Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have the double-exponential initial decay $\propto \exp(-{\rm constant}\times e^{2\lambda_0 t})$ in the main part of phase space. The coefficient $\lambda_0$ is the self-averaging Lyapunov exponent. The average decay $\bar{M}\propto e^{-\lambda_1 t}$ is single exponential with a different coefficient $\lambda_1$. The volume of phase space that contributes to $\bar{M}$ vanishes in the classical limit $\hbar\to 0$ for times less than the Ehrenfest time $\tau_E=\frac{1}{2}\lambda_0^{-1}|\ln \hbar|$. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.Comment: 4 pages, 4 figures, [2017: fixed broken postscript figures

Preparation information and optimal decompositions for mixed quantum states

Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.Comment: 13 pages, latex, 2 postscript figure

TIME-VARIANT SPECTRAL ANALYSIS OF SURFACE EMG SIGNALS – EXEMPLARILY SHOWN FOR ARCHERY

To analyse the spectral density of electromyographic (EMG) signals Fourier transforms are commonly used. The prerequisite of this transform is that the analysed signal is stationary. Generally, this can not be assumed for the electromyograms of muscle contractions of human movement. A new method to analyse non-stationary biological signals is the time-variant spectral analysis. The aim of this paper is to use the timevariant spectral analysis in a realistic sport application to show connections of the athlete’s level and the spectral density of the EMG. Five top-level archers participated in the study. The results suggest, that a higher level of performance generally corresponds to lower median-frequencies and a smaller variability of the median-frequencies of the EMG-signals

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.

The Effect of Flow Structure on Corrosion: Circling-Foil Studies on 90/10 Copper-Nickel, and Hydrodynamic Modeling of the Erosion-Corrosion Process

The effects of turbulent flow on the corrosion behavior of 90/10 Cu-Ni were studied experimentally in synthetic seawater electrolyte, using a circling foil apparatus at relative velocities up to about 6 m/sec. The flow field at the specimen surface was characterized by anemometric methods. Corrosion rates were determined by direct weight loss and by several electrochemical methods, including the linear polarization method and from Tafel plots; also zero resistance ammeter measurements were made on galvanic couples. Consideration was given to the question of the appropriate analytical approach to velocity (fluid flow) effects on corrosion processes. The contribution of convective diffusion is considered dominant over the velocity range studied, and the rate of eddy diffusivity (fine flow structure effects on mass transport) is described. The separate electrochemical and mechanical influences of high-intensity turbulent flows are considered.Office of Naval Research Metallurgy Program Office, Code 471N00014-78-WR-80105, NR-036-120Approved for public release; distribution is unlimited

A Quantum-Bayesian Route to Quantum-State Space

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special attention paid to making all assumptions explici

Semiclassical properties and chaos degree for the quantum baker's map

We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy

Classical limit in terms of symbolic dynamics for the quantum baker's map

We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the quantum baker's map approaches a classical Bernoulli shift in the limit of a small effective Plank's constant.Comment: 12 pages, LaTex, typos correcte