Diabatic aspects of single-particle motion within the time-dependent Hartree-Fock theory

Time-dependent Hartree-Fock (TDHF) calculations for central collisions of⁸⁶Kr on¹⁶⁶Er are investigated with respect to quasi-stationary properties for various energies in the center-of-mass system. A quasi-stationary potential as well as quasi-stationary single-particle levels are extracted as functions of the relative distance between the two nuclei. A quantitative comparison with the diabatic two-center shell-model yields surprising agreement with the results from TDHF-calculations for both the nucleus-nucleus potential and the single-particle levels. From this we conclude that the approach phase of a nucleus-nucleus collision can be well described within a diabatic approximation for the single-particle motion.     

Characteristic periodicities of collective behavior at the foreign exchange market

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation predicts stable coexistence of all four strategies. In this situation, we consider the effects of fluctuations stemming from a finite population size. We show that they unavoidably lead to extinction of two strategies in the population. However, the typical time until extinction occurs strongly prolongs with increasing system size. In the emerging time window, a quasi-stationary probability distribution forms that is anomalously flat in the vicinity of the coexistence state. This behavior originates in a vanishing linear deterministic drift near the fixed point. We provide numerical data as well as an analytical approach to the mean extinction time and the quasi-stationary probability distribution.     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser

Single-pass free-electron lasers constitute an example of systems with long-range interactions. The light-particle interplay leading to the power growth and successive relaxation towards a quasi-stationary state is governed by the Vlasov equation. A maximum entropy principle inspired to Lynden-Bell's theory of “violent relaxation" for the Vlasov equation can be invoked to analytically characterize the behaviour of the saturated system. In particular, we here concentrate on the case of coherent harmonic generation obtained from an externally seeded free-electron laser and provide a simple strategy to predict the laser intensity as well as the final electron-beam energy distribution.     

Quasi-stationary states in a circular geometry

The quasi-stationary final states of decaying two-dimensional turbulence on a circular domain, with an initial flow field containing either no or a substantial amount of angular momentum, have been investigated numerically. The production of angular momentum is almost absent for these flows on a circular domain with a no-slip wall. Its presence or absence essentially determines the character of the quasi-stationary final state. Based on a minimum-enstrophy principle a diagram is constructed that provides insight into the development of the typical late-time flow patterns on a circular domain with a no-slip wall. The quasi-stationary final states found in the present numerical study can be understood based on the predictions from the minimum-enstrophy principle.     

Electron-phonon relaxation and excited electron distribution in zinc oxide and anatase

We propose a first-principles method for evaluations of the time-dependent electron distribution function of excited electrons in the conduction band of semiconductors. The method takes into account the excitations of electrons by an external source and the relaxation to the bottom of the conduction band via electron-phonon coupling. The methods permit calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with a steady-in-time source of light, the time of setting of the quasi-stationary distribution and the time of energy loss via relaxation to the bottom of the conduction band. The actual calculations have been performed for titanium dioxide in the anatase structure and zinc oxide in the wurtzite structure. We find that the quasi-stationary electron distribution function has a peak near the bottom of the conduction band and a tail whose maximum energy rises linearly with increasing energy of excitation. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within a time of no more than 500?fs for ZnO and 100?fs for anatase. We also discuss the applicability of the effective phonon model to energy-independent electron-phonon transition probability. We find that the model only reproduces the trends in the change of the characteristic times whereas the precision of such calculations is not high. The rate of energy transfer to phonons at the quasi-stationary electron distribution also have been evaluated and the effect of this transfer on the photocatalysis has been discussed. We found that for ZnO this rate is about five times less than in anatase.     

Spin echo generated by resonance transitions between laboratory coordinate frame levels and quasi-energy levels

The general rules governing the transition to a new representation in which the Hamiltonian of interaction with an alternating field contains constant terms are formulated. Diagonalization of this Hamiltonian leads to the formation of quasi-stationary energy levels. The possibility of the existence of a temperature at the quasi-energy levels is considered separately. A three-level spin system is used as an example to show that another specially selected alternating magnetic field can excite resonance transitions between the energy levels in the laboratory coordinate frame and the energy levels in the new representation. Expressions for free-precession and spin echo signals, which carry information concerning quasi-stationary energy levels, are derived.     

Nonadiabatic transitions in collisions of a negative hydrogen ion with a hydrogen molecule

Nonadiabatic transitions of two types: (1) between discrete states and (2) between discrete and continuous spectrum states were considered for the detachment of a negative hydrogen ion in collisions with a hydrogen molecule. It was shown for the example of collinear collisions that, at low collision energies, the mechanism of the process was related to the quasi-stationary character of the ground electronic state of the quasi-molecule, whereas the mechanism related to the quasi-stationary character of the first excited state became noticeable as the energy of collisions increased.     

The design of reciprocal ferrite phase shifters

The design of a reciprocal ferrite phase shifter in a rectangular waveguide, using perturbation theory with a quasi-stationary approximation for the field perturbation of the system is considered. The theoretical results are compared with experimental data and with a design carried out without using the quasi-stationary approximation [5], The simplicity of the proposed method and the good agreement between the theoretical and experimental results enable it to be used in solving engineering problems.     

Quasi-stationary states of electrons and holes in an open composite cylindrical quantum wire

The energies of the quasi-stationary states of electrons and holes in an open composite cylindrical quantum wire are calculated within the effective-mass approximation by means of the S-matrix theory. Specific calculation is carried out for the HgS/CdS/HgS system. The poles of the S matrix in the complex energy plane are studied. The dependences of the lifetimes of quasiparticles in quasi-stationary resonance states on the longitudinal quasi-momentum and geometric parameters of the nanosystem are obtained. It is shown that the quasiparticle lifetimes in the resonance states exponentially diminish as the longitudinal quasi-momentum increases.     

