Related papers: Classical and Quantum Chaos from Continuous Quantu…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical…
The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here…
Signatures of chaos can be understood by studying quantum systems whose classical counterpart is chaotic. However, the concepts of integrability, non-integrability and chaos extend to systems without a classical analogue. Here, we first…
We examine whether the chaotic behavior of classical systems with a limited number of degrees of freedom can produce quantum dephasing, against the conventional idea that dephasing takes place only in large systems with a huge number of…
Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not…
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to…
The quantum dynamics of a classically chaotic model are studied in the approach to the macroscopic limit. The quantum predictions are compared and contrasted with the classical predictions of both Newtonian and Liouville mechanics. The…
Although the importance of the quantum-classical correspondence has been recognized in numerous studies of quantum chaos, whether it still holds for finite time dynamics remains less known. We address this question in this work by…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
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…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling…
The effect of repetitive measurement for quantum dynamics of driven by an intensive external force of the simple few-level systems as well as of the multilevel systems that exhibit the quantum localisation of classical chaos is…
Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to…
We have recently suggested a quantum action, which has the form of a classical action and takes into account quantum effects via renormalized action parameters. Here we apply it to quantum chaos. We study a system in 2-D with weak…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…