,8,9] This will help us to futher connect with the computation of SFF and derive the bound on quantum chaos of this paper
Summary
The connected part of the Green’s function Gc depends on the two point function δJ (λ)δJ (μ). From GUE based RMT the exact functional form near the centre of spectrum of the eigen values of the random distribution can be expressed in the following form: sin2[N (λ − μ)] 1. Which can be derived using the method of orthogonal polynomials for GUE.. There are two parts appearing in the above mentioned kernel, which give different physical measures:. (a) 1/N 2 part with sine squared function gives the ramp and have sub-dominant contribution in the integral kernel. (b) 1/N part with Delta function gives the plateau and dominant contribution in the integral kernel
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
