Convergence of matrices under random conjugation: wave packet scattering without kinematic entanglement

In previous work, it was shown numerically that under successive scattering events, a collection of particles with Gaussian wavefunctions retains the Gaussian property, with the spread of the Gaussian ('Δx') tending to a value inversely proportional to the square root of each particle's mass. We prove this convergence in all dimensions ≥3

Wave-packet scattering without kinematic entanglement: convergence of expectation values

The wave packet spread of a particle in a collection of different mass particles, all with Gaussian wave functions, evolves to a value that is inversely proportional to the mass of the particle. The assumptions underlying this result and its derivation are reviewed. A mathematical demonstration of the convergence of an iteration central to this assertion is presented. Finally, the question of in-principle measurement of wave packet spread is taken up

Experimental Test of the “Special State” Theory of Quantum Measurement

An experimental test of the “special state” theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern–Gerlach setup. The “special state” theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this article background material is given on both quantum measurement and statistical mechanics aspects. For example, it is shown that future boundary conditions would not contradict experience, indicating that the fundamental equal-a-priori-probability assumption at the foundations of statistical mechanics is far too strong (since future conditioning reduces the class of allowed states). The test is based on a feature of this theory that was found necessary in order to recover standard (Born) probabilities in quantum measurements. Specifically, certain systems should have “noise” whose amplitude follows the long-tailed Cauchy distribution. This distribution is marked by the occasional occurrence of extremely large signals as well as a non-self-averaging property. The proposed test is a variant of the Stern–Gerlach experiment in which protocols are devised, some of which will require the presence of this noise, some of which will not. The likely observational schemes would involve the distinction between detection and non-detection of that “noise”. The signal to be detected (or not) would be either single photons or electric fields (and related excitations) in the neighborhood of the ends of the magnets

Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$

Passage-time distributions from a spin-boson detector model

The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle's enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like $E^{-3/4}$, which improves previous $E^{-1}$ estimates, obtained with a quantum clock model.Comment: 11 pages, 6 figures; minor changes, references corrected; accepted for publication in Phys. Rev.

HINDERED DECAY : QUANTUM ZENO EFFECT THROUGH ELECTROMAGNETIC FIELD DOMINATION

The lifetime of an unstable atom can be extended by watching it closely, i.e., illuminating it with an intense electromagnetic field of appropriate frequency. This is an example of ``dominated evolution'' and is closely related to the so-called ``quantum Zeno effect.'' For a metastable atom bathed in a laser beam at the frequency of another of its transitions, we obtain an expression for the modified lifetime as a function of beam intensity. This provides an example of the quantum Zeno effect on a truly decaying system, and also should be useful for probing short distance features of atomic wave functions

Refractory chronic migraine: long-term follow-up using a refractory rating scale

Refractory chronic migraine (RCM) is often associated with disability and a low quality of life (QOL). RCM ranges in severity from mild to severe. There would be a benefit both clinically and in research use in categorizing RCM patients according to severity. This study utilized a unique RCM severity rating scale, tracking the clinical course over 10 years. A total of 129 patients, ages 19–72, were assigned a severity rating of 2–10 (10 = worst). Pain level and QOL were assessed. Over the 10 years, 73% of all pts. had a 30% or more decline in pain. Pain levels improved 45% in mild pts., 42% in mod. pts., and 36% in severe pts. Pain was the same, or worse, in 4% of mild, 15% of mod., and 18% of severe pts. QOL in the mild group improved 35% over 10 years. In moderate pts., QOL improved 32%, while for the severe group QOL improved 33%. While pain and QOL improved across all three groups at the end of 10 years, the severe group remained with significantly more pain and decreased QOL than in the milder groups. The medications that helped significantly included: opioids (63% of pts. utilized opioids), frequent triptans (31%), butalbital (17%), onabotulinumtoxinA (16%), stimulants (12%), and other “various preventives” (9%). RCM pts. were rated using a refractory rating scale with the clinical course assessed over 10 years. Pain and QOL improved in all groups. In the severe group, pain and QOL improved, but still lagged behind the mild and moderate groups. Opioids and (frequent) triptans were the most commonly utilized meds