Bichromatically driven double well: parametric perspective of the strong-field control landscape reveals the influence of chaotic states

The aim of this work is to understand the influence of chaotic states in control problems involving strong fields. Towards this end, we numerically construct and study the strong field control landscape of a bichromatically driven double well. A novel measure based on correlating the overlap intensities between Floquet states and an initial phase space coherent state with the parametric motion of the quasienergies is used to construct and interpret the landscape features. "Walls" of no control, robust under variations of the relative phase between the fields, are seen on the control landscape and associated with multilevel interactions involving chaotic Floquet states.Comment: 9 pages and 6 figures. Rewritten and expanded version of arXiv:0707.4547 [nlin.CD]. Accepted for publication in J. Chem. Phys. (2008

On the Strategic Advantage of Negatively Interdependent Preferences

We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. We show that these conditions are satisfied by a number of games of economic importance, and discuss the implications of these findings for the evolutionary theory of preference formation and the theory of Cournot competition.Interdependent Preferences, Submodular and Supermodular Games, Relative Profits, Cournot Oligopoly

Interdependent Preference Formation

A standard assumption in the economic approach to individual decision making is that people have independent preferences, that is, they care only about their absolute (material) payoffs. We study equilibria of the classic common pool resource extraction and public good games when some of the players have negatively interdependent preferences (in the sense that they care not only about their absolute payoffs but also about their relative payoffs) while the remainder have independent preferences. It is shown that at any equilibrium, those with interdependent preferences earn strictly higher absolute payoffs than do players with independent preferences. If the population composition evolves in accordance with any payoff monotonic evolutionary selection dynamics, then all players will have interdependent preferences in the long run. Similar (but weaker) results obtain for some other economically important classes of games in strategic form. The robustness of our findings with respect to other preference formation mechanisms such as myopic and rational socialization is also discussed.Interdependent Preferences, Evolution, Socialization.

Can We Detect the Anisotropic Shapes of Quasar HII Regions During Reionization Through The Small-Scale Redshifted 21cm Power Spectrum?

Light travel time delays distort the apparent shapes of HII regions surrounding bright quasars during early stages of cosmic reionization. Individual HII regions may remain undetectable in forthcoming redshifted 21 cm experiments. However, the systematic deformation along the line of sight may be detectable statistically, either by stacking tomographic 21cm images of quasars identified, for example, by JWST, or as small-scale anisotropy in the three-dimensional 21cm power spectrum. Here we consider the detectability of this effect. The anisotropy is largest when HII regions are large and expand rapidly, and we find that if bright quasars contributed to the early stages of reionization, then they can produce significant anisotropy, on scales comparable to the typical sizes of HII regions of the bright quasars (approx. 30 Mpc and below). The effect therefore cannot be ignored when analyzing future 21cm power spectra on small scales. If 10 percent of the volume of the IGM at redshift z=10 is ionized by quasars with typical ionizing luminosity of S= 5 x 10^{56} photons/second, the distortions can enhance by more than 10 percent the 21cm power spectrum in the radial (redshift) direction, relative to the transverse directions. The level of this anisotropy exceeds that due to redshift-space distortion, and has the opposite sign. We show that on-going experiments such as MWA should be able to detect this effect. A detection would reveal the presence of bright quasars, and shed light on the ionizing yield and age of the ionizing sources, and the distribution and small-scale clumping of neutral intergalactic gas in their vicinity.Comment: Version accepted by ApJ, with new fiducial model and improved discussio

Algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei

We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single-particle degrees of freedom in an application to elastic and inelastic proton scattering from $^{195}$Pt.Comment: latex, 14 pages, 4 figures uuencoded, to be published in Physical Review

Local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse oscillator

This work explores the possibility of controlling the dissociation of a monochromatically driven one-dimensional Morse oscillator by recreating barriers, in the form of invariant tori with irrational winding ratios, at specific locations in the phase space. The control algorithm proposed by Huang {\it et al.} (Phys. Rev. A {\bf 74}, 053408 (2006)) is used to obtain an analytic expression for the control field. We show that the control term, approximated as an additional weaker field, is efficient in recreating the desired tori and suppresses the classical as well as the quantum dissociation. However, in the case when the field frequency is tuned close to a two-photon resonance the local barriers are not effective in suppressing the dissociation. We establish that in the on-resonant case quantum dissociation primarily occurs via resonance-assisted tunneling and controlling the quantum dynamics requires a local perturbation of the specific nonlinear resonance in the underlying phase space.Comment: 12 pages, 6 figures (reduced quality), submitted to Phys. Rev.