Scrambling and quantum chaos indicators from long-time properties of operator distributions

Quadratic Growth of Out-of-Time-Ordered Correlators in Quantum Kicked Rotor Model

“…Firstly, evolving the initial state |ψ(t 0 )⟩ from t 0 to t n yields |ψ(t n )⟩ = U(t n , t 0 )|ψ(t 0 )⟩. Secondly, applying operator (5) indicates that C 1 is the expectation value of operator B 2 for |ψ R (t 0 )⟩. The process to derive C 2 at time t = t n involves four steps.…”

“…Quantum scrambling, a fundamental concept elucidating the spread of information across multiple degrees of freedom that is inaccessible via local measurements, has garnered extensive attention in quantum information [ 1 , 2 , 3 , 4 ], quantum chaos [ 5 , 6 , 7 , 8 , 9 ], and condensed matter physics [ 10 , 11 , 12 , 13 ]. It is well known that the out-of-time ordered correlators (OTOCs) can quantify the process of information scrambling with relevance to the operator growth [ 14 , 15 ].…”

Operator size distribution in large N quantum mechanics of Majorana fermions

“…However, it is challenging to obtain the analytic expression for operator size and its distribution. Progress has been made in quantum circuits models [16][17][18][19][20][21], numerical studies and experimental proposals for spin models [9,[22][23][24], and bounds on the operator size in various contexts [25][26][27][28][29]. For the large N quantum mechanics like the SYK model [30][31][32], analytic results were only achieved for the initial growth [10,33,34], leaving the saturation in the late time unexplained.…”