Power-law spin correlations in pyrochlore antiferromagnets

The ground state ensemble of the highly frustrated pyrochlore-lattice antiferromagnet can be mapped to a coarse-grained ``polarization'' field satisfying a zero-divergence condition From this it follows that the correlations of this field, as well as the actual spin correlations, decay with separation like a dipole-dipole interaction ($1/|R|^3$). Furthermore, a lattice version of the derivation gives an approximate formula for spin correlations, with several features that agree well with simulations and neutron-diffraction measurements of diffuse scattering, in particular the pinch-point (pseudo-dipolar) singularities at reciprocal lattice vectors. This system is compared to others in which constraints also imply diffraction singularities, and other possible applications of the coarse-grained polarization are discussed.Comment: 13 pp, revtex, two figure

Top quark forward-backward asymmetry and charge asymmetry in left-right twin Higgs model

In order to explain the Tevatron anomaly of the top quark forward-backward asymmetry $A_{FB}^t$ in the left-right twin Higgs model, we choose to give up the lightest neutral particle of $\hat{h}$ field as a stable dark matter candidate. Then a new Yukawa interaction for $\hat{h}$ is allowed, which can be free from the constraint of same-sign top pair production and contribute sizably to $A_{FB}^t$. Considering the constraints from the production rates of the top pair ($t\bar t$), the top decay rates and $t\bar{t}$ invariant mass distribution, we find that this model with such new Yukawa interaction can explain $A_{FB}^t$ measured at the Tevatron while satisfying the charge asymmetry $A_{C}^t$ measured at the LHC.Moreover, this model predicts a strongly correlation between $A_{C}^t$ at the LHC and $A_{FB}^t$ at the Tevatron, i.e., $A_{C}^t$ increases as $A_{FB}^t$ increases.Comment: 17 pages, 9 figures; matches the published versio

Boundary conditions and the entropy bound

The entropy-to-energy bound is examined for a quantum scalar field confined to a cavity and satisfying Robin condition on the boundary of the cavity. It is found that near certain points in the space of the parameter defining the boundary condition the lowest eigenfrequency (while non-zero) becomes arbitrarily small. Estimating, according to Bekenstein and Schiffer, the ratio $S/E$ by the $\zeta$-function, $(24\zeta (4))^{1/4}$, we compute $\zeta (4)$ explicitly and find that it is not bounded near those points that signals violation of the bound. We interpret our results as imposing certain constraints on the value of the boundary interaction and estimate the forbidden region in the parameter space of the boundary conditions.Comment: 16 pages, latex, v2: typos corrected, to appear in Phys.Rev.

Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints

We consider synthesis of control policies that maximize the probability of satisfying given temporal logic specifications in unknown, stochastic environments. We model the interaction between the system and its environment as a Markov decision process (MDP) with initially unknown transition probabilities. The solution we develop builds on the so-called model-based probably approximately correct Markov decision process (PAC-MDP) methodology. The algorithm attains an $\varepsilon$-approximately optimal policy with probability $1-\delta$ using samples (i.e. observations), time and space that grow polynomially with the size of the MDP, the size of the automaton expressing the temporal logic specification, $\frac{1}{\varepsilon}$, $\frac{1}{\delta}$ and a finite time horizon. In this approach, the system maintains a model of the initially unknown MDP, and constructs a product MDP based on its learned model and the specification automaton that expresses the temporal logic constraints. During execution, the policy is iteratively updated using observation of the transitions taken by the system. The iteration terminates in finitely many steps. With high probability, the resulting policy is such that, for any state, the difference between the probability of satisfying the specification under this policy and the optimal one is within a predefined bound.Comment: 9 pages, 5 figures, Accepted by 2014 Robotics: Science and Systems (RSS

Dark matter, dark energy, and dark radiation coupled with a transversal interaction

We investigate a cosmological scenario with three interacting components that includes dark matter, dark energy, and radiation in the spatially flat Friedmann-Robertson-Walker universe. We introduce a 3-dimensional internal space, the interaction vector $\mathbf{Q}=(Q_{x}, Q_{m}, Q_{r})$ satisfying the constraint plane $Q_{x}+ Q_{m}+ Q_{r}=0$, the barotropic index vector \boldmath {\gamma}=(\ga_x,\ga_m,\ga_r) and select a transversal interaction vector $\mathbf{Q_t}$ in a sense that \mathbf{Q_t}\cdot \boldmath {\gamma}$=0$. We exactly solve the source equation for a linear $\mathbf{Q_t}$, that depends on the total energy density and its derivatives up to third order, and find all the component energy densities. We obtain a large set of interactions for which the source equation admits a power law solution and show its asymptotic stability by constructing the Lyapunov function. We apply the $\chi^{2}$ method to the observational Hubble data for constraining the cosmic parameters, and analyze the amount of dark energy in the radiation era for the above linear $\mathbf{Q_t}$. It turns to be that our model fulfills the severe bound of $\Omega_{x}(z\simeq 1100)<0.1$ and is consistent with the future constraints achievable by Planck and CMBPol experiments.Comment: 9 pages, 4 figures. Accepted for publication in Physical Review