Space-time crystals of trapped ions

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.Comment: updated to the version published in PR

Thermodynamics of Quasi-Particles at Finite Chemical Potential

We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems of quasi-particles whose masses depend on both the temperature and the chemical potential. We work out several solutions for an interacting system of quarks and gluons and show that there is only one type of solution that reproduce both perturbative and lattice QCD.Comment: 33 pages, 1 figure. Accepted for publication in Nuclear Physics

Crystalline Color Superconductivity

In any context in which color superconductivity arises in nature, it is likely to involve pairing between species of quarks with differing chemical potentials. For suitable values of the differences between chemical potentials, Cooper pairs with nonzero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. Unlike the original LOFF state, these crystalline quark matter condensates include both spin zero and spin one Cooper pairs. We explore the range of parameters for which crystalline color superconductivity arises in the QCD phase diagram. If in some shell within the quark matter core of a neutron star (or within a strange quark star) the quark number densities are such that crystalline color superconductivity arises, rotational vortices may be pinned in this shell, making it a locus for glitch phenomena.Comment: 40 pages, LaTeX with eps figs. v2: New paragraph on Ginzburg-Landau treatment of LOFF phase in section 5. References added. v3: Small changes only. Version to appear in Phys. Rev.

Inhomogeneous Superconductivity in Condensed Matter and QCD

Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, differently from the usual BCS state, for the Cooper pair to have a non zero total momentum. For this reason in this state the gap varies in space, the ground state is inhomogeneous and a crystalline structure might be formed. This situation was considered for the first time by Fulde, Ferrell, Larkin and Ovchinnikov, and the corresponding state is called LOFF. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated to the presence of long wave-length excitations of zero mass. The situation described here is of interest both in solid state and in elementary particle physics, in particular in Quantum Chromo-Dynamics at high density and small temperature. In this review we present the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.Comment: RevTex, 83 pages, 26 figures. Submitted to Review of Modern Physic

Unsupervised model-based clustering for typological classification of Middle Bronze Age flanged axes

The classification of Western European flanged axes dating to the Middle Bronze Age (1650–1350 BC) is very complex. Many types of axe have been identified, some of which have numerous variant forms. In the current French terminology, all axes are divided into two generic groups: namely "Atlantic" (Atlantique) and "Eastern" (Orientale). Each of these generic groups, however, is highly polymorphic, so that it is often very difficult for the operator to classify individual axes with absolute confidence and certainty. In order to overcome such problems, a new shape classification is proposed, using morphometric analysis (Elliptic Fourier Analysis) followed by unsupervised model-based clustering and discriminant analysis, both based on Gaussian mixture modelling. Together, these methods produce a clearer pattern, which is independently validated by the spatial distribution of the findings, and multinomial scan statistics. This approach is fast, reproducible, and operator-independent, allowing artefacts of unknown membership to be classified rapidly. The method is designed to be amendable by the introduction of new artefacts, in the light of future discoveries. This method can be adapted to suit many other archaeological artefacts, providing information about the material, social and cultural relations of ancient populations

An explanatory model of temperature influence on flowering through whole-plant accumulation of <i>FT<b> </b></i>in <i>Arabidopsis thaliana</i><i> </i>

We assessed mechanistic temperature influence on flowering by incorporating temperature-responsive flowering mechanisms across developmental age into an existing model. Temperature influences the leaf production rate as well as expression of FLOWERING LOCUS T (FT), a photoperiodic flowering regulator that is expressed in leaves. The Arabidopsis Framework Model incorporated temperature influence on leaf growth but ignored the consequences of leaf growth on and direct temperature influence of FT expression. We measured FT production in differently aged leaves and modified the model, adding mechanistic temperature influence on FT transcription, and causing whole-plant FT to accumulate with leaf growth. Our simulations suggest that in long days, the developmental stage (leaf number) at which the reproductive transition occurs is influenced by day length and temperature through FT, while temperature influences the rate of leaf production and the time (in days) the transition occurs. Further, we demonstrate that FT is mainly produced in the first 10 leaves in the Columbia (Col-0) accession, and that FT accumulation alone cannot explain flowering in conditions in which flowering is delayed. Our simulations supported our hypotheses that: (i) temperature regulation of FT, accumulated with leaf growth, is a component of thermal time, and (ii) incorporating mechanistic temperature regulation of FT can improve model predictions when temperatures change over time