Can culture be solely inferred from the absence of genetic or environmental factors ?

Rendell & Whitehead's minimalist definition of culture does not allow for the important gaps between cetaceans and Inimans. A more complete analysis reveals important discontinuities that may be more instnictive for comparative purposes than the continuities emphasized by the authors

Fragmented superfluid due to frustration of cold atoms in optical lattices

A one dimensional optical lattice is considered where a second dimension is encoded in the internal states of the atoms giving effective ladder systems. Frustration is introduced by an additional optical lattice that induces tunneling of superposed atomic states. The effects of frustration range from the stabilization of the Mott insulator phase with ferromagnetic order, to the breakdown of superfluidity and the formation of a macroscopically fragmented phase.Comment: New version, more results, about 20 page

Dynamical creation of bosonic Cooper-like pairs

We propose a scheme to create a metastable state of paired bosonic atoms in an optical lattice. The most salient features of this state are that the wavefunction of each pair is a Bell state and that the pair size spans half the lattice, similar to fermionic Cooper pairs. This mesoscopic state can be created with a dynamical process that involves crossing a quantum phase transition and which is supported by the symmetries of the physical system. We characterize the final state by means of a measurable two-particle correlator that detects both the presence of the pairs and their size

Coupling single molecule magnets to quantum circuits

In this work we study theoretically the coupling of single molecule magnets (SMMs) to a variety of quantum circuits, including microwave resonators with and without constrictions and flux qubits. The main results of this study is that it is possible to achieve strong and ultrastrong coupling regimes between SMM crystals and the superconducting circuit, with strong hints that such a coupling could also be reached for individual molecules close to constrictions. Building on the resulting coupling strengths and the typical coherence times of these molecules (of the order of microseconds), we conclude that SMMs can be used for coherent storage and manipulation of quantum information, either in the context of quantum computing or in quantum simulations. Throughout the work we also discuss in detail the family of molecules that are most suitable for such operations, based not only on the coupling strength, but also on the typical energy gaps and the simplicity with which they can be tuned and oriented. Finally, we also discuss practical advantages of SMMs, such as the possibility to fabricate the SMMs ensembles on the chip through the deposition of small droplets.Comment: 23 pages, 12 figure

Collocation of Next-Generation Operators for Computing the Basic Reproduction Number of Structured Populations

We contribute a full analysis of theoretical and numerical aspects of the collocation approach recently proposed by some of the authors to compute the basic reproduction number of structured population dynamics as spectral radius of certain infinite-dimensional operators. On the one hand, we prove under mild regularity assumptions on the models coefficients that the concerned operators are compact, so that the problem can be properly recast as an eigenvalue problem thus allowing for numerical discretization. On the other hand, we prove through detailed and rigorous error and convergence analyses that the method performs the expected spectral accuracy. Several numerical tests validate the proposed analysis by highlighting diverse peculiarities of the investigated approach

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde

Split-merge cycle, fragmented collapse, and vortex disintegration in rotating Bose-Einstein condensates with attractive interactions

The dynamical instabilities and ensuing dynamics of singly- and doubly-quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full 3D numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly-quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly-quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of the MIT group.Comment: 11 pages, 10 figure

Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules

Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are exactly conserved locally. A general scheme to derive transport coefficients for such biased, velocity dependent collision rules is developed. Analytic expressions for the self-diffusion coefficient and the shear viscosity are obtained, and very good agreement is found with numerical results at small and large mean free paths. The viscosity turns out to be proportional to the square root of temperature, as in a real gas. In addition, the theoretical framework is applied to a two-component version of the model, and expressions for the viscosity and the difference in diffusion of the two species are given.Comment: 31 pages, 8 figures, accepted by J. Phys. Cond. Matte

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric