金属中自由电子气体的非广延统计研究

采用分解近似的方法讨论了在Tsallis量子统计物理框架中，金属中自由电子气体的非广延参数q的热力学统计处理，计算出了总粒子数、总能量、自由能、热容量等热力学量，得出结论：在低温区域，q→1时，所有结果都可以回到传统的Fermi-Dirac分布，非广延参数q控制着系统的非广延程度.最后，详细讨论了q与热容量之间的关系，并与以前的结果作了比较. 关键词： Tsallis广义统计 非广延参数q 自由电子气体 Fermi-Dirac分布     

非广延统计力学与完全开放系统的统计分布

简介了非广延统计力学的Tsallis统计,用其计算了理想气体;推导出了以含有非广延熵常数的Shannon熵为基础和以Tsallis熵为基础的非广延统计力学的完全开放系统的统计分布及计算热力学量的公式;讨论表明:Tsallis熵对应的统计分布及计算热力学量的公式在非广延参量q→1时,完全过渡到了Shannon熵对应的形式.     

用晶格玻尔兹曼方法研究螺旋波的产生机制和演化行为

采用五速正方晶格玻尔兹曼模型，由晶格玻尔兹曼方程推导得到了反应扩散方程.分析了Selkov反应扩散系统螺旋波的形成机制.零流边界条件下计算机数值模拟螺旋波的形成和破碎过程，发现Selkov反应扩散系统的失稳属于Doppler失稳.改变参数模拟系统的演化行为，发现不同的参数下系统可能到达三种不同的状态：均匀定态、混沌状态和螺旋波. 关键词： 晶格玻尔兹曼方法 螺旋波 计算机模拟     

非平衡统计信息理论

阐述了以表述信息演化规律的信息（熵）演化方程为核心的非平 衡统计信息理论.推导出了 Shannon信息（熵）的非线性演化方程，引入了统计物理信息并 推导出了它的非线性演化方程.这两种信息（熵）演化方程一致表明：统计信息（熵）密度 随时间的变化率是由其在坐标空间（和态变量空间）的漂移、扩散和减损（产生）三者引起 的.由此方程出发，给出了统计信息减损率和统计熵产生率的简明公式、漂移信息流和扩散 信息流的表达式，证明了非平衡系统内的统计信息减损（或增加）率等于它的统计熵产生（ 或减少）率、信息扩散与信息减损同时 关键词： 统计信息（熵）演化方程 统计信息减损率 统计熵产 生率 信息（熵）流 信息（熵）扩散 动态互信息     

位错密度的演化动力学方程

 将位错的增殖、淹没与相互反应看作化学反应，位错在热激活作用下具有扩散性质。因此，位错系统是一个反应-扩散系统。依据自组织理论，给出了两个位错密度演化动力学方程，当系统发生结构失稳之后，第一个方程变成第二个方程；第一个方程含有对称性破缺，按Higgs机制将发射偶极子。     

脉冲激发三能级体系半导体量子点的单光子发射效率

研究了脉冲激发下单个半导体量子点中单光子发射的统计特性.在旋转波近似条件下，由系统粒子数演化主方程并结合量子回归理论推导了二阶相关函数的运动方程，利用此方程讨论了二阶相关函数随输入脉冲面积的关系.在窄脉冲宽度的脉冲激发下，单光子的发射概率p和效率η都随着强度的增强而产生振荡.研究表明，采用窄脉冲宽度，当输入脉冲面积在π附近时可以得到较高的单光子发射效率. 关键词： 半导体量子点 单光子发射 三能级系统     

基于非广延熵纠缠平方的严格单配性不等式

非广延熵纠缠是一种很好的纠缠度量方式，其本身在参数q∈［2，3］范围服从严格单配性关系.我们提出基于非广延熵纠缠平方服从的严格单配性关系，将参数范围扩展至q∈[（5-√13]）/2，（5+√13）/2].该单配性关系更加严格，比非广延熵纠缠的严格单配性不等式成立范围更广.     

谐振势阱中旋转广义玻色系统的热力学性质

以非广延Tsallis统计理论为基础,导出了广义玻色-爱因斯坦统计分布表达式,并用其分别讨论了三维和二维谐振势阱约束的旋转广义玻色气体的热力学性质.结合系统粒子数、玻色-爱因斯坦凝聚(BEC)临界温度、基态粒子占据率和比热等物理量的解析表达式,分析了非广延参数和势阱旋转频率等因素对系统热力学性质的影响.     

