The First Principle Calculation of Green—Kubo Formula with the Two—Time Ensemble Technique

For weak-coupling electronic plasmas in the presence of small fluctuations,we calculate Green-Kuboformula for transport coefficients employing the ab initio theory,i.e.,the two-time ensemble technique.The microscopic interpretations of Onsager‘s hypothesis on fluctuations are presented in the framework.     

The Green-Kubo Formula and the Onsager Reciprocity Relations in Quantum Statistical Mechanics

We study linear response theory in the general framework of algebraic quantum statistical mechanics and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated by temperature differentials. Our derivation is axiomatic and the key assumptions concern ergodic properties of non-equilibrium steady states.     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.     

微光成像系统视距理论公式的修正

介绍了微光成像系统视距理论的基本概念，在对微光成像系统视距探测方程推导的基础上，分析了各参量间的关系及其对整体性能的影响，从大气透过率和光谱匹配等诸多方面进行修正，建立了更为实用和完善的视距探测方程，并结合车辆驾驶夜视仪进行了视距估算，验证了经修正后的视距公式的实用性，为微光成像系统的优化设计以及寻求实现中远距离观察的最优技术途径提供了理论帮助，这对微光成像系统的改进、提高和发展也具有一定的指导意义。最后提出了一些改进微光成像系统视距性能的途径。     

二维可积系统的求迹公式和周期轨道的量子化

从Berry–Tabor求迹公式出发,导出了二维可积系统周期轨道作用量的半经典量子化条件.利用此量子化条件,考虑周期轨道满足的周期条件,得到了二维无关联四次振子系统周期轨道作用量的半经典量子化条件,并给出了半经典能级公式.对能级与周期轨道的对应关系做了分析.     

The Quest for a Microscopic Nuclear Mass Formula

After stressing how well the purely macroscopic 1935 mass formula of von Weizsäcker works, we discuss the general problem of deriving nuclear masses from basic nucleonic interactions. We then describe the very recent Skyrme-Hartree-Fock-BCS mass formula of Goriely et al., the first and only to be entirely microscopic. We conclude by stressing how much more work has to be done before reliable extrapolations can be made from the mass data out to the highly neutron-rich part of the nuclear chart where the r-process of nucleosynthesis takes place.     

The Rutherford Formula Generalized for the Synthesis of Gravity Assist Chains

Doklady Physics - Rutherford’s formula for the scattering of charged α-particles in a Coulomb field can easily be generalized to the case of gravitational scattering. One of the types of...     

Transport Theory and Collective Modes II: Long-Time Tail and Green-Kubo Formalism

The long-time tail effect (i.e., a non-Markovian effect) in a velocity autocorrelation function for moderately dense classical gases in d-dimensional space is estimated for arbitray n-mode coupling by superposition of the Markov equations for the collective modes which has been introduced through the complex spectral representation of the Liouville operator in the previous paper. Taking into account intermediate nonhydrodynamic modes in a transition between hydrodynamic states, we found slower decay processes in the long-time tail. These new processes lead to a critical dimension at d = 4 as in the renormalization group, that is, higher modes processes lead to slower decay process in the autocorrelation function for d = 4, while they lead to quicker decay process for d > 4. This conclusion clashes with the traditional point of view, which leads to the critical dimension d = 2. These slower processes invalidate the traditional kinetic equations for bare distribution functions obtained by a truncation of the BBGKY hierarchy for d < 4, as well as the Green-Kubo formalism, as there appear contributions of order t^–1, t^–1/2, ... coming from multiple mode-mode couplings even for d = 3.     

The Legendre Structure of the Parisi Formula

We study easy quantum groups, a combinatorial class of orthogonal quantum groups introduced by Banica–Speicher in 2009. We show that there is a countable descending chain of easy quantum groups interpolating between Bichon’s free wreath product with the permutation group S_n and a semi-direct product of a permutation action of S_n on a free product. This reveals a series of new commutation relations interpolating between a free product construction and the tensor product. Furthermore, we prove a dichotomy result saying that every hyperoctahedral easy quantum group is either part of our new interpolating series of quantum groups or belongs to a class of semi-direct product quantum groups recently studied by the authors. This completes the classification of easy quantum groups. We also study combinatorial and operator algebraic aspects of the new interpolating series.     

The Entropy Formula for SRB-Measures of Lattice Dynamical Systems

We give a detailed proof of the entropy formula for SRB-measures of coupled hyperbolic attractors over integer lattices. We show that the topological pressure for the potential function of the SRB-measure is zero.     

Formula for the absorption coefficient for multi-wall nanotubes

We present a formalism for calculating the absorption coefficient of a pair of coaxial tubules. A spatially nonlocal, dynamical self-consistent field theory is obtained by calculating the electrostatic potential produced by the charge density fluctuations as well as the external electric field. There are peaks in the absorption spectrum arising from plasma excitations corresponding either to plasmon or particle-hole modes. In this Letter, we numerically calculate the plasmon contribution to the absorption spectrum when an external electric field is applied. The number of peaks depends on the radius of the inner as well as outer tubule. The height of each peak is determined by the plasmon wavelength and energy. For a chosen wave number, the most energetic plasmon has the highest peak corresponding to the largest oscillator strength of the excited modes. Some of the low-frequency plasmon modes have such weak coupling to an external electric field that they are not seen on the same scale as the modes with larger energy of excitation. We plot the peak positions of the plasmon excitations for a pair of coaxial tubules. The coupled modes on the two tubules are split by the Coulomb interaction. The energies of the two highest plasmon branches increase with the radius of the outer tubule. On the contrary, the lowest modes decrease in energy as this radius is increased. No effects due to inter-tubule hopping are included in these calculations.     

Green-Kubo Formulas with Symmetrized Correlation Functions for Quantum Systems in Steady States: The Shear Viscosity of a Fluid in a Steady Shear Flow

For a quantum system in a steady state with a constant current of heat or particles driven by a temperature or chemical potential difference between two reservoirs attached to the system, the fluctuation theorem for the current was previously shown to lead to the Green-Kubo formula for the linear response coefficient for the current expressed in terms of the symmetrized correlation function of the current density operator. In this article, we show that for a quantum system in a steady state with a constant rate of work done on the system, the fluctuation theorem for a quantity induced in the system also leads to the Green-Kubo formula expressed in terms of the symmetrized correlation function of the induced quantity. As an example, we consider a fluid in a steady shear flow driven by a constant velocity of a solid plate moving above the fluid.     

常见的错误矢量式及其分析纠正

指出了某些教材、资料中的错误的矢量式,并进行了分析及纠正．     

An Explicit Formula for the Berezin Star Product

We prove an explicit formula of the Berezin star product on K?hler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Engli??? work on the asymptotic expansion of the Laplace integral.     

Trace Formula for Noisy Flows

A trace formula is derived for the Fokker–Planck equation associated with Itô stochastic differential equations describing noisy time-continuous nonlinear dynamical systems. In the weak-noise limit, the trace formula provides estimations of the eigenvalues of the Fokker–Planck operator on the basis of the Pollicott–Ruelle resonances of the noiseless deterministic system, which is assumed to be non-bifurcating. At first order in the noise amplitude, the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo-energy of the Onsager–Machlup–Freidlin–Wentzell scheme.