By Ioannis Antoniou, Baidyanath Misra, Zdzislaw Suchanecki

The time operator is a robust technique for the research of risky dynamics and chaos idea. This synthesis of classical and glossy fabric offers a hugely utilized method of the improvement of either spectral research and prediction for chaotic complicated structures for which the time operator is defined by way of a semigroup of operators.

Show description

Read or Download Time Operator, Innovation and Complexity (Draft) PDF

Best physics books

Type 2 Gaucher Disease - A Bibliography and Dictionary for Physicians, Patients, and Genome Researchers

In March 2001, the nationwide Institutes of healthiness issued the next caution: "The variety of sites delivering health-related assets grows each day. Many websites supply useful details, whereas others can have info that's unreliable or deceptive. " additionally, end result of the swift elevate in Internet-based details, many hours should be wasted looking out, picking, and printing.

Molecular Physics and Elements of Quantum Chemistry: Introduction to Experiments and Theory

This textbook introduces the molecular physics and quantum chemistry had to comprehend the actual houses of molecules and their chemical bonds. It follows the authors' previous textbook "The Physics of Atoms and Quanta" and offers either experimental and theoretical basics for college students in physics and actual and theoretical chemistry.

Additional info for Time Operator, Innovation and Complexity (Draft)

Sample text

Let us, however, add that a great variety of systems of physical interest, including infinite ideal gas, hard rods system, a hard sphere gas and geodesic flow on a compact, connected smooth Riemanian manifold with negative curvature are known to be K-flows. Geodesic flows have been studied since the beginning of the 20th century, starting with Hadamard. In the case the manifold X has dim X = 2, the geodesic flow has an especially simple interpretation. It describes the notion of a point that moves on the surface X in the absence of external forces and without friction.

Since the entropy is a quantitative measure of information carried by a σ-algebra we can say that the filtration is innovative if H(Fs ) < H(Ft ) , for each s < t . In this way, by introducing entropy, we give a rigorous meaning to innovation in each system having countably generated filtration. However, from the practical point of view entropy, as the criterion of innovations, is not so useful as it seems to be. This concerns especially stochastic processes. Although each stochastic process determines a filtration it does not mean that the σ-algebras are generated by countable partitions.

About the strong convergence of truncated operators). 7). e. 7) we have T ρt |ρt = T ρ|ρ + t . The above equality means that the average age of the evolved state keeps step with the external clock time t. The above theorem suggests the following generalization of time operator. Let H be a (separable) Hilbert space and {Ut } a unitary group of evolution. : Ut D(T ) ⊂ D(T ) and T Ut = Ut T + tUt , for each t. This generalization of the notion of time operator can go further. The group {Ut } can be replaced by a semigroup, and/or the Hilbert space can be replaced by a Banach space.

Download PDF sample

Rated 4.18 of 5 – based on 6 votes