Large-amplitude inviscid fluid motion in an accelerating container

Study of dynamic behavior of the liquid-vapor interface of an inviscid fluid in an accelerating cylindrical container includes an analytical-numerical method for determining large amplitude motion. The method is based on the expansion of the velocity potential in a series of harmonic functions with time dependent coefficients

Normal forms approach to diffusion near hyperbolic equilibria

We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighborhood of a hyperbolic critical point. We show that if the distribution of the initial condition has a scaling limit then the exit distribution and exit time also have a joint scaling limit as the noise intensity goes to zero. The limiting law is computed explicitly. The result completes the theory of noisy heteroclinic networks in two dimensions. The analysis is based on normal forms theory.Comment: 21 page

Positrons in Cosmic Rays from Dark Matter Annihilations for Uplifted Higgs Regions in MSSM

We point out that there are regions in the MSSM parameter space which successfully provide a dark matter (DM) annihilation explanation for observed positron excess (e.g. PAMELA), while still remaining in agreement with all other data sets. Such regions (e.g. the uplifted Higgs region) can realize an enhanced neutralino DM annihilation dominantly into leptons via a Breit-Wigner resonance through the CP-odd Higgs channel. Such regions can give the proper thermal relic DM abundance, and the DM annihilation products are compatible with current antiproton and gamma ray observations. This scenario can succeed without introducing any additional degrees of freedom beyond those already in the MSSM.Comment: 11 pages, 9 figure

Extended Quintessence with non-minimally coupled phantom scalar field

We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(\psi, \psi')$. We formulate simple conditions on the value of coupling constant $\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.Comment: revtex4, 15 pages, 9 figures; (v2) published versio

Search complexity and resource scaling for the quantum optimal control of unitary transformations

The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources required, particularly for systems with large Hilbert spaces. Prior work on unitary transformation control indicates that (i) for controllable systems, local extrema in the search landscape for optimal control of quantum gates have null measure, facilitating the convergence of local search algorithms; but (ii) the required time for convergence to optimal controls can scale exponentially with Hilbert space dimension. Depending on the control system Hamiltonian, the landscape structure and scaling may vary. This work introduces methods for quantifying Hamiltonian-dependent and kinematic effects on control optimization dynamics in order to classify quantum systems according to the search effort and control resources required to implement arbitrary unitary transformations

An asymptotic formula for marginal running coupling constants and universality of loglog corrections

Given a two-loop beta function for multiple marginal coupling constants, we derive an asymptotic formula for the running coupling constants driven to an infrared fixed point. It can play an important role in universal loglog corrections to physical quantities.Comment: 16 pages; typos fixed, one appendix removed for quick access to the main result; to be published in J. Phys.

Non-minimally coupled scalar field cosmology on the phase plane

In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term $\xi R \psi^{2}$ in the scalar field action. The quadratic potential function $V(\psi)\propto \psi^{2}$ is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling $\xi$ plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field cosmological models can be avoided due to non-minimal coupling constant effects. We have shown the existence of a finite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverges.Comment: revtex4, 20 pages, 12 figs; (v2) title changed, analysis of critical points at infinity added, accepted to JCA

Low-lying bifurcations in cavity quantum electrodynamics

The interplay of quantum fluctuations with nonlinear dynamics is a central topic in the study of open quantum systems, connected to fundamental issues (such as decoherence and the quantum-classical transition) and practical applications (such as coherent information processing and the development of mesoscopic sensors/amplifiers). With this context in mind, we here present a computational study of some elementary bifurcations that occur in a driven and damped cavity quantum electrodynamics (cavity QED) model at low intracavity photon number. In particular, we utilize the single-atom cavity QED Master Equation and associated Stochastic Schrodinger Equations to characterize the equilibrium distribution and dynamical behavior of the quantized intracavity optical field in parameter regimes near points in the semiclassical (mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that the semiclassical limit sets are qualitatively preserved in the quantum stationary states, although quantum fluctuations apparently induce phase diffusion within periodic orbits and stochastic transitions between attractors. We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR