Lawlessness on the maritime frontier of the greater Chesapeake, 1650-1750

When historians have addressed the issue of maritime lawlessness in the English colonies of North America their attention almost invariably has been drawn to New England where, according to the commonly held belief, opposition to the navigation system of the home government was most fervent, concerted, and pervasive. Rarely have researchers examined local involvement in piracy, illicit trade, and the unauthorized salvage of stranded or sunken vessels, or wrecking, in the Chesapeake region where, scholars customarily have maintained, the colonists willingly participated in the imperial navigation scheme. Traditional historical investigations of freebooters and smugglers have also tended to focus on the lawbreakers themselves, generally neglecting the activities of coastal inhabitants without whose support the outlaws could not have operated and prospered.;Contrary to the conventional wisdom, however, not only did residents of the greater Chesapeake personally engage in piracy, contraband trade, customs fraud, and wrecking, but many more supported their actions by assisting and harboring the perpetrators or by refusing to convict the lawbreakers in the common-law courts. In the provincial assemblies, other colonists opposed legislative initiatives designed to improve the enforcement of imperial policy in the maritime sphere. Compounding the enforcement problem in the greater Chesapeake was the participation of both royal and provincial officials--including customs officers, guardship commanders, and even colonial governors--in various contraband, duty fraud, and piratical schemes themselves. If British authorities wondered about the sources of such behavior they did not have far to look for precedents. English piracy, smuggling, and wrecking--often tacitly approved and even actively promoted by high-ranking government officials--dated back centuries before the colonial era.;The coincidence of the periods of greatest complaint about maritime lawbreaking in the Chesapeake with the intervals of most active regulation of colonial affairs by the home government suggests that inhabitants of the bay region conducted illegal maritime activities continuously between 1650 and 1750 and beyond. Reports by customs officials and guardship captains in the decade preceding the Revolution, including accounts of violent resistance to royal authority, indicate that compliance with the Navigation Acts was no better than it had been in the late seventeenth century when English authorities undertook a major reform initiative designed to end abuses of the system

Residence time statistics for NN blinking quantum dots and other stochastic processes

We present a study of residence time statistics for $N$ blinking quantum dots. With numerical simulations and exact calculations we show sharp transitions for a critical number of dots. In contrast to expectation the fluctuations in the limit of $N \to \infty$ are non-trivial. Besides quantum dots our work describes residence time statistics in several other many particle systems for example $N$ Brownian particles. Our work provides a natural framework to detect non-ergodic kinetics from measurements of many blinking chromophores, without the need to reach the single molecule limit

Evidence for a diffusion-controlled mechanism for fluorescence blinking of colloidal quantum dots

Fluorescence blinking in nanocrystal quantum dots is known to exhibit power-law dynamics, and several different mechanisms have been proposed to explain this behavior. We have extended the measurement of quantum-dot blinking by characterizing fluctuations in the fluorescence of single dots over time scales from microseconds to seconds. The power spectral density of these fluctuations indicates a change in the power-law statistics that occurs at a time scale of several milliseconds, providing an important constraint on possible mechanisms for the blinking. In particular, the observations are consistent with the predictions of models wherein blinking is controlled by diffusion of the energies of electron or hole trap states

Distribution of Time-Averaged Observables for Weak Ergodicity Breaking

We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $$.Comment: 5 pages, 2 figure

Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals

We investigate the non-ergodic properties of blinking nano-crystals using a stochastic approach. We calculate the distribution functions of the time averaged intensity correlation function and show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe non-ergodicity in systems stochastically modeled using the Levy walk framework for anomalous diffusion, for example certain types of chaotic dynamics, currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure

Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence

The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963-67. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to ITISE 2016 meeting in Granada, Spai

Quantum Mechanics at Planck's scale and Density Matrix

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies on the fact that here density matrix subjects to deformation whereas so far commutators have been deformed. The density matrix obtained by deformation of quantum-mechanical density one is named throughout this paper density pro-matrix. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows to describe dynamics. In particular, the explicit form of deformed Liouville's equation and the deformed Shr\"odinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that obtained results allow to deduce in a simple and natural way the Bekenstein-Hawking's formula for black hole entropy in semiclassical approximation.Comment: 18 pages,Latex,new reference