Tunable Lyapunov exponent in inverse magnetic billiards

The stability properties of the classical trajectories of charged particles are investigated in a two dimensional stadium-shaped inverse magnetic domain, where the magnetic field is zero inside the stadium domain and constant outside. In the case of infinite magnetic field the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (performed with a novel method) and the integrable/chaotic phase space volume ratio show that both quantities can be smoothly tuned by varying the external magnetic field. A possible experimental realization of the arrangement is also discussed.Comment: 4 pages, 6 figure

Does timing of decisions in a mixed duopoly matter?

We determine the endogenous order of moves in a mixed pricesetting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payo equivalence of the games with an exogenously given order of moves if the most plausible equilibrium is realized in the market. Hence, in this case it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand-Edgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists

On the relation of Thomas rotation and angular velocity of reference frames

In the extensive literature dealing with the relativistic phenomenon of Thomas rotation several methods have been developed for calculating the Thomas rotation angle of a gyroscope along a circular world line. One of the most appealing concepts, introduced in \cite{rindler}, is to consider a rotating reference frame co-moving with the gyroscope, and relate the precession of the gyroscope to the angular velocity of the reference frame. A recent paper \cite{herrera}, however, applies this principle to three different co-moving rotating reference frames and arrives at three different Thomas rotation angles. The reason for this apparent paradox is that the principle of \cite{rindler} is used for a situation to which it does not apply. In this paper we rigorously examine the theoretical background and limitations of applicability of the principle of \cite{rindler}. Along the way we also establish some general properties of {\it rotating reference frames}, which may be of independent interest.Comment: 14 pages, 2 figure

High-Pressure Synthesis of Dirac Materials: Layered van der Waals Bonded BeN4 Polymorph

High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. Here, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material BeN4. A triclinic phase of beryllium tetranitride tr-BeN4 was synthesized from elements at ∼85 GPa. Upon decompression to ambient conditions, it transforms into a compound with atomic-thick BeN4 layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated π systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN4 layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The BeN4 layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions. © 2021 American Physical Society.Parts of this research were carried out at the Extreme Conditions Beamline (P02.2) at DESY, a member of Helmholtz Association (HGF). Portions of this work were performed on beamline ID15 at the European Synchrotron Radiation Facility (ESRF), Grenoble, France. Portions of this work were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13) and at HPCAT (sector 16) of the Advanced Photon Source (APS), Argonne National Laboratory. Research was sponsored by the Army Research Office and was accomplished under the Cooperative Agreement No. W911NF-19-2-0172. N. D. and L. D. thank the Deutsche Forschungsgemeinschaft (DFG Projects No. DU 954-11/1, No. DU 393-9/2, and No. DU 393-13/1) and the Federal Ministry of Education and Research, Germany (BMBF, Grant No. No. 05K19WC1) for financial support. D. L. thanks the Alexander von Humboldt Foundation for financial support. Theoretical analysis of chemical bonding was supported by the Russian Science Foundation (Project No. 18-12-00492). Calculations of the phonon dispersion relations were supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of Increase Competitiveness Program of NUST MISIS (No. K2-2020-026) implemented by governmental decree No. 211. Support from the Knut and Alice Wallenberg Foundation (Wallenberg Scholar Grant No. KAW-2018.0194), the Swedish Government Strategic Research Areas in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971) and SeRC, the Swedish Research Council (VR) Grant No. 2019-05600 and Vinnova VINN Excellence Center Functional Nanoscale Materials (FunMat-2) Grant No. 2016–05156 is gratefully acknowledged. The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) partially funded by the Swedish Research Council through Grant Agreement No. 2016-07213. The work of M. I. K. was supported by the JTC-FLAGERA Project GRANSPORT. GeoSoilEnviroCARS is supported by the National Science Foundation–Earth Sciences (EAR–1634415) and Department of Energy-Geosciences (DE-FG02-94ER14466). HPCAT operations are supported by DOE-NNSA’s Office of Experimental Sciences. Advanced Photon Source is U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357

Quantity-setting games with a dominant firm

Forchheimer, Dominant firm, Price leadership, D43, L13,