Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories

An essential ingredient in many examples of the conflict between quantum theory and noncontextual hidden variables (e.g., the proof of the Kochen-Specker theorem and Hardy's proof of Bell's theorem) is a set of atomic propositions about the outcomes of ideal measurements such that, when outcome noncontextuality is assumed, if proposition $A$ is true, then, due to exclusiveness and completeness, a nonexclusive proposition $B$ ($C$) must be false (true). We call such a set a {\em true-implies-false set} (TIFS) [{\em true-implies-true set} (TITS)]. Here we identify all the minimal TIFSs and TITSs in every dimension $d \ge 3$, i.e., the sets of each type having the smallest number of propositions. These sets are important because each of them leads to a proof of impossibility of noncontextual hidden variables and corresponds to a simple situation with quantum vs classical advantage. Moreover, the methods developed to identify them may be helpful to solve some open problems regarding minimal Kochen-Specker sets.Comment: 9 pages, 7 figure

The right angle to look at orthogonal sets

If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable families of commensurable subgroups is shown

Pairing correlations with single Cooper pair transfer to individual quantal states

With the help of the static and dynamic mean field spectroscopic amplitudes, taking into account successive and simultaneous transfer channels properly corrected because of non-orthogonality effects, as well as describing the associated elastic channels in terms of experimentally determined optical potentials, one obtains absolute, two-particle transfer differential cross sections which provide an overall account of the data within experimental errors. One of the first results connected with such quantitative studies of pairing correlations in nuclei is the observation of phonon mediated pairing in the exotic halo nucleus $^{11}$Li, and the associated discovery of a new mechanism to break nuclear gauge symmetry: bootstrap, pigmy-resonance-mediated Cooper pair binding.Comment: Contributed chapter in "50 Years of Nuclear BCS", edited by R. A. Broglia and V. Zelevinsk

Electron Counting Statistics and Coherent States of Electric Current

A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons. We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current states with quantum-mechanical coherent states.Comment: 43 pages, LaTeX, to appear in the Journal of Mathematical Physics special volume on Mesoscopic Physic

Inflatino-less Cosmology

We construct inflationary models in the context of supergravity with orthogonal nilpotent superfields [1]. When local supersymmetry is gauge-fixed in the unitary gauge, these models describe theories with only a single real scalar (the inflaton), a graviton and a gravitino. Critically, there is no inflatino, no sgoldstino, and no sinflaton in these models. This dramatically simplifies cosmological models which can simultaneously describe inflation, dark energy and SUSY breaking.Comment: 4 page