Energy spectra and lifetimes of quasiparticles in an open quantum dot surrounded by identical barriers in a cylindrical quantum wire

A theory of quasi-stationary states and lifetimes of electrons, holes, and excitons in an open cylindrical semiconductor quantum wire containing a quantum dot surrounded by two identical antidots (with potential barriers of finite height) is developed using the scattering matrix method. The energy spectra and lifetimes of electrons, holes, and excitons in a β-HgS/β-CdS/β-HgS/β-CdS/β-HgS nanoheterosystem are calculated and analyzed as functions of the geometric parameters of the quantum dot involved. It is demonstrated that an increase in the height of the quantum dot leads to a decrease in the energy of quasi-stationary exciton states of the Breit-Wigner type and to an increase in their lifetimes. The lifetime of exciton states is long enough for these states to be observed in the experiment.     

A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model

We give a closer look at the Central Limit Theorem (CLT) behavior in quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one for long-range-interacting classical many-body systems. We present new calculations which show that, following their time evolution, we can observe and classify three kinds of long-standing quasi-stationary states (QSS) with different correlations. The frequency of occurrence of each class depends on the size of the system. The different microscopic nature of the QSS leads to different dynamical correlations and therefore to different results for the observed CLT behavior.     

Resonant interaction of the Langmuir wave with quasi-stationary plasma electrons

Evolution of the Langmuir wave in quasi-stationary plasma is considered. A consistent solution to the closed system of the Vlasov–Poisson equations is obtained in the adiabatic approximation. Dispersion of the wave evolving in the electron distribution tail with variable electron concentration or plasma temperature is described. It is established that the plasma oscillation energy increases with decreasing electron concentration or increasing temperature. After plasma regains its initial state, the wave parameters also restore their initial values. That is, the wave evolution in the quasi-stationary plasma is a completely reversible process.     

Evolution of the spectral parameters of quasiparticles in an open symmetrical three-barrier resonant tunneling nanostructure

The spectral parameters (resonance energies and resonance widths) of quasi-stationary states in an open symmetrical three-barrier resonant tunneling nanostructure have been theoretically calculated in terms of the model of spatially dependent effective masses and rectangular potentials of quasiparticles (electrons, holes, excitons) by using the methods of transmission coefficient, scattering matrix, and probability distribution function. The evolution of the spectral parameters of quasi-stationary states of quasiparticles as a function of the variation in the geometric sizes of the nanosystem has been calculated and analyzed for the open three-barrier resonant tunneling structure consisting of three barriers (GaAs) and two wells (In_0.25Ga_0.75As) as an example. It has been established that the experimental and theoretical results are in satisfactory agreement for the model without fitting parameters in the case of a heavy exciton.     

Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall

A branching random walk in presence of an absorbing wall moving at a constant velocity v undergoes a phase transition as the velocity v of the wall varies. Below the critical velocity v _c , the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time T. We study the quasi-stationary regime for v<v _c when T is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time T. We then use this construction to show that the properties of the quasi-stationary regime are universal when v→v _c . We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.     

Evolutionary model on market ecology of investors and investments

The interactions between investors and investments are of significant importance to understand the dynamics of financial markets. An evolutionary model is proposed to investigate the dynamic behaviors of investors and investments in a market ecology. The investors are divided into two groups, active ones and passive ones, distinguished by different selection capabilities based on the partial information, while the investments are simply categorized as good ones and bad ones. Without external influence, the system consisting of both investors and investments can self-organize to a quasi-stationary state according to their own strategies associating with the gains of market information. The model suggests that the partial information asymmetry of investors and various qualities of investments commonly give rise to a diverse dynamic behavior of the system by quantifying the fraction of active investors and of good investment at the quasi-stationary state.     

Laser-induced radiative recombination of antihydrogen in a magnetic field through a quasi-stationary state

To increase the efficiency of laser-induced recombination of antihydrogen from cold antihydrogen—positron plasma in a trap, it is proposed to use a new resonance mechanism with the participation of positron quasi-stationary states, arising under the joint action of an antiproton Coulomb field and a strong magnetic field of the trap. The recombination rate is expressed through the atomic laser ionization cross section whose frequency dependence is nonmonotonic due to the presence of quasi-stationary states against the background of the continuum. The estimates with the use of the ionization cross sections calculated earlier demonstrate the possibility of improving the efficiency of the laser-induced recombination at an optimally selected laser frequency.     

Mathematical modeling of ceramics metallization technology

Metallization of ceramics by an incoherent light beam has been simulated. A ceramic substrate with a metal-containing paste deposited on its surface is considered as an infinite planar two-layer medium. The Stefan problem with phase transitions is formulated and solved by the quasi-stationary Leibenzon method.     

Generalization of the equation for the quasi-stationary relativistic electron beam envelope to the case of Resistive Hose instability

The statement of an equation for the envelope of a quasi-stationary relativistic electron beam experiencing Resistive Hose instability is considered. The well-known Nordsieck equation is generalized to the case of Resistive Hose instability using analytical methods.     

Doublet resonances of an electron in symmetric three-barrier resonant tunneling structures

The evolution and collapse of electron resonances and their spectral parameters in a symmetric three-barrier resonant tunneling structure (TBRTS) are studied theoretically. The resonance energy and width of the quasi-stationary states of an electron are analyzed. The quasi-stationary states are calculated by the transmission coefficient method, the method of the probability distribution function (the probability of finding an electron in a TBRTS), and the scattering cross section method.