Strange properties of early time evolution of the projection of a state vector

Using the equation for a projection of a state vector, the exponent of a damping factor for a given state, corresponding to the effective decay width appearing in the case of multiple measured unstable states, is obtained numerically in some models for early time period t 0. is found to be nonzero (even for stable states) at this time period; thus, for early times, this damping factor is always smaller than unity. It is shown that at finitet's may be smaller or greater than the standard decay width in Weisskopf-Wigner theory depending on the parameters of a model considered.     

General properties of the evolution of unstable states at long times

An effect generated by the non-exponential behaviour of the survival amplitude of an unstable state at long times is considered. It is known that this amplitude tends to zero more slowly as t goes to infinity than any exponential function of t. Using methods of asymptotic analysis we find the asymptotic form of this amplitude at long times in a general, model-independent case. We find that the long time behaviour of this amplitude affects the form of the instantaneous energy of unstable states: this energy should be much smaller for suitably long times, t, than the energy of this state for t of the order of the lifetime of the considered unstable state.     

On the decay width of multiply measured unstable state

In the case of multiple measurements we have found that there is nonzero decay width () (even for bound states) and that, for relatively long time intervals separating successive measurements, () tends like ^–k (k 1 according to the investigated model) to the asymptotic value _o for unstable states and to zero for bound states. We have shown that the detector efficiencyZ 1 is responsible for this effect and that the evolution operator acting in the considered subspace of states should be renormalized to avoid this effect. As an illustration we have considered electromagnetic levels in the Coulomb field as an example of unstable states.     

Nonlinear analysis of the time evolution of an unstable flat charged fluid surface

Nonlinear second-and fourth-order corrections to the critical Tonks-Frenkel parameter (which characterizes the stability of the uniformly charged flat surface of an ideal conducting incompressible fluid) are found by asymptotic calculations of the fifth order of smallness in ratio of the wave amplitude to the capillary constant of the fluid. A nonlinear integral equation for the time evolution of the unstable wave amplitude is derived and solved. It turns out that the linear stage of instability development takes a major part of the total time, while the nonlinear stage is very short. It is shown that the characteristic time of instability development on the fluid surface is a rapidly decreasing function of the initial amplitude of a virtual wave and the overcritical surface charge (i.e., the excess of the charge over the critical value).     

Aspects of the Theory and Computation of Resonances, with Applications to Field-Free and Field-Dressed Atomic States

A review of certain aspects of the theory and computation of resonance states is presented, from the point of view of the work by the author and his colleagues in atomic physics. Two issues are mainly discussed: one is the understanding and ab initio calculation of resonance states of real systems from a time-dependent point of view. The other is the derivation and application of the complex eigenvalue Schrödinger equation from a superposition of the localized wave packet ₀ with the orthogonal to it scattering wave functions (E), when outgoing-wave boundary conditions are imposed. It is shown how two complex adjoint solutions, the hallmark of resonance state theory, correspond to the Fano solution for a resonance state on the real energy axis, obtained from the application of Hermitian quantum mechanics. The forms of the complex eigenfunctions are used for non-Hermitian calculations of resonance states in polyelectronic atoms. The question of time-asymmetry at the quantum level is tackled by observing that the time-evolution has to be considered with boundary conditions t 0 and > E > 0 and a complex energy distribution given by the diagonal matrix element of the Green's function with respect to ₀. Using a model whereby the self-energy of the decaying state, A(z), is approximated by A(z) A(E ₀), where E ₀ = ₀|H|₀, it is shown that time-asymmetry, if present as defined in this work, should have an effect on the as yet unobserved long-time deviation from exponential decay. Although not described explicitly, it is indicated, via the forms of the trial wave functions and via the references, how poly-electronic calculations have been carried out, for field-free resonance states as well as for resonance states that are created by the presence of an external electromagnetic field.     

Time evolution of non-Hermitian quantum systems and generalized master equations

We inquire into the time evolution of quantum systems associated with pseudo-or quasi-Hermitian Hamiltonians. We obtain, in the pseudo-Hermitian case, a generalized Liouville-von Neumann equation for closed systems. We show that quantum systems with quasi-Hermitian Hamiltonians admit the proper interpretation in terms of open quantum system and derive a generalized Lindblad-Kossakowski equation. Finally, we extend such formalism to the study of decaying systems. Partially supported by PRIN “Sintesi”.     

Oscillating Decay of an Unstable System

We study the medium-time behavior of the survival probability in the frame of the N-level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may oscillate significantly during the so-called exponential era. This result explains qualitatively the experimental observations of the NaI decay. The Gamow states for N-level Friedrichs model are constructed. The time evolution in terms of the complex spectral representation including the Gamow states is discussed.     

