Growth, competition and cooperation in spatial population genetics

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.Comment: 29 pages, 14 figures; revised version including a section with results in the presence of fluid flow

Spin dynamics of a trapped spin-1 Bose Gas above the Bose-Einstein transition temperature

We study collective spin oscillations in a spin-1 Bose gas above the Bose-Einstein transition temperature. Starting from the Heisenberg equation of motion, we derive a kinetic equation describing the dynamics of a thermal gas with the spin-1 degree of freedom. Applying the moment method to the kinetic equation, we study spin-wave collective modes with dipole symmetry. The dipole modes in the spin-1 system are found to be classified into the three type of modes. The frequency and damping rate are obtained as functions of the peak density. The damping rate is characterized by three relaxation times associated with collisions.Comment: 19 pages, 5 figur

Instabilities in a Two-Component, Species Conserving Condensate

We consider a system of two species of bosons of equal mass, with interactions $U^{a}(|x|)$ and $U^{x}(|x|)$ for bosons of the same and different species respectively. We present a rigorous proof -- valid when the Hamiltonian does not include a species switching term -- showing that, when $U^{x}(|x|)>U^{a}(|x|)$, the ground state is fully "polarized" (consists of atoms of one kind only). In the unpolarized phase the low energy excitation spectrum corresponds to two linearly dispersing modes that are even a nd odd under species exchange. The polarization instability is signaled by the vani shing of the velocity of the odd modes.Comment: To appear in Phys. Rev.

The dynamics of quantum phases in a spinor condensate

We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground state distribution of the phases associated with the total atom number ($N$), the total magnetization (${\cal M}$), and the alignment (or hypercharge) ($Y$) of the system. The mean field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recover the two broken continuous symmetries [U(1) and SO(2)] when $N$ and ${\cal M}$ are conserved as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with anti-ferromagnetic interactions.Comment: 5 figures, an extended version of cond-mat/030117

Coherent dynamics of Bose-Einstein condensates in high-finesse optical cavities

We study the mutual interaction of a Bose-Einstein condensed gas with a single mode of a high-finesse optical cavity. We show how the cavity transmission reflects condensate properties and calculate the self-consistent intra-cavity light field and condensate evolution. Solving the coupled condensate-cavity equations we find that while falling through the cavity, the condensate is adiabatically transfered into the ground state of the periodic optical potential. This allows time dependent non-destructive measurements on Bose-Einstein condensates with intriguing prospects for subsequent controlled manipulation.Comment: 5 pages, 5 figures; revised version: added reference

Dynamically turning off interactions in a two component condensate

We propose a mechanism to change the interaction strengths of a two component condensate. It is shown that the application of pi/2 pulses allows to alter the effective interspecies interaction strength as well as the effective interaction strength between particles of the same kind. This mechanism provides a simple method to transform spatially stable condensates into unstable once and vice versa. It also provides a means to store a squeezed spin state by turning off the interaction for the internal states and thus allows to gain control over many body entangled states.Comment: 7 pages 5 figures, symbols changed, minor changes, to appear in Phys. Rev.

On the single mode approximation in spinor-1 atomic condensate

We investigate the validity conditions of the single mode approximation (SMA) in spinor-1 atomic condensate when effects due to residual magnetic fields are negligible. For atomic interactions of the ferromagnetic type, the SMA is shown to be exact, with a mode function different from what is commonly used. However, the quantitative deviation is small under current experimental conditions (for $^{87}$Rb atoms). For anti-ferromagnetic interactions, we find that the SMA becomes invalid in general. The differences among the mean field mode functions for the three spin components are shown to depend strongly on the system magnetization. Our results can be important for studies of beyond mean field quantum correlations, such as fragmentation, spin squeezing, and multi-partite entanglement.Comment: Revised, newly found analytic proof adde

Solutions of Gross-Pitaevskii equations beyond the hydrodynamic approximation: Application to the vortex problem

We develop the multiscale technique to describe excitations of a Bose-Einstein condensate (BEC) whose characteristic scales are comparable with the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory we derive approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times of the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by the numerical simulations.Comment: To appear in Phys. Rev.

Environmental policy in dynamic models with pollution by consumers: The greening and blackening of preferences

The paper discusses questions resulting from a study of the interaction of a change of preferences and environmental policy. In a model with pollution as a side effect of consumption environmental policy is introduced in the form of a consumption tax with or without a subsidy on eco-friendly investments. In simulations we observe the dynamic behavior of models before and after sudden changes of exogenous variables. These shocks are jumps in the preference structure of individuals towards more environmental-friendly or consumption-friendly attitudes. Additionally we examine the effect of a lagged reaction of the policy agents

Mutations in the LRRK2 Roc-COR tandem domain link Parkinson's disease to Wnt signalling pathways

Mutations in PARK8, encoding LRRK2, are the most common known cause of Parkinson's disease. The LRRK2 Roc-COR tandem domain exhibits GTPase activity controlling LRRK2 kinase activity via an intramolecular process. We report the interaction of LRRK2 with the dishevelled family of phosphoproteins (DVL1-3), key regulators of Wnt (Wingless/Int) signalling pathways important for axon guidance, synapse formation and neuronal maintenance. Interestingly, DVLs can interact with and mediate the activation of small GTPases with structural similarity to the LRRK2 Roc domain. The LRRK2 Roc-COR domain and the DVL1 DEP domain were necessary and sufficient for LRRK2–DVL1 interaction. Co-expression of DVL1 increased LRRK2 steady-state protein levels, an effect that was dependent on the DEP domain. Strikingly, LRRK2–DVL1-3 interactions were disrupted by the familial PARK8 mutation Y1699C, whereas pathogenic mutations at residues R1441 and R1728 strengthened LRRK2–DVL1 interactions. Co-expression of DVL1 with LRRK2 in mammalian cells resulted in the redistribution of LRRK2 to typical cytoplasmic DVL1 aggregates in HEK293 and SH-SY5Y cells and co-localization in neurites and growth cones of differentiated dopaminergic SH-SY5Y cells. This is the first report of the modulation of a key LRRK2-accessory protein interaction by PARK8 Roc-COR domain mutations segregating with Parkinson's disease. Since the DVL1 DEP domain is known to be involved in the regulation of small GTPases, we propose that: (i) DVLs may influence LRRK2 GTPase activity, and (ii) Roc-COR domain mutations modulating LRRK2–DVL interactions indirectly influence kinase activity. Our findings also link LRRK2 to Wnt signalling pathways, suggesting novel pathogenic mechanisms and new targets for genetic analysis in Parkinson's disease