Related papers: Global Symmetry and Maximal Chaos
We investigate why the Lyapunov exponents $\lambda$ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound $\lambda < 2 \pi k_B T/{\hbar}$ by probing imaginary-time path-integral space using ring-polymer molecular dynamics…
We compute the Lyapunov exponents for test particles orbiting in unstable circular trajectories around D-dimensional Reissner-Nordstr\"om (RN) black holes, scrutinizing instances of the chaos bound violation. Notably, we discover that an…
In maximally chaotic quantum systems, a class of out-of-time-order correlators (OTOCs) saturate the Maldacena-Shenker-Stanford (MSS) bound on chaos. Recently, it has been shown that the same OTOCs must also obey an infinite set of…
We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes effectively a…
Classical arguments for thermalization of isolated systems do not apply in a straightforward way to the quantum case. Recently, there has been interest in diagnostics of quantum chaos in many- body systems. In the classical case, chaos is a…
We explore the quantum chaos of the coadjoint orbit action. We study quantum fluctuation around a saddle point to evaluate the soft mode contribution to the out-of-time-ordered correlator. We show that the stability condition of the…
We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular…
We study the Lyapunov exponent $\lambda_L$ in quantum field theories with spacetime-independent disorder interactions. Generically $\lambda_L$ can only be computed at isolated points in parameter space, and little is known about the way in…
We consider a quantum system with $N$ degrees of freedom which is classically chaotic. When $N$ is large, and both $\hbar$ and the quantum energy uncertainty $\Delta E$ are small, quantum chaos theory can be used to demonstrate the…
Quantum chaos in many-body systems may be characterized by the Lyapunov exponent defined as the exponential growth rate of out-of-time-order correlators (OTOC). So far Lyaponov exponents around various quantum critical points (QCP) remain…
The article presents results of preliminary study of solutions to recently offered basic thermodynamic equation for equilibrium in chemical systems with focus on chaotic behavior. Classical part of that equation was investigated earlier in…
A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the…
Quantum chaos cannot develop faster than $\lambda \leq 2 \pi/(\hbar \beta)$ for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent $\lambda$ is set by the width of the…
There are two types of quantum chaos: eigenbasis chaos and spectral chaos. The first type controls the early-time physics, e.g. the thermal relaxation and the sensitivity of the system to initial conditions. It can be traced back to the…
Classical particle motions in an inverse harmonic potential show the exponential sensitivity to initial conditions, where the Lyapunov exponent $\lambda_L$ is uniquely fixed by the shape of the potential. Hence, if we naively apply the…
A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…
In classical chaotic systems the entropy, averaged over initial phase space distributions, follows an universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the…
A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so…
We discuss quantum field theories with global $SU(N)$ and $O(N)$ symmetries for which the temporal direction is compactified on a circle of size $L$ with periodicity of fields up to a global symmetry transformation, i.e. twisted boundary…
Eigenstate thermalization hypothesis is a detailed statement of the matrix elements of few-body operators in energy eigenbasis of a chaotic Hamiltonian. Part of the statement is that the off-diagonal elements fall exponential for large…