TY - JOUR AB - African cichlids display a remarkable assortment of jaw morphologies, pigmentation patterns, and mating behaviors. In addition to this previously documented diversity, recent studies have documented a rich diversity of sex chromosomes within these fishes. Here we review the known sex-determination network within vertebrates, and the extraordinary number of sex chromosomes systems segregating in African cichlids. We also propose a model for understanding the unusual number of sex chromosome systems within this clade. AU - Gammerdinger, William J AU - Kocher, Thomas ID - 63 IS - 10 JF - Genes TI - Unusual diversity of sex chromosomes in African cichlid fishes VL - 9 ER - TY - JOUR AB - The thermodynamic description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. Recent studies on many-body localization have revealed the existence of systems that strongly violate ergodicity in the presence of quenched disorder. Here, we demonstrate that ergodicity can be weakly broken by a different mechanism, arising from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems. In the single-particle case, quantum scars correspond to wavefunctions that concentrate in the vicinity of unstable periodic classical trajectories. We show that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space that has recently been experimentally realized in a Rydberg-atom quantum simulator. The quantum scarred eigenstates are embedded throughout the otherwise thermalizing many-body spectrum but lead to direct experimental signatures, as we show for periodic recurrences that reproduce those observed in the experiment. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, opening up opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable. AU - Turner, Christopher AU - Michailidis, Alexios AU - Abanin, Dmitry AU - Serbyn, Maksym AU - Papić, Zlatko ID - 296 JF - Nature Physics TI - Weak ergodicity breaking from quantum many-body scars VL - 14 ER - TY - JOUR AB - We study the Fokker-Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker-Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain's boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker-Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one. AU - Bodova, Katarina AU - Haskovec, Jan AU - Markowich, Peter ID - 607 JF - Physica D: Nonlinear Phenomena TI - Well posedness and maximum entropy approximation for the dynamics of quantitative traits VL - 376-377 ER - TY - JOUR AB - We developed a method to calculate two-photon processes in quantum mechanics that replaces the infinite summation over the intermediate states by a perturbation expansion. This latter consists of a series of commutators that involve position, momentum, and Hamiltonian quantum operators. We analyzed several single- and many-particle cases for which a closed-form solution to the perturbation expansion exists, as well as more complicated cases for which a solution is found by convergence. Throughout the article, Rayleigh and Raman scattering are taken as examples of two-photon processes. The present method provides a clear distinction between the Thomson scattering, regarded as classical scattering, and quantum contributions. Such a distinction lets us derive general results concerning light scattering. Finally, possible extensions to the developed formalism are discussed. AU - Fratini, Filippo AU - Safari, Laleh AU - Amaro, Pedro AU - Santos, José ID - 294 IS - 4 JF - Physical Review A - Atomic, Molecular, and Optical Physics TI - Two-photon processes based on quantum commutators VL - 97 ER - TY - JOUR AB - We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in certain regimes in as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data. AU - Duerinckx, Mitia AU - Fischer, Julian L ID - 606 IS - 5 JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis TI - Well-posedness for mean-field evolutions arising in superconductivity VL - 35 ER -