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Register a new userThe Cheshire Cat revisited
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V. Vento
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The concept of effective field theory leads in a natural way to a construction principle for phenomenological sensible models known under the name of the Cheshire Cat Principle. We review its formulation in the chiral bag scenario and discuss its realization for the flavor singlet axial charge. Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. The presence of this surface term allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. We show that one can obtain a striking Cheshire-Cat phenomenon with a negligibly small singlet axial charge.
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It is shown that discrete-event simulation accurately reproduces the experimental data of a single-neutron interferometry experiment [T. Denkmayr {sl et al.}, Nat. Commun. 5, 4492 (2014)] and provides a logically consistent, paradox-free, cause-and-effect explanation of the quantum Cheshire cat effect without invoking the notion that the neutron and its magnetic moment separate. Describing the experimental neutron data using weak-measurement theory is shown to be useless for unravelling the quantum Cheshire cat effect.
A kind of paradoxical effects has been demonstrated that the pigeonhole principle, i.e., if three pigeons are put in two pigeonholes then at least two pigeons must stay in the same hole, fails in certain quantum mechanical scenario. Here we shall show how to associate a proof of Kochen-Specker theorem with a quantum pigeonhole effect and vise versa, e.g., from state-independent proofs of Kochen-Specker theorem some kind of state-independent quantum pigeonhole effects can be demonstrated. In particular, a state-independent version of the quantum Cheshire cat, which can be rendered as a kind of quantum pigeonhole effect about the trouble of putting two pigeons in two or more pigeonholes, arises from Peres-Mermins magic square proof of contextuality.
We show that the recent proposal to describe the $N_f=1$ baryon in the large number of color limit as a quantum Hall droplet, can be understood as a chiral bag in a 1+2 dimensional strip using the Cheshire cat principle. For a small bag radius, the bag reduces to a vortex line which is the smile of the cat with flowing gapless quarks all spinning in the same direction. The disc enclosed by the smile is described by a topological field theory due to the Callan-Harvey anomaly out-flow. The chiral bag carries naturally unit baryon number and spin $frac 12 N_c$. The generalization to arbitrary $N_f$ is discussed.
The Cheshire Cat is a relatively poor group of galaxies dominated by two luminous elliptical galaxies surrounded by at least four arcs from gravitationally lensed background galaxies that give the system a humorous appearance. Our combined optical/X-ray study of this system reveals that it is experiencing a line of sight merger between two groups with a roughly equal mass ratio with a relative velocity of ~1350 km/s. One group was most likely a low-mass fossil group, while the other group would have almost fit the classical definition of a fossil group. The collision manifests itself in a bimodal galaxy velocity distribution, an elevated central X-ray temperature and luminosity indicative of a shock, and gravitational arc centers that do not coincide with either large elliptical galaxy. One of the luminous elliptical galaxies has a double nucleus embedded off-center in the stellar halo. The luminous ellipticals should merge in less than a Gyr, after which observers will see a massive 1.2-1.5 x 10^14 solar mass fossil group with an M_r = -24.0 brightest group galaxy at its center. Thus, the Cheshire Cat offers us the first opportunity to study a fossil group progenitor. We discuss the limitations of the classical definition of a fossil group in terms of magnitude gaps between the member galaxies. We also suggest that if the merging of fossil (or near-fossil) groups is a common avenue for creating present-day fossil groups, the time lag between the final galactic merging of the system and the onset of cooling in the shock-heated core could account for the observed lack of well-developed cool cores in some fossil groups.
A common-sense perception of a physical system is that it is inseparable from its physical properties. The notion of Quantum Cheshire Cat challenges this, as far as quantum systems are concerned. It shows that a quantum system can be decoupled from its physical property under suitable pre and postselections. However, in the Quantum Cheshire Cat setup, the decoupling is not permanent. The photon, for example, and its circular polarization is separated and then recombined. In this paper, we present a thought experiment where we decouple two photons from their respective polarizations and then interchange them during recombination. Thus, our proposal shows that the belongingness of a property for a physical system is very volatile in the quantum world. This raises the question of reality of an observable at a much deeper level.
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