Hardy-Type Inequalities on H-Type Groups andAnisotropic Heisenberg Groups

The author obtains some weighted Hardy-type inequalities on H-type groups and anisotropic Heisenberg groups. These inequalities generalize some recent results due to N. Garofalo, E. Lanconelli, I. Kombe and P. Niu et al.     

Improved Sobolev inequalities on groups of Iwasawa type in presence of symmetry

Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. We prove a refined version of the Sobolev inequality on N in presence of symmetry.     

关于Heisenberg群上次Laplace算子的唯一延拓性

在Heisenberg群Hn中对微分不等式|△Hnu|≤C/d(z,t)2ψ|u|的非负解证明了某个唯一延拓性结果.     

The time-local view of nonequilibrium statistical mechanics. II. Generalized Langevin equations

On a semiphenomenological level, generalized Langevin equations are usually obtained by adding a random force (RF) term to macroscopic deterministic equations assumed to be known. Here this procedure is made rigorous by conveniently redefining the RF, which is shown to be colored noise weakly correlated with the observables at earlier times due to the finite lifetime of microscopic events. Corresponding fluctuation-dissipation theorems are derived. Explicit expressions for the spectral density of the fluctuations are obtained in a particularly simple form, with the deviation of the line shape from the Lorentzian being related most explicitly to the spectral density of the RF. Well-known low-frequency expressions and the Einstein relation of (generalized) Brownian motion theory are modified so as to include lifetime effects. New sum rules are obtained relating dissipative quantities to contour integrals (in the complex frequency domain) over spectral densities or corresponding response functions. The Heisenberg dynamics of a complete set of macroobservables is shown to be equivalent to a generalized Orstein-Uhlenbeck stochastic process which is a non-Markovian process due to the lifetime effects.     

From Kerr to Heisenberg

In this paper, we consider the space-time of a charged mass endowed with an angular momentum. The geometry is described by the exact Kerr–Newman solution of the Einstein equations. The peculiar symmetry, though exact, is usually described in terms of the gravito-magnetic field originated by the angular momentum of the source. A typical product of this geometry is represented by the generalized Sagnac effect. We write down the explicit form for the right/left asymmetry of the times of flight of two counter-rotating light beams along a circular trajectory. Letting the circle shrink to the origin the asymmetry stays finite. Furthermore it becomes independent both from the charge of the source (then its electromagnetic field) and from Newton’s constant: it is then associated only to the symmetry produced by the gravitomagnetic field. When introducing, for the source, the spin of a Fermion, the lowest limit of the Heisenberg uncertainty formula for energy and time appears.     

量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。