反常扩散与分数阶对流-扩散方程

反常扩散现象在自然界和社会系统中广泛存在.考虑了扩散过程的时间相关和时空相关性，用非局域性的处理方法，在传统的二阶对流 扩散方程基础上，得到了分数阶对流 扩散方程，以此方程来描述反常扩散.在此方程中，弥散项和对时间的导数为分数阶导数所代替.由此分数阶对流 扩散方程，对传统的费克扩散定律进行推广，得到了广义的分数费克扩散定律，分数费克扩散定律说明某时刻空间中某点的流量不仅与其领域内的浓度梯度有关，而且与整个空间中其他不同点的粒子浓度、浓度变化的历史，甚至初始时刻的浓度有关.讨论了方程的解——分数稳定分布，并由此说明了扩散运动的平均平方位移是运移时间的非线性函数. 关键词： 扩散 分数阶微积分 稳定分布（Lévy分布） 费克扩散定律     

激光系统的Ginzburg-Landau方程及其相位扩散方程

讨论了激光系统Ginzburg-Landau方程的主要动力学行为,它描述激光系统的自发时空对称性破缺。当方程有非均匀静态解时,它存在合作频率锁定效应;而当方程有时空振荡解时,各横模仍有一个共同的光学载频。此模型还表明,混沌解可以发生在低抽运条件下。在较小失谐时,该方程的约化相位扩散方程能较精确地再现原方程的全程动力学行为。这说明在激光横向图形分布的自发形成中,电场的相位分布导引其动力学行为。 关键词：     

Jeans'' criterion and nonextensive velocity distribution function in kinetic theory

The effect of nonextensivity of self-gravitating systems on the Jeans' criterion for gravitational instability is studied in the framework of Tsallis statistics. The nonextensivity is introduced in the Jeans problem by a generalized q-nonextensive velocity distribution function through the equation of state of ideal gas in nonextensive kinetic theory. A new Jeans' criterion is deduced with a factor that, however, differs from that one in [Astron. Astrophys. 396 (2002) 309] and new results of gravitational instability are analyzed for the nonextensive parameter q. An understanding of physical meaning of q and a possible seismic observation to find astronomical evidence for a value of q different from unity are also discussed.     

Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We discuss a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium for self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions. Tsallis’ equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.     

Nonextensive statistical effects in protoneutron stars

We investigate the bulk properties of protoneutron stars in the framework of a relativistic mean-field theory based on nonextensive statistical mechanics, characterized by power-law quantum distributions. We study the relevance of nonextensive statistical effects on the b \beta -stable equation of state at fixed entropy per baryon, in the presence and in the absence of trapped neutrinos, for nucleonic and hyperonic matter. We show that nonextensive statistical effects could play a crucial role in the structure and in the evolution of the protoneutron stars also for small deviations from the standard Boltzmann-Gibbs statistics.     

Nonextensive statistical mechanics of ionic solutions

Classical mean-field Poisson–Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson–Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye–Hückel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q.     

Nonextensive formalism and continuous Hamiltonian systems

A recurring question in nonequilibrium statistical mechanics is what deviation from standard statistical mechanics gives rise to non-Boltzmann behavior and to nonlinear response, which amounts to identifying the emergence of “statistics from dynamics” in systems out of equilibrium. Among several possible analytical developments which have been proposed, the idea of nonextensive statistics introduced by Tsallis about 20 years ago was to develop a statistical mechanical theory for systems out of equilibrium where the Boltzmann distribution no longer holds, and to generalize the Boltzmann entropy by a more general function Sq while maintaining the formalism of thermodynamics. From a phenomenological viewpoint, nonextensive statistics appeared to be of interest because maximization of the generalized entropy Sq yields the q-exponential distribution which has been successfully used to describe distributions observed in a large class of phenomena, in particular power law distributions for q>1. Here we re-examine the validity of the nonextensive formalism for continuous Hamiltonian systems. In particular we consider the q-ideal gas, a model system of quasi-particles where the effect of the interactions are included in the particle properties. On the basis of exact results for the q-ideal gas, we find that the theory is restricted to the range q<1, which raises the question of its formal validity range for continuous Hamiltonian systems.     

Blackbody radiation in nonextensive Tsallis statistics: Exact solution

An exact analysis of n-dimensional blackbody radiation in the recently proposed nonextensive Tsallis statistics is given here. Thus, the main relationships of blackbody radiation are generalized in the Tsallis context. In particular, it is verified that the relation between pressure, volume, and internal energy is form invariant with respect to the nonextensive entropic index, q. The results and procedure presented here are expected to be useful in the discussion of nonextensive systems possessing large or infinite numbers of degrees of freedom.     

On different q-systems in nonextensive thermostatistics

It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same q. In this paper, the existence of composite system with different q subsystems is investigated by fitting the power law degree distribution of air networks with q-exponential distribution. Then a possible extension the nonextensive statistics to different q systems is provided on the basis of an entropy nonadditivity rule and an unnormalized expectation of energy.