New wine in old bottles: Quantum measurement - direct, indirect, weak - with some applications

In this, partly pedagogical review, I attempt to give a self-contained overview of the basis of (non-relativistic) QM measurement theory expressed in density matrix formalism. The focus is on applications to the theory of weak measurement, as developed by Aharonov and Vaidman and their collaborators. Their development of weak measurement combined with what they call 'post-selection' - judiciously choosing not only the initial state of a system ('pre-selection') but also its final state - has received much attention recently. Not the least has it opened up new, fruitful experimental vistas, like novel approaches to amplification. But the approach has also attached to it some air of mystery. I will attempt to 'de-mystify' it by showing that (almost) all results can be derived in a straight-forward way from conventional QM. Among other things, I develop the formalism not only to first order but also to second order in the weak interaction responsible for the measurement. This also allows me to derive, more or less as a by-product, the master equation for the density matrix of an open system in interaction with an environment. One particular application I shall treat of the weak measurement is the so called Leggett-Garg inequalities, a k a 'Bell inequalities in time'. I also give an outline, even if rough, of some of the ingenious experiments that the work by Aharonov, Vaidman and collaborators has inspired. If anything is magic in the weak measurement + post-selection approach, it is the interpretation of the so called weak value of an observable. Is it a bona fide property of the system considered? I have no answer to this question; I shall only exhibit the pros and cons of the proposed interpretation.Comment: 65 pages, 8 figure

Optical-NIR analysis of globular clusters in the IKN dwarf spheroidal: a complex star formation history

Age, metallicity and spatial distribution of globular clusters (GCs) provide a powerful tool to reconstruct major star-formation episodes in galaxies. IKN is a faint dwarf spheroidal (dSph) in the M81 group of galaxies. It contains five old GCs, which makes it the galaxy with the highest known specific frequency (SN=126). We estimate the photometric age, metallicity and spatial distribution of the poorly studied IKN GCs. We search SDSS for GC candidates beyond the HST field of view, which covers half of IKN. To break the age-metallicity degeneracy in the V-I colour we use WHT/LIRIS Ks-band photometry and derive photometric ages and metallicities by comparison with SSP models in the V,I,Ks colour space. IKN GCs' VIKs colours are consistent with old ages ($\geq\!8$ Gyr) and a metallicity distribution with a higher mean than typical for such a dSph ([Fe/H$]\!\simeq\!-1.4_{-0.2}^{+0.6}$ dex). Their photometric masses range ($0.5 <{\cal M_{\rm GC}}<4\times10^5M_\odot$) implies a high mass ratio between GCs and field stars, of $10.6\%$. Mixture model analysis of the RGB field stars' metallicity suggests that 72\% of the stars may have formed together with the GCs. Using the most massive GC-SFR relation we calculate a SFR of $\sim\!10M_\odot/$yr during its formation epoch. We note that the more massive GCs are closer to the galaxy photometric centre. IKN GCs also appear spatially aligned along a line close to the IKN major-axis and nearly orthogonal to the plane of spatial distribution of galaxies in the M81 group. We identify one new IKN GC candidate based on colour and PSF analysis of the SDSS data. The evidence towards i) broad and high metallicity distribution of the field IKN RGB stars and its GCs, ii) high fraction and iii), spatial alignment of IKN GCs, supports a scenario for tidally triggered complex IKN's SFH in the context of interactions with galaxies in the M81 group.Comment: 12 pages, 9 figures, accepted to A&

Thermal broadening of the Coulomb blockade peaks in quantum Hall interferometers

We demonstrate that the differential magnetic susceptibility of a fractional quantum Hall disk, representing a Coulomb island in a Fabry--Perot interferometer, is exactly proportional to the island's conductance and its paramagnetic peaks are the equilibrium counterparts of the Coulomb blockade conductance peaks. Using as a thermodynamic potential the partition functions of the edge states' effective conformal field theory we find the positions of the Coulomb blockade peaks, when the area of the island is varied, the modulations of the distance between them as well as the thermal decay and broadening of the peaks when temperature is increased. The finite-temperature estimates of the peak's heights and widths could give important information about the experimental observability of the Coulomb blockade. In addition, the predicted peak asymmetry and displacement at finite temperature due to neutral multiplicities could serve to distinguish different fractional quantum Hall states with similar zero-temperature Coulomb blockade patterns.Comment: 6 pages, 6 figures; published versio

An Investigation of the Large-scale Variability of the Apparently Single Wolf-Rayet Star WR 1

In recent years, much studies have focused on determining the origin of the large-scale line-profile and/or photometric patterns of variability displayed by some apparently single Wolf-Rayet stars, with the existence of an unseen (collapsed?) companion or of spatially extended wind structures as potential candidates. We present observations of WR 1 which highlight the unusual character of the variations in this object. Our narrowband photometric observations reveal a gradual increase of the stellar continuum flux amounting to Delta v = 0.09 mag followed by a decline on about the same timescale (3-4 days). Only marginal evidence for variability is found during the 11 following nights. Strong, daily line-profile variations are also observed but they cannot be easily linked to the photometric variations. Similarly to the continuum flux variations, coherent time-dependent changes are observed in 1996 in the centroid, equivalent width, and skewness of He II 4686. Despite the generally coherent nature of the variations, we do not find evidence in our data for the periods claimed in previous studies. While the issue of a cyclical pattern of variability in WR 1 is still controversial, it is clear that this object might constitute in the future a cornerstone for our understanding of the mechanisms leading to the formation of largely anisotropic outflows in Wolf-Rayet stars.Comment: 11 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Nuclear star cluster formation in energy-space

In a virialized stellar system, the mean-square velocity is a direct tracer of the energy per unit mass of the system. Here, we exploit this to estimate and compare root-mean-square velocities for a large sample of nuclear star clusters and their host (late- or early-type) galaxies. Traditional observables, such as the radial surface brightness and second-order velocity moment profiles, are subject to short-term variations due to individual episodes of matter infall and/or star formation. The total mass, energy and angular momentum, on the other hand, are approximately conserved. Thus, the total energy and angular momentum more directly probe the formation of galaxies and their nuclear star clusters, by offering access to more fundamental properties of the nuclear cluster-galaxy system than traditional observables. We find that there is a strong correlation, in fact a near equality, between the root-mean-square velocity of a nuclear star cluster and that of its host. Thus, the energy per unit mass of a nuclear star cluster is always comparable to that of its host galaxy. We interpret this as evidence that nuclear star clusters do not form independently of their host galaxies, but rather that their formation and subsequent evolution are coupled. We discuss how our results can potentially be used to offer a clear and observationally testable prediction to distinguish between the different nuclear star cluster formation scenarios, and/or quantify their relative contributions.Comment: 12 pages, 3 figures, 4 tables; accepted for publication in MNRA