A Uniform Approximation for the Coherent State Propagator using a Conjugate Application of the Bargmann Representation

We propose a conjugate application of the Bargmann representation of quantum mechanics. Applying the Maslov method to the semiclassical connection formula between the two representations, we derive a uniform semiclassical approximation for the coherent state propagator which is finite at phase space caustics.Comment: 4 pages, 1 figur

Chaotic and deterministic switching in a two-person game

We study robust long-term complex behaviour in the Rock-Scissors-Paper game with two players, played using reinforcement learning. The complex behaviour is connected to the existence of a heteroclinic network for the dynamics. This network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them. We provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network, leading to behaviour ranging from almost deterministic actions to chaotic-like dynamics. Our results are obtained by making use of the symmetry of the original problem, a new approach in the context of learning.learning process, dynamics, switching, chaos

Semiclassical Tunneling of Wavepackets with Real Trajectories

Semiclassical approximations for tunneling processes usually involve complex trajectories or complex times. In this paper we use a previously derived approximation involving only real trajectories propagating in real time to describe the scattering of a Gaussian wavepacket by a finite square potential barrier. We show that the approximation describes both tunneling and interferences very accurately in the limit of small Plank's constant. We use these results to estimate the tunneling time of the wavepacket and find that, for high energies, the barrier slows down the wavepacket but that it speeds it up at energies comparable to the barrier height.Comment: 23 pages, 7 figures Revised text and figure

Rutherford scattering with radiation damping

We study the effect of radiation damping on the classical scattering of charged particles. Using a perturbation method based on the Runge-Lenz vector, we calculate radiative corrections to the Rutherford cross section, and the corresponding energy and angular momentum losses.Comment: Latex, 11 pages, 4 eps figure

Chromosome Segregation Is Biased by Kinetochore Size

Chromosome missegregation during mitosis or meiosis is a hallmark of cancer and the main cause of prenatal death in humans. The gain or loss of specific chromosomes is thought to be random, with cell viability being essentially determined by selection. Several established pathways including centrosome amplification, sister-chromatid cohesion defects, or a compromised spindle assembly checkpoint can lead to chromosome missegregation. However, how specific intrinsic features of the kinetochore—the critical chromosomal interface with spindle microtubules—impact chromosome segregation remains poorly understood. Here we used the unique cytological attributes of female Indian muntjac, the mammal with the lowest known chromosome number (2n = 6), to characterize and track individual chromosomes with distinct kinetochore size throughout mitosis. We show that centromere and kinetochore functional layers scale proportionally with centromere size. Measurement of intra-kinetochore distances, serial-section electron microscopy, and RNAi against key kinetochore proteins confirmed a standard structural and functional organization of the Indian muntjac kinetochores and revealed that microtubule binding capacity scales with kinetochore size. Surprisingly, we found that chromosome segregation in this species is not random. Chromosomes with larger kinetochores bi-oriented more efficiently and showed a 2-fold bias to congress to the equator in a motor-independent manner. Despite robust correction mechanisms during unperturbed mitosis, chromosomes with larger kinetochores were also strongly biased to establish erroneous merotelic attachments and missegregate during anaphase. This bias was impervious to the experimental attenuation of polar ejection forces on chromosome arms by RNAi against the chromokinesin Kif4a. Thus, kinetochore size is an important determinant of chromosome segregation fidelity

Synchronization and Stability in Noisy Population Dynamics

We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered, random perturbations tend to destabilize the populations, leading to extinction. If the number of patches is small, stabilization in the presence of noise is maintained at the expense of synchronization. As the number of patches increases, both the stability and the synchrony among patches increase. However, a residual asynchrony, large compared with the noise amplitude, seems to persist even in the limit of infinite number of patches. Therefore, the mechanism of stabilization by asynchrony recently proposed by R. Abta et. al., combining noise, diffusion and nonlinearities, seems to be more general than first proposed.Comment: 3 pages, 3 figures. To appear in Phys. Rev.

State sum construction of two-dimensional open-closed Topological Quantum Field Theories

We present a state sum construction of two-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, which generalizes the state sum of Fukuma--Hosono--Kawai from triangulations of conventional two-dimensional cobordisms to those of open-closed cobordisms, i.e. smooth compact oriented 2-manifolds with corners that have a particular global structure. This construction reveals the topological interpretation of the associative algebra on which the state sum is based, as the vector space that the TQFT assigns to the unit interval. Extending the notion of a two-dimensional TQFT from cobordisms to suitable manifolds with corners therefore makes the relationship between the global description of the TQFT in terms of a functor into the category of vector spaces and the local description in terms of a state sum fully transparent. We also illustrate the state sum construction of an open-closed TQFT with a finite set of D-branes using the example of the groupoid algebra of a finite groupoid.Comment: 33 pages; LaTeX2e with xypic and pstricks macros; v2: typos correcte

Evaluation of the semiclassical coherent state propagator in the presence of phase space caustics

A uniform approximation for the coherent state propagator, valid in the vicinity of phase space caustics, was recently obtained using the Maslov method combined with a dual representation for coherent states. In this paper we review the derivation of this formula and apply it to two model systems: the one-dimensional quartic oscillator and a two-dimensional chaotic system.Comment: 15 pages, 3 figure