相关论文: Orders of chaoticity of unitaries

Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…

There are various statements in the physics literature about the stratification of quantum states, for example into orbits of a unitary group, and about generalized differentiable structures on it. Our aim is to clarify and make precise…

Any real interaction process produces many incompatible system versions, or realisations, giving rise to omnipresent dynamic randomness and universally defined complexity (arXiv:physics/9806002). Since quantum behaviour dynamically emerges…

Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent, generic approaches suggest the presence of many-body…

The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…

We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation…

Decoherence in quantum systems which are classically chaotic is studied. It is well-known that a classically chaotic system when quantized loses many prominent chaotic traits. We show that interaction of the quantum system with an…

We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…

It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…

A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…

The presence of quantum chaos in nuclear mass systematics is analyzed by considering the differences between measured and calculated nuclear masses as a time series described by the power law 1/ f^alpha. While for the liquid droplet model…

Canonical quantization of general relativity does not yield a unique quantum theory for gravity. This is in part due to operator ordering ambiguities. In this paper, we investigate the role of different operator orderings on the question of…

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…

We propose a mathematical framework that we call quantum, higher-order Fourier analysis. This generalizes the classical theory of higher-order Fourier analysis, which led to many advances in number theory and combinatorics. We define a…

We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the…

The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this…

Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…