Related papers: Quantum Chaos and Statistical Mechanics
It is widely believed that quantum mechanics cannot exhibit chaos, since unitarity of time evolution ensures that distances between quantum states are preserved. However, a parallel argument can be constructed in classical mechanics that…
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…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Model interactions between classical and quantum systems are briefly reviewed. These include: general measurement - like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, piecewise deterministic Markov processes…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation…
If quantum mechanics is taken for granted the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. "Random" quantum events are intimately related to the emergence of both space-time as…
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…
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
Relaxation in the time correlation between operators is studied. Quantized chaotic systems are shown to have distinct relaxation fluctuations that are universal and can be usefully modelled by Random Matrix Theory. Various quantized maps…
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the…
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…
In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on…