Quantum Chaos Of Unitary Fermi Gases In Strong Pairing Fluctuation Region

Abstract

The growth rate of the out-of-time-ordered correlator in a N-flavor Fermi gas is investigated and the Lyapunov exponent λL is calculated to the order of 1/N . We find that the Lyapunov exponent monotonically increases as the interaction strength increases from the BCS limit to the unitary region. At the unitarity, the Lyapunov exponent increases while the temperature drops and it can reach to the order of λL ∼ T around the critical temperature for the N = 1 case. For N → ∞, the Lyapunov exponent reaches its maximum λL ≈ 4.35T /N at the critical temperature. The system scrambles faster for stronger pairing fluctuations. At the BCS limit, the Lyapunov exponentbehaviorsasλL ∝e^μ/Ta_s^2T2/N.