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

Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability

We prove that the separable and local approximations of the discontinuity-inducing zero-range interaction in one-dimensional quantum mechanics are equivalent. We further show that the interaction allows the perturbative treatment through the coupling renormalization. Keywords: one-dimensional system, generalized contact interaction, renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website http://www.mech.kochi-tech.ac.jp/cheon

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

Quantum phenomenology of conjunction fallacy

A quantum-like description of human decision process is developed, and a heuristic argument supporting the theory as sound phenomenology is given. It is shown to be capable of quantitatively explaining the conjunction fallacy in the same footing as the violation of sure-thing principle.Comment: LaTeX 8 pages, 2 figure

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

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Breakdown pressure and fracture surface morphology of hydraulic fracturing in shale with H2O, CO2 and N2

Slick-water fracturing is the most routine form of well stimulation in shales; however N2, LPG and CO2 have all been used as “exotic” stimulants in various hydrocarbon reservoirs. We explore the use of these gases as stimulants on Green River shale to compare the form and behavior of fractures in shale driven by different gas compositions and states and indexed by breakdown pressure and the resulting morphology of the fracture networks. Fracturing is completed on cylindrical samples containing a single blind axial borehole under simple triaxial conditions with confining pressure ranging from 10 to 25 MPa and axial stress ranging from 0 to 35 MPa (σ1 > σ2 = σ3). Results show that: (1) under the same stress conditions, CO2 returns the highest breakdown pressure, followed by N2, and with H2O exhibiting the lowest breakdown pressure; (2) CO2 fracturing, compared to other fracturing fluids, creates nominally the most complex fracturing patterns as well as the roughest fracture surface and with the greatest apparent local damage followed by H2O and then N2; (3) under conditions of constant injection rate, the CO2 pressure build-up record exhibits condensation between ~5 and 7 MPa and transits from gas to liquid through a mixed-phase region rather than directly to liquid as for H2O and N2 which do not; (4) there is a positive correlation between minimum principal stress and breakdown pressure for failure both by transverse fracturing (σ3axial) and by longitudinal fracturing (σ3radial) for each fracturing fluid with CO2 having the highest correlation coefficient/slope and lowest for H2O. We explain these results in terms of a mechanistic understanding of breakdown, and through correlations with the specific properties of the stimulating fluids

Crystal Structure Search with Random Relaxations Using Graph Networks

Materials design enables technologies critical to humanity, including combating climate change with solar cells and batteries. Many properties of a material are determined by its atomic crystal structure. However, prediction of the atomic crystal structure for a given material's chemical formula is a long-standing grand challenge that remains a barrier in materials design. We investigate a data-driven approach to accelerating ab initio random structure search (AIRSS), a state-of-the-art method for crystal structure search. We build a novel dataset of random structure relaxations of Li-Si battery anode materials using high-throughput density functional theory calculations. We train graph neural networks to simulate relaxations of random structures. Our model is able to find an experimentally verified structure of Li15Si4 it was not trained on, and has potential for orders of magnitude speedup over AIRSS when searching large unit cells and searching over multiple chemical stoichiometries. Surprisingly, we find that data augmentation of adding Gaussian noise improves both the accuracy and out of domain generalization of our models.Comment: Removed citations from the abstract, paper content is unchange

Scale Anomaly and Quantum Chaos in the Billiards with Pointlike Scatterers

We argue that the random-matrix like energy spectra found in pseudointegrable billiards with pointlike scatterers are related to the quantum violation of scale invariance of classical analogue system. It is shown that the behavior of the running coupling constant explains the key characteristics of the level statistics of pseudointegrable billiards.Comment: 10 pages, RevTex file, uuencode