On birth and death processes in symmetric random environment

We prove a limit theorem for a process in a random one-dimensional medium, which has been considered before as a model for hopping conduction in a disordered medium. To the edge between the two integersj and (j+ 1) a rate _j > 0 is attached. These _j :j integral are taken as independent, identically distributed random variables, and represent the medium. For given values _j, X(t) is a Markov chain in continuous time which jumps fromj to (j + 1) and from (j + 1) toj at the same rate _j. We show that in many cases there exists normalizing constants y(t) (which tend to oo witht) such that the distribution of X(t)/(t), or more generally of the whole processX(st)/(t) _S0, converges to a limit as t . The limit process is continuous and self-similar.     

控制Tavis-Cummings模型中两原子X态的纠缠突然死亡与突然产生

研究了初态为X态时Tavis-Cummings模型中具有偶极相互作用两原子的纠缠演化特性,在演化过程中,同时号码出现了两原子的纠缠突然死亡(ESD)与突然产生(ESB)两种有趣的现象.详细分析了两原子初始态的纯度、偶极相互作用、光场粒子数对这两种现象出现时间的影响,进一步给出了初始为混态时ESB与ESD的转换条件.计算结果表明,上述系统参量对两原子的纠缠演化、ESB与ESD有重要的影响,偶极相互作用会改变纠缠度的振荡周期,使出现ESD的时间间隔减少;随着初始两原子纠缠纯度的增大,纠缠突然产生以及纠缠突然死亡存在的时间缩短,并且可以提高两原子之间的纠缠;对于特殊的初态,产生了纠缠不变性以及固定的两原子纠缠,该定值受两原子初始状态的纯度控制。     

Fluctuation and relaxation of macrovariables

Assuming that a macrovariable follows a Markovian process, the extensive property of its probability distribution is proved to propagate. This is a generalization of the Gaussian properties of the equilibrium distribution to nonequilibrium nonstationary processes. It is basically a WKB-like asymptotic evaluation in the inverse of the size of the macrosystem. Evolution of the variable along the most probable path and fluctuation properties around the path are considered from a general point of view with an emphasis on the relation of nonlinearity of evolution and the associated fluctuation. Anomalous behavior of the fluctuation is discussed in connection with unstable, critical, or marginal states. A general treatment is given for the asymptotic properties of relaxation eigenmodes.     

Modeling of Self-Diffusion and Relaxation Time NMR in Multi-Compartment Systems

The theory of pulsed field gradient (pfg) NMR applied to molecules in cellular systems which contain different subcellular compartments separated by permeable membranes, acting as diffusion barriers, has been extended. A numerical model of restricted diffusion and magnetization relaxation behavior in pfg-CPMG NMR experiments, based on the Fick's second law of diffusion, is presented. This model is applicable to a wide range of systems and allows the exploration of temporal and spatial behavior of the magnetization with and without the influence of gradient pulses. Results of the numerical experiments show their correspondence to the previously observed ones and demonstrate the importance of the inclusion of the time domain data in analyzing diffusion measurements.     

Influence of Reversible and Irreversible Relaxation on the Single-Pulse Echo Signal

An analytical expression for a signal of the single-pulse echo generated in nonresonant pulse excitation of an inhomogeneously broadened two-level quantum system has been obtained, with the reversible and irreversible relaxation taken into account. It is shown that the rate of decay of the single-pulse echo is determined by the rate of reversible and irreversible transverse relaxation. It has been established that the contribution of the reversible and irreversible relaxations to decay of the single-pulse echo depends on the ratio between the detuning of the pulse-carrying frequency from resonance to the Rabi frequency. The difference between the times of transverse irreversible relaxation measured in manganese ferrite MnFe₂O₄ by the methods of single and two-pulse echo of nuclear magnetic resonance has been explained within the framework of the theoretical expressions obtained.     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Fluctuation,relaxation, and extensivity of macrovariables in nonequilibrium systems

The extensive property of a macrovariable is proved for a quantal system whose Hamiltonian depends on time and for a stochastic system whose temporal evolution operator depends on time. These generalized situations are concerned with bulk-contact open systems. The extensive property, fluctuation, and nonlinear relaxation are investigated explicitly by calculating rigorously generating functions in exactly soluble models such as the linear stochastic model and linearXY model. The relation between the nonlinear critical slowing down and linear critical slowing down is also discussed.     

Analysis and control of ultrafast photodissociation processes in organometallic molecules

In this paper we characterize the ultrafast fragmentation in electronically excited Fe(CO)₂(NO)₂ and CpMn(CO)₃ by means of femtosecond time-resolved spectroscopy combined with mass spectrometry. From the transient two-color multi-photon ionization data, it was possible to record the transients of the parent molecule ions and their photofragment ions. The experimentally observed decay times indicated an ultrafast loss of the first ligands (sub-100 fs decay times). Further we performed a feedback control experiment on the photofragmenting CpMn(CO)₃ molecular system in order to maximize the yield of desired ionic products through pulse modulation. The shape of the pulses obtained from optimization reflect well the intrinsic molecular dynamics during photofragmentation and the change of the CpMn(CO)⁺/CpMn(CO)₃ ⁺ ratio shows a clear evidence for the capability of the optimization method to find tailor-made system-specific pulses. Received 9 January 2001     

Irreversibility and entropy production in transport phenomena,III—Principle of minimum integrated entropy production including nonlinear responses

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager–Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented.