Zeno effect and ergodicity in finite-time quantum measurements

We demonstrate that an attempt to measure a non-local in time quantity, such as the time average \la A\ra_T of a dynamical variable $A$, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator \a. Conversely, in a long measurement of \la A\ra_T to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which von Neumann ensemble average of \a coincides with \la A\ra_T. Both effects are conveniently analysed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behaviour is shown to be a consequence of conservation of probability

Correlated Equilibria of Classical Strategic Games with Quantum Signals

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve even better efficiency than in any correlated equilibrium with classical signals, and find the answer to be positive.Comment: 8 pages, LaTe

Properties of the first excited state of 9Be derived from (gamma,n) and (e,e') reactions

Properties of the first excited state of the nucleus 9Be are discussed based on recent (e,e') and (gamma,n) experiments. The parameters of an R-matrix analysis of different data sets are consistent with a resonance rather than a virtual state predicted by some model calculations. The energy and the width of the resonance are deduced. Their values are rather similar for all data sets, and the energy proves to be negative. It is argued that the disagreement between the extracted B(E1) values may stem from different ways of integration of the resonance. If corrected, fair agreement between the (e,e') and one of the (gamma,n) data sets is found. A recent (gamma,n) experiment at the HIgS facility exhibits larger cross sections close to the neutron threshold which remain to be explained.Comment: 5 pages, accepted fro publication in Phys. Rev.

Measurement of the total energy of an isolated system by an internal observer

We consider the situation in which an observer internal to an isolated system wants to measure the total energy of the isolated system (this includes his own energy, that of the measuring device and clocks used, etc...). We show that he can do this in an arbitrarily short time, as measured by his own clock. This measurement is not subjected to a time-energy uncertainty relation. The properties of such measurements are discussed in detail with particular emphasis on the relation between the duration of the measurement as measured by internal clocks versus external clocks.Comment: 7 pages, 1 figur

No-cloning theorem in thermofield dynamics

We discuss the relation between the no-cloning theorem from quantum information and the doubling procedure used in the formalism of thermofield dynamics (TFD). We also discuss how to apply the no-cloning theorem in the context of thermofield states defined in TFD. Consequences associated to mixed states, von Neumann entropy and thermofield vacuum are also addressed.Comment: 16 pages, 3 figure

Bubble statistics and coarsening dynamics for quasi-two dimensional foams with increasing liquid content

We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling state, all bubble distributions are independent not only of time but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and with decreasing bubble size. We successfully model this behavior by explicitly incorporating the border blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry

Measure Recognition Problem

This is an article in mathematics, specifically in set theory. On the example of the Measure Recognition Problem (MRP) the article highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra \algB and a property $\Phi$ of measures one can recognize by purely combinatorial means if \algB supports a strictly positive measure with property $\Phi$. The most famous instance of this problem is MRP(countable additivity), and in the first part of the article we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v zamonja and Plebanek (2006) gives an easy solution to the former of these problems, and gives some partial information about the latter. The long term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem which gives such a structure theorem for measure algebras

Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate

We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.Comment: 4 pages, 3 figures, lette

The Hartman effect and weak measurements "which are not really weak"

We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays the role of the initial pointer state. Under tunnelling conditions such 'self measurement' is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as post-selection in the final state becomes improbable. We also demonstrate that it is a good precision, or 'not really weak' quantum measurement: no matter how wide the barrier d, it is possible to transmit a wavepacket with a width {\sigma} small compared to the observed advancement. As is the case with all weak measurements, the probability of transmission rapidly decreases with the ratio {\sigma}/d.Comment: 6 pages, 1 figur

Coarsening of Two Dimensional Foam on a Dome

In this paper we report on bubble growth rates and on the statistics of bubble topology for the coarsening of a dry foam contained in the narrow gap between two hemispheres. By contrast with coarsening in flat space, where six-sided bubbles neither grow nor shrink, we observe that six sided bubbles grow with time at a rate that depends on their size. This result agrees with the modification to von Neumann's law predicted by J.E. Avron and D. Levine. For bubbles with a different number of sides, except possibly seven, there is too much noise in the growth rate data to demonstrate a difference with coarsening in flat space. In terms of the statistics of bubble topology, we find fewer 3, 4, and 5 sided bubbles, and more 6 and greater sided bubbles, in comparison with the stationary distribution for coarsening in flat space. We also find good general agreement with the Aboav-Weaire law for the average number of sides of the neighbors of an n-sided bubble