Related papers: Quantum analogues of exponential sensitivity: from…
We investigate the classical-quantum correspondence in the inverted harmonic oscillator (IHO) system. It is shown that the out-of-time-order correlators (OTOCs) which the initial states are located at any position in the IHO system possess…
Quantum chaos is an intriguing topic and has attracted a great deal of interests in quantum mechanics and black hole physics. Recently, the exponential growth of out-of-time-ordered correlator (OTOC) has been proposed to diagnose quantum…
Classical chaos refers to the property of trajectories to diverge exponentially as time tends to infinity. It is characterized by a positive Lyapunov exponent. There are many different descriptions of quantum chaos. The one related to the…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators. Focusing on the chaotic behaviors under the perturbation, we analytically derive the Lyapunov exponent and scrambling time of the inverted…
We suggest a new indicator of quantum chaos based on the logarithmic out-of-time-order correlator. On the one hand, this indicator correctly reproduces the average classical Lyapunov exponent in the semiclassical limit and directly links…
While classical chaos has been successfully characterized with consistent theories and intuitive techniques, such as with the use of Lyapunov exponents, quantum chaos is still poorly understood, as well as its relation with multi-partite…
We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators with anharmonic coupling. We compare the classical system with quantum system. Via the quantum action, we construct Poincar\'e sections and compute Lyapunov exponents…
Out-of-time-order correlators (OTOCs) can be used to probe how quickly a quantum system scrambles information when the initial conditions of the dynamics are changed. In sufficiently large quantum systems, one can extract from the OTOC the…
Recently, the out-of-time-ordered correlator(OTOC) and Krylov complexity have been studied actively as a measure of operator growth. OTOC is known to exhibit exponential growth in chaotic systems, which was confirmed in many previous works.…
We study universal chaotic dynamics of a large class of periodically driven critical systems described by spatially inhomogeneous conformal field theories. By employing an effective curved spacetime approach, we show that the onset of…
The quantum-to-classical correspondence is often quantified in dynamics by a quantity referred to as the out-of-time-order correlator (OTOC). In chaotic systems, the OTOC is expected to grow exponentially at early time, characteristic of a…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time…
We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_g where F_g scales…
Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks…
Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has…
The different time-dependent distances of two arbitrarily close quantum or classical-statistical states to a third fixed state are shown to imply an experimentally relevant notion of state sensitivity to initial conditions. A quantitative…
Krylov complexity has recently been proposed as a quantum probe of chaos. The Krylov exponent characterising the exponential growth of Krylov complexity is conjectured to upper-bound the Lyapunov exponent. We compute the Krylov and the…
Chaotic evolutions exhibit exponential sensitivity to initial conditions. This suggests that even very small perturbations resulting from weak coupling of a quantum chaotic environment to the position of a system whose state is a non-local…