非稳腔中调腔孔对光束质量的影响

在中、远红外波段的激光器中，组成谐振腔的反射镜基底材料多数是对可见光不透明的，采用在腔镜上开一小孔输入调腔光方法是最简便的。本文用Ｆｏｘ－Ｌｉ迭代法计算了无开孔及有开孔时正支非稳共焦腔空腔的模式，结果表明当调腔光开孔直径小于３ｍｍ时，对光束质量基本没有影响。     

非稳腔输出环状激光束的传输特性

本文从菲涅耳衍射积分公式出发研究了激光器非稳腔输出环状光束在空间的传输规律.由轴上光强的极值点位置给出了划分非稳腔传输空间的近场、中场和远场区域公式.理论计算结果表明,非稳腔输出端环状光束在中场区域激光能量逐渐向轴心方向转移,而在远场变为爱里型圆盘状光束的过程.在非稳腔脉冲TEA CO_2激光器上测得的实验结果与理论计算结果很好地符合.     

类锌金离子Au~(49+)M壳层激发态的能级结构及衰变性质的理论研究

在相对论多组态Dirac-Fock(MCDF)理论方法基础上,通过系统考虑量子电动力学(QED)效应、Breit相互作用和弛豫效应,详细研究了类锌金离子Au49+的能级结构以及涉及M壳层激发态各种可能的辐射和Auger衰变过程.总结了QED效应和Breit相互作用对类锌金离子Au49+的M壳层激发态能级影响的一般规律.指出了随M壳层洞态的变化,主要的辐射衰变和Auger衰变的退激发特性.计算得到的部分辐射衰变能与已有的实验观测和理论计算结果作了比较,符合的很好.     

Experimental studies of an unstable confocal resonator alexandrite laser

The effects of excited converging wave in an unstable confocal resonator onthe properties of an alexandrite laser are investigated experimentally.The results show thatexciting the converging wave inside the resonator is an effective method to reduce the diver-gence of the laser beam for low gain laser medium.     

Deep penetration welding using a CO laser with an unstable resonator

An unstable resonator (M = 2) has been applied to reduce the beam divergence of a gas-dynamically cooled supersonic CO laser operating at 105 K in a semiclosed gas cycle. A 4.7 kW laser beam with a total divergence of 2.5 mrad is obtained with an efficiency of 9.4%. The results of welding experiments are compared with those using a CO₂ laser. The weld depths obtained with the CO₂ laser are drastically reduced using argon as the assist gas, whereas the results with the CO laser are independent of the assist gas because of the lower plasma absorption coefficient for the shorter CO laser wavelength.     

On the time evolution of the states of infinitely extended particles systems

We consider an infinite classical system of interacting particles in , . We study the time evolution of a particular class of nonequilibrium states. More precisely, the states we consider are Gibbs with respect to a Hamiltonian which differs from the Hamiltonian governing the motion by an external field (possibly not localized), satisfying certain conditions. It is proved that the time-evolved states satisfy superstable estimate and are described by correlation functions obeying the BBGKY hierarchy in a weak form.     

Operator properties of generalized coherent state systems

The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufficient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.     

On the description of multiple measurements of an unstable state

The nondecay probability of an unstable particle at a definite moment of time is investigated provided this particle existed at all earlier observation moments separated with the time interval Δ. Using the usual postulates for quantum measurements it is proved that this probability is described by the exponential function of Δ>0, and it tends to 1 as Δ → 0. An approximate formula is found for the effective decay width Γ(Δ) appearing in the case of multiple measurements. It is shown that Γ(Δ) → 0 as Δ → 0. For Δ → ∞, the width Γ(Δ) → Γ₀, with Γ₀ being the standard decay with in Weisskopf-Wigner theory. At finite δ's Γ(Δ) may be smaller or greater than Γ₀ depending on the parameters of the theory.     

腔内像散扰动对正支共焦腔模式影响的数值分析

 针对激光器出光过程中腔内像差扰动带来的输出光束质量和光束能量下降问题,分析了腔内像差扰动对非稳腔模式的影响,并采用数值迭代法计算了理想情形和腔内像散扰动对无源正支共焦腔输出模式强度和相位分布的影响,进一步采用Zernike模式法对光束相位进行了像差拟合,得到了前35阶Zernike像差系数、点扩散函数(PSF)分布和环围能量曲线,计算了腔内像散扰动量与远场Strehl比的关系。结果表明：对小菲涅耳数正支共焦腔,腔内像散扰动对输出光束强度和相位分布均有明显影响,相位分布中一些高阶Zernike像差也有所增大。因此在进行腔内像差校正时,应优先考虑此类像差的校正。     

微晶硅薄膜的结构及光学性质的研究

借助RF-PECVD辅助RTP技术，采用高沉积气压的技术路线制备了优质的微晶硅薄膜，并利用拉曼光谱、反射谱和透射谱分别研究了微晶硅的晶化率和光学性质.实验中发现微晶硅的吸收边出现了相对红移，此相对红移可归结于薄膜晶化率的提高和带尾态密度的降低. 关键词： 微晶硅 拉曼光谱 快速热处理 红移