Related papers: Operator front broadening in chaotic and integrabl…
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…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
The symmetry of chaotic systems plays a pivotal role in determining the universality class of spectral statistics and dynamical behaviors, which can be described within the framework of random matrix theory. Understanding the influence of…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time, but the situation for their quantum counterparts is less well understood. As a first example, we examine the quantum Lyapunov…
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…
Out of time ordered correlator (OTOC) is recently introduced as a powerful diagnose for quantum chaos. To go beyond, here we present an analytical solution of OTOC for a non-chaotic many body localized (MBL) system, showing distinct feature…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because in the semi-classical limit, $\hbar \to 0$, its rate of exponential growth…
We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises…
Quantum operator scrambling describes the spreading of local operators into the whole system in the picture of Heisenberg evolution, which is often quantified by the operator size growth. Here we propose a measure of quantum operator…
Out-of-time-ordered correlators (OTOCs) have been suggested as a means to study quantum chaotic behavior in various systems. In this work, I calculate OTOCs for the quantum mechanical anharmonic oscillator with quartic potential, which is…
While a wealth of results has been obtained for chaos in single-particle quantum systems, much less is known about chaos in quantum many-body systems. We contribute to recent efforts to make a semiclassical analysis of such systems…
We study a model of free fermions on a chain with dynamics generated by random unitary gates acting on nearest neighbor bonds and present an exact calculation of time-ordered and out-of-time-ordered correlators. We consider three distinct…
The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with $N$ components in the $(2+1)$-dimensional $O(N)$ nonlinear…
Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and…
Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-$N$ systems such as the SYK…
We calculate the third-order out-of-time-order correlator (OTOC) of a simple harmonic oscillator with an additional quartic interaction using the second quantization method. We obtain analytic relations for the spectrum, Fock space states,…
We study second-order Consensus-Based Optimization (CBO), a derivative-free global optimization algorithm in which the consensus force and the multiplicative exploratory noise act on particle velocities. We prove quantitative…
Transfer operators have been used widely to study the long time properties of chaotic maps or flows. We describe quantum analogues of these operators, which have been used as toy models by the quantum chaos community, but are also relevant…
We argue that two distinct probes of quantum chaos, i.e., the growth of noncommutativity of two unequal-time operators and the degree of irreversibility in a time-reversal test, are equivalent for initially localized states. We confirm this…