The dynamics of one species chemical kinetics is studied. Chemical reactions are modelled by means of continuous time Markov processes whose probability distribution obeys a suitable master equation. A large deviation theory is formally introduced, which allows developing a Hamiltonian dynamical system able to describe the system dynamics. Using this technique we are able to show that the intrinsic fluctuations, originated in the discrete character of the reagents, may sustain oscillations and chaotic trajectories which are impossible when these fluctuations are disregarded. An important point is that oscillations and chaos appear in systems whose mean-field dynamics has too low a dimensionality for showing such a behavior. In this sense these phenomena are purely induced by noise, which does not limit itself to shifting a bifurcation threshold. On the other hand, they are large deviations of a short transient nature which typically only appear after long waiting times. We also discuss the implications of our results in understanding extinction events in population dynamics models expressed by means of stoichiometric relations.
Origin of combination frequencies in quantum magnetization oscillations of two-dimensional multiband metals
研究了二维多带金属中化学势振荡对磁化强度振荡的影响。在第一部分中，Alexandrov和Bratkovsky [Phys. Rev. B \textbf{63}，033105（2001）]对具有固定电子数的二维多带金属中的磁量子振荡的分析推导被证明在数学上是不正确的;没有考虑傅立叶分量的自变量中出现的化学势振荡。在第二部分中，我们推导出一个近似的傅立叶级数的磁化振荡的小化学势振荡的制度。主要的结果是，组合频率与显着的幅度被发现，如果个别频带频率显着不同。
Reply to "Comment on 'Origin of combination frequencies in quantum magnetic oscillations of two-dimensional multiband metals' " by A.S. Alexandrov and A.M. Bratkovsky [cond-mat/0207173]
在他们对这篇论文的评论（Phys. Rev. B 65，153403（2002）; cond-mat/0110154）中，Alexandrov和Bratkovsky（cond-mat/0207173）认为，他们在多带低维金属组合频率的分析理论中正确地考虑了化学势振荡，方法是将自由能扩展为化学势振荡的幂。在这个答复中，我们表明，这种说法与他们的原始论文（物理评论B 63，033105（2001））相矛盾。我们证明，条件的扩展是数学上不正确的。正确的条件允许理解分析理论的有效性的限度。
