Words of Engel type are concise in residually finite groups

Given a group-word w and a group G, the verbal subgroup w(G) is the one generated by all w-values in G. The word w is said to be concise if w(G) is finite whenever the set of w-values in G is finite. In the sixties P. Hall asked whether every word is concise but later Ivanov answered this question in the negative. On the other hand, Hall\u2019s question remains wide open in the class of residually finite groups. In the present article we show that various generalizations of the Engel word are concise in residually finite groups

Ground State Laser Cooling Beyond the Lamb-Dicke Limit

We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state $|0>$. The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.Comment: 6 pages, 4 figures, to appear in Europhysics Letter

Over and beyond the Primate baubellum Surface: A “Jewel Bone” Shielded in Museums

Computed Tomography (CT), mostly used in the medical field, has also recently been involved in Cultural Heritage studies, thanks to its efficiency and total non-invasiveness. Due to the large variety of sizes and compositions typical of Cultural Heritage objects, different X-ray sources, detectors, and setups are necessary to meet the different needs of various case studies. Here, we focus on the use of micro-CT to explore the morphology and shape of a small, neglected bone found inside the clitoris of non-human primates (the baubellum), which we obtained by accessing two prestigious primatological collections of the American Museum of Natural History (New York, NY, USA) and the National Museum of Natural History (Washington, DC, USA). Overcoming methodological limits imposed by the absence of homologous landmarks, we combined the use of the non-invasive 3D micro-CT and a recently released landmark-free shape analysis (the alpha-shape technique) to objectively describe and quantify the shape complexity of scanned primate baubella. Micro-CT provided high-resolution results, overcoming constraints linked to museum policy about non-disruptive sampling and preserving samples for future research. Finally, it proved appropriate as post-mortem sampling had no impact on protected wild primate populations

A Geometric Feature-Based Algorithm for the Virtual Reading of Closed Historical Manuscripts

X-ray Computed Tomography (CT), a commonly used technique in a wide variety of research fields, nowadays represents a unique and powerful procedure to discover, reveal and preserve a fundamental part of our patrimony: ancient handwritten documents. For modern and well-preserved ones, traditional document scanning systems are suitable for their correct digitization, and, consequently, for their preservation; however, the digitization of ancient, fragile and damaged manuscripts is still a formidable challenge for conservators. The X-ray tomographic approach has already proven its effectiveness in data acquisition, but the algorithmic steps from tomographic images to real page-by-page extraction and reading are still a difficult undertaking. In this work, we propose a new procedure for the segmentation of single pages from the 3D tomographic data of closed historical manuscripts, based on geometric features and flood fill methods. The achieved results prove the capability of the methodology in segmenting the different pages recorded starting from the whole CT acquired volume

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

Dynamics of an ion chain in a harmonic potential

Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, and thus the eigenmodes are not phononic-like waves. We study chains of N 1 ions and evaluate analytically the long-wavelength modes and the density of states in the short-wavelength limit. These results reproduce with good approximation the dynamics of chains consisting of dozens of ions. Moreover, they allow one to determine the critical transverse frequency required for the stability of the linear structure, which is found to be in agreement with results obtained by different theoretical methods [D. H. E. Dubin, Phys. Rev. Lett. 71, 2753 (1993)] and by numerical simulations [J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993)]. We introduce and explore the thermodynamic limit for the ion chain. The thermodynamic functions are found to exhibit deviations from extensivity

Microscopic physics of quantum self-organisation of optical lattices in cavities

We study quantum particles at zero temperature in an optical lattice coupled to a resonant cavity mode. The cavity field substantially modifies the particle dynamics in the lattice, and for strong particle-field coupling leads to a quantum phase with only every second site occupied. We study the growth of this new order out of a homogeneous initial distribution for few particles as the microscopic physics underlying a quantum phase transition. Simulations reveal that the growth dynamics crucially depends on the initial quantum many-body state of the particles and can be monitored via the cavity fluorescence. Studying the relaxation time of the ordering reveals inhibited tunnelling, which indicates that the effective mass of the particles is increased by the interaction with the cavity field. However, the relaxation becomes very quick for large coupling.Comment: 14 pages 6 figure

Quantum stability of self-organized atomic insulator-like states in optical resonators

We investigate a paradigm example of cavity quantum electrodynamics with many body systems: an ultracold atomic gas inside a pumped optical resonator. In particular, we study the stability of atomic insulator-like states, confined by the mechanical potential emerging from the cavity field spatial mode structure. As in open space, when the optical potential is sufficiently deep, the atomic gas is in the Mott-like state. Inside the cavity, however, the potential depends on the atomic distribution, which determines the refractive index of the medium, thus altering the intracavity field amplitude. We derive the effective Bose-Hubbard model describing the physics of the system in one dimension and study the crossover between the superfluid -- Mott insulator quantum states. We determine the regions of parameters where the atomic insulator states are stable, and predict the existence of overlapping stability regions corresponding to competing insulator-like states. Bistable behavior, controlled by the pump intensity, is encountered in the vicinity of the shifted cavity resonance.Comment: 13 pages, 6 figures. Replaced with revised version. Accepted for publication in New J. Phys., special issue "Quantum correlations in tailord matter

Thermal and quantum fluctuations in chains of ultracold polar molecules

Ultracold polar molecules, in highly anisotropic traps and interacting via a repulsive dipolar potential, may form one-dimensional chains at high densities. According to classical theory, at low temperatures there exists a critical value of the density at which a second order phase transition from a linear to a zigzag chain occurs. We study the effect of thermal and quantum fluctuations on these self-organized structures using classical and quantum Monte Carlo methods, by means of which we evaluate the pair correlation function and the static structure factor. Depending on the parameters, these functions exhibit properties typical of a crystalline or of a liquid system. We compare the thermal and the quantum results, identifying analogies and differences. Finally, we discuss experimental parameter regimes where the effects of quantum fluctuations on the linear - zigzag transition can be observed.Comment: Submitted to the Special issue on modern applications of trapped ions, J. Phys. B: At. Mol. Opt. Phy