The growth rate of the out-of-time-ordered correlator in a $N$ -flavor Fermi gas is investigated and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ 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 ${\ensuremath{\lambda}}_{L}\ensuremath{\sim}T$ around the critical temperature for the $N=1$ case. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the Lyapunov exponent reaches its maximum ${\ensuremath{\lambda}}_{L}\ensuremath{\approx}4.35T/N$ at the critical temperature. The system scrambles faster for stronger pairing fluctuations. At the BCS limit, the Lyapunov exponent behaviors as ${\ensuremath{\lambda}}_{L}\ensuremath{\propto}{e}^{\ensuremath{\mu}/T}{a}_{s}^{2}{T}^{2}/N$.The growth rate of the out-of-time-ordered correlator in a $N$-flavor Fermi gas is investigated and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ 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 ${\ensuremath{\lambda}}_{L}\ensuremath{\sim}T$ around the critical temperature for the $N=1$ case. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the Lyapunov exponent reaches its maximum ${\ensuremath{\lambda}}_{L}\ensuremath{\approx}4.35T/N$ at the critical temperature. The system scrambles faster for stronger pairing fluctuations. At the BCS limit, the Lyapunov exponent behaviors as ${\ensuremath{\lambda}}_{L}\ensuremath{\propto}{e}^{\ensuremath{\mu}/T}{a}_{s}^{2}{T}^{2}/N$.

arXiv:2002.05759Physical review. B./Physical review. BJul 17, 20201 citation

The growth rate of the out-of-time-ordered correlator in a

N

-flavor Fermi gas is investigated and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ 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 ${\ensuremath{\lambda}}_{L}\ensuremath{\sim}T$ around the critical temperature for the

N=1

case. For $N\ensuremath{\rightarrow}\ensuremath{\infty}$, the Lyapunov exponent reaches its maximum ${\ensuremath{\lambda}}_{L}\ensuremath{\approx}4.35T/N$ at the critical temperature. The system scrambles faster for stronger pairing fluctuations. At the BCS limit, the Lyapunov exponent behaviors as ${\ensuremath{\lambda}}_{L}\ensuremath{\propto}{e}^{\ensuremath{\mu}/T}{a}_{s}^{2}{T}^{2}/N$.