Long-time limit behavior of the solution to an atom’s master equation

We study the long-time limit behavior of the solution to an atom’s master equation.For the first time we derive that the probability of the atom being in the α-th(α = j + 1-j z,j is the angular momentum quantum number,j z is the z-component of angular momentum) state is {(1- K/G)/[1-(K/G) 2j+1 ]}(K/G) α-1 as t → +∞,which coincides with the fact that when K/G > 1,the larger the α is,the larger the probability of the atom being in the α-th state(the lower excited state) is.We also consider the case for some possible generalizations of the atomic master equation.     

The corrections to scaling within Mazenko’s theory in the limit of low and high dimensions

We consider corrections to scaling within an approximate theory developed by Mazenko for nonconserved order parameter in the limit of low (d → 1) and high (d → ∞) dimensions. The corrections to scaling considered here follows from the departures of the initial condition from the scaling morphology. Including corrections to scaling, the equal time correlation function has the form: C(r, t) = f ₀(r/L)+L ^−ω f ₁(r/L)+…, where L is a characteristic length scale (i.e. domain size). The correction-to-scaling exponent ω and the correction-to-scaling functions f ₁(x) are calculated for both low and high dimensions. In both dimensions the value of ω is found to be ω = 4 similar to 1D Glauber model and OJK theory (the theory developed by Ohta, Jasnow and Kawasaki).     

Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures

A method has been proposed for calculating the two-dimensional Young??s modulus and the Poisson??s ratio for planar and nanotubular structures through the components of the two-dimensional elastic rigidity tensor obtained by numerical methods. The method has been tested for graphene and two-dimensional supracrystalline sheets.     

A possible testbed for warped extra dimension from the angle of Buchdahl’s limit

The European Physical Journal C - We point out a misleading treatment in a recent paper published in this Journal (Sobhani et al., Eur Phys J C 78:106, 2018) regarding solutions for the...     

Elastic Properties of Graphene-Like Compounds: the Keating’s and Harisson’s Models

Physics of the Solid State - The third-order elastic constants, the pressure dependences of the second-order elastic constants, the Kleinman and Grüneisen parameters, and the thermal expansion...     

Degree and connectivity of the Internet’s scale-free topology

This paper theoretically and empirically studies the degree and connectivity of the Internet's scale-free topology at an autonomous system (AS) level. The basic features of scale-free networks influence the normalization constant of degree distribution p(k). It develops a new mathematic model for describing the power-law relationships of Internet topology. From this model we theoretically obtain formulas to calculate the average degree, the ratios of the k_min-degree (minimum degree) nodes and the k_max-degree (maximum degree) nodes, and the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. It finds that the average degree is larger for a smaller power-law exponent λ and a larger minimum or maximum degree. The ratio of the k_min-degree nodes is larger for larger λ and smaller k_min or k_max. The ratio of the k_max-degree ones is larger for smaller λ and k_max or larger k_min. The richer nodes hold most of the total degrees of Internet AS-level topology. In addition, it is revealed that the increased rate of the average degree or the ratio of the k_min-degree nodes has power-law decay with the increase of k_min. The ratio of the k_max-degree nodes has a power-law decay with the increase of k_max, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the '73/27 rule'). Finally, empirically calculations are made, based on the empirical data extracted from the Border Gateway Protocol, of the average degree, ratio and fraction using this method and other methods, and find that this method is rigorous and effective for Internet AS-level topology.     

Density inhomogeneities of the Earth’s mantle and core

Lateral density variations are determined at depth and are characterized by the anomalies of the seismic waves velocities, which are consistent with both the anomalies of the external gravity field and with the data from the analysis of Earth’s free-oscillation minimizing the deviations of the internal Earth structure from a hydrostatically equilibrated structure. It is shown that the obtained anomalous structures cause anomalies of the gravity field inside the Earth, which may be conducive to convective movements in the mantle and core.     

Onsager and Kaufman’s Calculation of the Spontaneous Magnetization of the Ising Model

Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C.N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman’s method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.     

Review and suggested resolution of the problem of Schrodinger’s cat

This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.     

Characterization of atomic avoided crossings by means of Fisher’s information

Atomic avoided crossings in strong magnetic and electric fields are usually identified by the energy level repulsion and by the sharp extremal value of the Shannons entropy of the two involved states. In this work the proposal of a new information-theoretic parameter, the continuous Fisher information, for the prediction and characterization of these nonlinear phenomena is done. For just around the irregular region it is found that Fishers informations of the two states cross over and show that the states exchange their informational character. Moreover, the state Fisher information sum keeps constant through the avoided crossing. This is illustrated for some hydrogenic excited states in strong magnetic fields as well as in parallel magnetic and electric fields.     

Coxeter’s frieze patterns and discretization of the Virasoro orbit

We show that the space of classical Coxeter’s frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov’s symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.     

On wave and rheidity properties of the Earth’s crust

The properties of the Earth’s solid crust have been studied on the assumption that this crust has a block structure. According to the rotation model, the motion of such a medium (geomedium) follows the angular momentum conservation law and can be described in the scope of the classical elasticity theory with a symmetric stress tensor. A geomedium motion is characterized by two types of rotation waves with shortand long-range actions. The first type includes slow solitons with velocities of 0 ≤ V_sol ≤ c0, max = 1–10 cm s^–1; the second type, fast excitons with V₀ ≤ V_ex ≤ V_S–V_P. The exciton minimal velocity (V₀ = 0) depends on the energy of the collective excitation of all seismically active belt blocks proportional to the Earth’s pole vibration frequency (the Chandler vibration frequency). The exciton maximal velocity depends on the velocities of S (V_S ≈ 4 km s^–1) and/or P (V_P ≈ 8 km s^–1) seismic (acoustic) waves. According to the rotation model, a geomedium is characterized by the property physically close to the corpuscular–wave interaction between blocks that compose this medium. The possible collective wave motion of geomedium blocks can be responsible for the geomedium rheidity property, i.e., a superplastic volume flow. A superplastic motion of a quantum fluid can be the physical analog of the geomedium rheid motion.     

Hochschild cohomology of the Weyl algebra and Vasiliev’s equations

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as well as for the smash products of the Weyl algebra and a finite group of linear symplectic transformations. A relationship with the higher-spin field theory is briefly discussed.