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Recently the bound on the Lyapunov exponent $lambda_L le 2pi T/ hbar$ in thermal quantum systems was conjectured by Maldacena, Shenker, and Stanford. If we naively apply this bound to a system with a fixed Lyapunov exponent $lambda_L$, it might predict the existence of the lower bound on temperature $T ge hbar lambda_L/ 2pi $. Particularly, it might mean that chaotic systems cannot be zero temperature quantum mechanically. Even classical dynamical systems, which are deterministic, might exhibit thermal behaviors once we turn on quantum corrections. We elaborate this possibility by investigating semi-classical particle motions near the hyperbolic fixed point and show that indeed quantum corrections may induce energy emission which obeys a Boltzmann distribution. We also argue that this emission is related to acoustic Hawking radiation in quantum fluid. Besides, we discuss when the bound is saturated and show that a particle motion in an inverse harmonic potential and $c=1$ matrix model may saturate the bound although they are integrable.
Out-of-time-order correlator (OTOC) $langle [x(t),p]^2 rangle $ in an inverted harmonic oscillator (IHO) in one-dimensional quantum mechanics exhibits remarkable properties. The quantum Lyapunov exponent computed through the OTOC precisely agrees wit
Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this paper, we emphasize (1) that this peculiar manifestation of unitarity is not specific
We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towa
We study the spectral representation of finite temperature, out of time ordered (OTO) correlators on the multi-time-fold generalised Schwinger-Keldysh contour. We write the contour-ordered correlators as a sum over time-order permutations acting on a
We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the N-by-N hermitian two-matrix model with the introduction of a loop-counting parameter and linear terms in the potential. We show that in the larg