Related papers: Chaos and Quantum Mechanics
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly assume Markovian dynamics. Here, a logistic map endowed with…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
The agenda of Dissipative Quantum Chaos is to create a toolbox which would allow us to categorize open quantum systems into "chaotic" and "regular" ones. Two approaches to this categorization have been proposed recently. One of them is…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
We discuss the possibility of having "quantum dissipation" due to the interaction with chaotic degrees of freedom. We define the conditions that should be satisfied in order to have a dissipative effect similar to the one due to an…
Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure…
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…
We consider the dynamics of continuously measured many-body chaotic quantum systems. Focusing on the observable of state purification, we analytically describe the limits of strong and weak measurement rate, where in the latter case…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
Quantum chaos has recently received increasing attention due to its relationship with experimental and theoretical studies of nonequilibrium quantum dynamics, thermalization, and the scrambling of quantum information. In an isolated system,…
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum…
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is…
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be…
Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we…
A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function…
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…
The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate…