Bayesian Nash Equilibria and Bell Inequalities

Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the game of Battle of Sexes clarifies the two distinct roles of nonlocal strategies, and establish the direct link between the true quantum gain of game's payoff and the breaking of Bell inequalities.Comment: 6 pages, LaTeX JPSJ 2 column format, changes in sections 1, 3 and 4, added reference

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Constructing quantum games from non-factorizable joint probabilities

A probabilistic framework is developed that gives a unifying perspective on both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct quantum games. In our framework a game attains classical interpretation when joint probabilities are factorizable and a quantum game corresponds when these probabilities cannot be factorized. We analyze how non-factorizability changes Nash equilibria in two-player games while considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this framework we find that for the game of Prisoner's Dilemma even non-factorizable EPR joint probabilities cannot be helpful to escape from the classical outcome of the game. For a particular version of the Chicken game, however, we find that the two non-factorizable sets of joint probabilities, that maximally violates the Clauser-Holt-Shimony-Horne (CHSH) sum of correlations, indeed result in new Nash equilibria.Comment: Revised in light of referee's comments, submitted to Physical Review

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Quantum Matching Pennies Game

A quantum version of the Matching Pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct the quantum game without using the state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We embed the classical game within the quantum game such that the classical MP game results when the quantum mechanical joint probabilities become factorizable. We report new Nash equilibria in the quantum MP game that emerge when the quantum mechanical joint probabilities maximally violate the Clauser-Horne-Shimony-Holt form of Bell's inequality.Comment: Revised in light of referees' comments, submitted to Journal of the Physical Society of Japan, 14 pages, 1 figur

Duality between N=5 and N=6 Chern-Simons matter theory

We provide evidences for the duality between ${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons matter theory and ${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$ theory for a suitable $\hat{M},\hat{N}$ by working out the superconformal index, which shows perfect matching. For ${\cal N}=5$ theories, we show that supersymmetry is enhanced to ${\cal N}=6$ by explicitly constructing monopole operators filling in $SO(6)_R$ $R$-currents. Finally we work out the large $N$ index of $O(2N)_{2k} \times USp(2N)_{-k}$ and show that it exactly matches with the gravity index on $AdS_4 \times S^7/D_k$, which further provides additional evidence for the duality between the ${\cal N}=5$ and ${\cal N}=6$ theory for $k=1$Comment: 15 pages; references adde

Evidence for CP Violation in B0 -> D+D- Decays

We report measurements of the branching fraction and CP violation parameters in B0 -> D+D- decays. The results are based on a data sample that contains 535 x 10^6 BBbar pairs collected at the Upsilon(4S) resonance, with the Belle detector at the KEKB asymmetric-energy e+e- collider. We obtain [1.97 +- 0.20 (stat) +- 0.20 (syst)] x 10^(-4) for the branching fraction of B0 -> D+D-. The measured values of the CP violation parameters are: S = -1.13 +- 0.37 +- 0.09, A = 0.91 +- 0.23 +- 0.06, where the first error is statistical and the second is systematic. We find evidence of CP violation in B0 -> D+D- at the 4.1 sigma confidence level. While the value of S is consistent with expectations from other measurements, the value of the parameter A favors large direct CP violation at the 3.2 sigma confidence level, in contradiction to Standard Model expectations.Comment: 12 pages, 3 figures, submitted to PR

An Analysis of the Quantum Penny Flip Game using Geometric Algebra

We analyze the quantum penny flip game using geometric algebra and so determine all possible unitary transformations which enable the player Q to implement a winning strategy. Geometric algebra provides a clear visual picture of the quantum game and its strategies, as well as providing a simple and direct derivation of the winning transformation, which we demonstrate can be parametrized by two angles. For comparison we derive the same general winning strategy by conventional means using density matrices.Comment: 8 Pages, 1 Figure, accepted for publication in the Journal of Physical Society of Japa

Search for the h_c meson in B^+- ->h_c K^+-

We report a search for the $h_c$ meson via the decay chain $B^{\pm}\to h_c K^{\pm}$, \etac \gamma with $\eta_c \to K_S^0 K^{\pm} \pi^{\mp}$ and $p\bar{p}$. No significant signals are observed. We obtain upper limits on the branching fractions for $B^{\pm} \to \eta_c\gamma K^{\pm}$ in bins of the $\eta_c\gamma$ invariant mass. The results are based on an analysis of 253 fb$^{-1}$ of data collected by the Belle detector at the KEKB $e^+e^-$ collider.Comment: 12 pages, 6 figures, submitted to Phys. Rev.

Towards a fully self-consistent spectral function of the nucleon in nuclear matter

We present a calculation of nuclear matter which goes beyond the usual quasi-particle approximation in that it includes part of the off-shell dependence of the self-energy in the self-consistent solution of the single-particle spectrum. The spectral function is separated in contributions for energies above and below the chemical potential. For holes we approximate the spectral function for energies below the chemical potential by a $\delta$-function at the quasi-particle peak and retain the standard form for energies above the chemical potential. For particles a similar procedure is followed. The approximated spectral function is consistently used at all levels of the calculation. Results for a model calculation are presented, the main conclusion is that although several observables are affected by the inclusion of the continuum contributions the physical consistency of the model does not improve with the improved self-consistency of the solution method. This in contrast to expectations based on the crucial role of self-consistency in the proofs of conservation laws.Comment: 26 pages Revtex with 4 figures, submitted to Phys. Rev.