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This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76, 186 (1998)] that the chaotic tumbling of the satellite Hyperion would become non-classical within 20 years, but for the effects of environmental decoherence. The…
The famous Nils Bohr's quantum-classical correspondence principle states that the classical mechanics is a limiting case of the more general quantum mechanics. This implies that ``under certain conditions" quantum laws of motion become…
We analyze seemingly contradictory claims in the literature about the role played by decoherence in ensuring classical behavior for the chaotically tumbling satellite Hyperion. We show that the controversy is resolved once the very…
We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of…
The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess)to the correspondence principle. We will introduce a formalism for this classical limit…
The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC)…
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…
We investigate how decoherence affects the short-time separation between quantum and classical dynamics for classically chaotic systems, within the framework of a specific model. For a wide range of parameters, the distance between the…
Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. By virtue of the correspondence principle, the properties of the system that lead to chaotic dynamics at the classical…
The correspondence principle plays an important role in understanding the emergence of classical chaos from an underlying quantum mechanics. Here we present an infinite family of quantum dynamics that never resembles the analogous classical…
We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the…
In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence…
The quite different behaviors exhibited by microscopic and macroscopic systems with respect to quantum interferences suggest the existence of a borderline beyond which quantum systems loose their coherences and can be described classically.…
The recovery of classical chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper we discuss…
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 decoherence mechanism signals the limits beyond which the system dynamics approaches the classical behavior. We show that in some cases decoherence may also signal the limits beyond which the system dynamics has to be described by…
We consider the claim that decoherence explains the emergence of classicality in quantum systems, and conclude that it does not. We show that, given a randomly chosen universe composed of a variety of subsystems, some of which are…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
The environment -- external or internal degrees of freedom coupled to the system -- can, in effect, monitor some of its observables. As a result, the eigenstates of these observables decohere and behave like classical states: Continuous…
The decay of the overlap between a wave packet evolved with a Hamiltonian H and the same state evolved with H}+$\Sigma $ serves as a measure of the decoherence time $\tau_{\phi}$. Recent experimental and analytical evidence on classically…