Related papers: An Introduction to Quantum Chaos
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
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…
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
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…
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
We briefly review the well known connection between classical chaos and classical statistical mechanics, and the recently discovered connection between quantum chaos and quantum statistical mechanics.
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The other is…
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 true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
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…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the…
We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum…
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian…
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…