Related papers: Linear and Nonlinear Dynamical 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…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
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.
How classical chaos emerges from the underlying quantum world is a fundamental problem in physics. The origin of this question is in the correspondence principle. Classical chaos arises due to non-linear dynamics, whereas quantum mechanics,…
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…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
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…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
A new generic dynamical phenomenon of pseudochaos and its relevance to the statistical physics both modern as well as traditional one are considered and explained in some detail. The pseudochaos is defined as a statistical behavior of 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…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
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…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
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…
Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct…
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…
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…
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system…
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…