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

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

Voting contagion: modeling and analysis of a century of U.S. presidential elections

Sem informaçãoSocial influence plays an important role in human behavior and decisions. Sources of influence can be divided as external, which are independent of social context, or as originating from peers, such as family and friends. An important question is how to disentangle the social contagion by peers from external influences. While a variety of experimental and observational studies provided insight into this problem, identifying the extent of contagion based on large-scale observational data with an unknown network structure remains largely unexplored. By bridging the gap between the large-scale complex systems perspective of collective human dynamics and the detailed approach of social sciences, we present a parsimonious model of social influence, and apply it to a central topic in political science-elections and voting behavior. We provide an analytical expression of the county vote-share distribution, which is in excellent agreement with almost a century of observed U.S. presidential election data. Analyzing the social influence topography over this period reveals an abrupt phase transition from low to high levels of social contagion, and robust differences among regions. These results suggest that social contagion effects are becoming more instrumental in shaping large-scale collective political behavior, with implications on democratic electoral processes and policies.125130Sem informaçãoSem informaçãoSem informaçã

Turing Patterns And Apparent Competition In Predator-prey Food Webs On Networks.

Reaction-diffusion systems may lead to the formation of steady-state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and plays central roles in many fields of biology, such as ecology and morphogenesis. Here we show that Turing patterns may have a decisive role in shaping the abundance distribution of predators and prey living in patchy landscapes. We extend the original model proposed by Nakao and Mikhailov [Nat. Phys. 6, 544 (2010)] by considering food chains with several interacting pairs of prey and predators distributed on a scale-free network of patches. We identify patterns of species distribution displaying high degrees of apparent competition driven by Turing instabilities. Our results provide further indication that differences in abundance distribution among patches can be generated dynamically by self organized Turing patterns and not only by intrinsic environmental heterogeneity.8605620

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

Semiclassical coherent state propagator for systems with spin

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin 1/2.Comment: 19 pages, no figure

Semiclassical Approximations Based On Complex Trajectories.

The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z*. In this work we study mostly the case z' = z. The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.6906620

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.