Møller’s Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane

Møller’s energy-momentum complex is employed in order to determine the energy and momentum distributions for a spacetime described by a “generalized Schwarzschild” geometry in (3+1)-dimensions on a noncommutative curved D3-brane in an effective, open bosonic string theory. The geometry considered is obtained by an effective theory of gravity coupled with a nonlinear electromagnetic field and depends only on the generalized (effective) mass and charge which incorporate corrections of first order in the noncommutativity parameter.     

Electronic transport properties of carbon chains between Au and Ag electrodes: A first-principles study

We report first-principles calculations of the current-voltage characteristic and the conductance of carbon-based molecular wires with different length capped with sulfur ends between two metallic electrodes made of different metals. The optimized molecular structure of carbon chain in the junction is presented on the structure of polyyne. The conductance of the polyyne wires shows oscillatory behavior depending on the number of carbon atoms (triple bonds). Current rectification is found and rectification direction presents inversion with the odd and even number of carbon atoms.     

Electrical properties of highly (111)-oriented lead zirconate thin films

Antiferroelectric PbZrO₃ thin films were grown on Pt/Ti/SiO₂/Si substrates with predominant (111) orientation using a sol-gel process. The Pt/PbZrO₃/Pt film capacitor showed well-saturated hysteresis loops at an applied voltage of 5 V with remanent polarisation (P_r) and coercive electric field (E_c) values of 8.97 μC/cm² and 162 kV/cm, respectively. The leakage current density of the highly (111)-oriented PbZrO₃ film was less than 1.0×10⁻⁷ A/cm² over electric field ranges from 0 to 105 kV/cm. The conduction current depended on the voltage polarity. The PbZrO₃/Pt interface forms a Schottky barrier at electric fields from 20 to 160 kV/cm. The dielectric relaxation current behaviour of Pt/PbZrO₃/Pt capacitor obeys the well-known Curie-Von Schweidler law at electric field of 20-80 kV/cm, the currents have contributions of both dielectric relaxation current and leakage current.     

Quasiperiodicity and randomness in tilings of the plane

We define new tilings of the plane with Robinson triangles, by means of generalized inflation rules, and study their Fourier spectrum. Penrose's matching rules are not obeyed; hence the tilings exhibit new local environments, such as three different bond lengths, as well as new patterns at all length scales. Several kinds of such generalized tilings are considered. A large class of deterministic tilings, including chiral tilings, is strictly quasiperiodic, with a tenfold rotationally symmetric Fourier spectrum. Random tilings, either locally (with extensive entropy) or globally random (without extensive entropy), exhibit a mixed (discrete+continuous) diffraction spectrum, implying a partial perfect long-range order.     

Schrödinger Operators with Random Sparse Potentials. Existence of Wave Operators

We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δ _h (γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ | representation we find that Δ _h (γ,ε;κ) is just a pure squeezed coherent state density operator | γ,ε〉 _{κ κ} 〈γ,ε |, which brings much convenience for studying Husimi distribution, so we name Δ _h (γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution. Work supported by the National Natural Science Foundation under the grant: 10775097.     

Crime and punishment: Does it pay to punish?

Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension.     

Strong coupling constants of light pseudoscalar mesons with heavy baryons in QCD

We calculate the strong coupling constants of light pseudoscalar mesons with heavy baryons within the light cone QCD sum rules method. It is shown that sextet–sextet, sextet–antitriplet and antitriplet–antitriplet transitions are described by one universal invariant function for each class. A comparison of our results on the coupling constants with the predictions existing in literature is also presented.     

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.