On asymptotic constants in the theory of extremes for Gaussian processes

This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for estimating these constants. A detailed error analysis illustrates the strength of our approach.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ534 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Optimal detection of homogeneous segment of observations in stochastic sequence

A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is obtained.Comment: 13 page

A classical analog to topological non-local quantum interference effect

The two main features of the Aharonov-Bohm effect are the topological dependence of accumulated phase on the winding number around the magnetic fluxon, and non-locality -- local observations at any intermediate point along the trajectories are not affected by the fluxon. The latter property is usually regarded as exclusive to quantum mechanics. Here we show that both the topological and non-local features of the Aharonov-Bohm effect can be manifested in a classical model that incorporates random noise. The model also suggests new types of multi-particle topological non-local effects which have no quantum analog.Comment: 4 pages, to be published in Phys. Rev. Let

``Weighing'' a closed system and the time-energy uncertainty principle

A gedanken-experiment is proposed for `weighing'' the total mass of a closed system from within the system. We prove that for an internal observer the time $\tau$, required to measure the total energy with accuracy $\Delta E$, is bounded according to $\tau \Delta E >\hbar$. This time-energy uncertainty principle for a closed system follows from the measurement back-reaction on the system. We generally examine what other conserved observables are in principle measurable within a closed system and what are the corresponding uncertainty relations.Comment: 8 page

Quantum limitations on superluminal propagation

Unstable systems such as media with inverted atomic population have been shown to allow the propagation of analytic wavepackets with group velocity faster than that of light, without violating causality. We illuminate the important role played by unstable modes in this propagation, and show that the quantum fluctuations of these modes, and their unitary time evolution, impose severe restrictions on the observation of superluminal phenomena.Comment: RevTeX 4 page

AB and Berry phases for a quantum cloud of charge

We investigate the phase accumulated by a charged particle in an extended quantum state as it encircles one or more magnetic fluxons, each carrying half a flux unit. A simple, essentially topological analysis reveals an interplay between the Aharonov-Bohm phase and Berry's phase.Comment: 10 pages, TAUP 2110-93. Te

Superoscillations and tunneling times

It is proposed that superoscillations play an important role in the interferences which give rise to superluminal effects. To exemplify that, we consider a toy model which allows for a wave packet to travel, in zero time and negligible distortion a distance arbitrarily larger than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Similar reasoning applies to the dwell time.Comment: 12 page