Quantum Diffusion of the Random Schrödinger Evolution in the Scaling Limit II. The Recollision Diagrams

We consider random Schrödinger equations on \({\mathbb{R}^{d}}\) for d≥ 3 with a homogeneous Anderson-Poisson type random potential. Denote by λ the coupling constant and ψ _t the solution with initial data ψ₀. The space and time variables scale as \({x\sim \lambda^{-2 -\kappa/2}, t \sim \lambda^{-2 -\kappa}}\) with 0 < κ <  κ₀(d). We prove that, in the limit λ → 0, the expectation of the Wigner distribution of ψ _t converges weakly to the solution of a heat equation in the space variable x for arbitrary L ² initial data. The proof is based on a rigorous analysis of Feynman diagrams. In the companion paper [10] the analysis of the non-repetition diagrams was presented. In this paper we complete the proof by estimating the recollision diagrams and showing that the main terms, i.e. the ladder diagrams with renormalized propagator, converge to the heat equation.     

Quasinormal modes of a Schwarzschild black hole surrounded by free static spherically symmetric quintessence: electromagnetic perturbations

In this paper, we evaluated the quasinormal modes of electromagnetic perturbation in a Schwarzschild black hole surrounded by the static spherically symmetric quintessence by using the third-order WKB approximation when the quintessential state parameter w _q in the range of −1/3 < w _q < 0. Due to the presence of quintessence, Maxwell field damps more slowly. And when at −1 < w _q < −1/3, it is similar to the black hole solution in the ds/Ads spacetime. The appropriate boundary conditions need to be modified.     

Vanishing Shear Viscosity Limit in the Magnetohydrodynamic Equations

We study an initial boundary value problem for the equations of plane magnetohydrodynamic compressible flows, and prove that as the shear viscosity goes to zero, global weak solutions converge to a solution of the original equations with zero shear viscosity. As a by-product, this paper improves the related results obtained by Frid and Shelukhin for the case when the magnetic effect is neglected. Supported by NSFC (Grant No. 10301014, 10225105) and the National Basic Research Program (Grant No. 2005CB321700) of China.     

Non-locality and Gauge Freedom in Deutsch and Hayden’s Formulation of Quantum Mechanics

Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must be understood as having a form of ‘gauge freedom’ according to which mathematically distinct states are physically equivalent. Once this gauge freedom is taken into account, their formulation is no longer local.      

Ternary eutectic growth of Ag-Cu-Sb alloy within ultrasonic field

The liquid to solid transformation of ternary Ag42.4Cu21.6Sb36 eutectic alloy was accomplished in an ultrasonic field with a frequency of 35 kHz, and the growth mechanism of this ternary eutectic was examined. Theoretical calculations predict that the sound intensity in the liquid phase at the solidification interface increases gradually as the interface moves up from the sample bottom to its top. The growth mode of (ε θ Sb) ternary eutectic exhibits a transition of "divorced eutectic- mixture of anomalous and regular structures-regular eutectic" along the sample axis due to the inhomogeneity of sound field distribution. In the top zone with the highest sound intensity, the cavitation effect promotes the three eutectic phases to nucleate independently, while the acoustic streaming efficiently suppresses the coupled growth of eutectic phases. In the meantime, the ultrasonic field accelerates the solute transportation at the solid-liquid interface, which reduces the solute solubility of eutectic phases.     

The Transport Properties of the Cell Membrane Ion Channels in Electric Fields: Bethe Lattice Treatment

The interactive two-state model of cell membrane ion channels in an electric field is formulated on the Bethe lattice by means of the exact recursion relations. The probability of channel opening or maximum fractions of open potassium and sodium channels are obtained by solving a non-linear algebraic equation. Using known parameters for the conventional mean-field theory the model gives a good agreement with the experiment both at low and high trans-membrane potential values. For intermediate voltages, the numerical results imply that collective effects are introduced by trans-membrane voltage.     

Facile fabrication and optical properties of novel Pb(OH)Cl nanotubes

Uniform Pb(OH)Cl nanotubes were synthesized for the first time through a reverse micelles system. The system was consisting of C₁₂E₉ as a surfactant, n-pentanol as a cosurfactant, hexamethylene as the continuous oil phase and lead acetate or sodium chloride solution as the dispersed aqueous phase. The obtained Pb(OH)Cl nanotubes have an average outer diameter of 60 nm, inner diameter of about 40 nm, and an length up to 3 μm as TEM picture showed. And the range of the nanotube diameter is from 50 nm to 70 nm. XRD result indicated that Pb(OH)Cl crystallized in an orthorhombic phase. Photoluminescent (PL) spectrum showed that the product emit in near ultraviolet region and visible region at 335 nm and 439 nm respectively. The experimental results show that reaction temperature have effect on the shape of Pb(OH)Cl nanotubes. A possible formation mechanism was also discussed.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

Decoupling Problem for Systems of Quasi-Linear pde’s

The necessary and sufficient conditions for the decoupling of a quasi-linear system of partial differential equations into k non-interacting subsystems are derived. Several necessary conditions for the decoupling are found and applied to the Benney system.     

Conformal Klein-Gordon Equations and Quasinormal Modes

Using conformal coordinates associated with conformal relativity—associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime—we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Pöschl-Teller potential, here we deduce and analytically solve a conformal ‘radial’ d’Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this ‘radial’ equation can be identified with a Schrödinger-like equation in which the potential is exactly the second Pöschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.