Theory of the Domino Dynamics Via Nonadiabatic Transitions

Photoinduced nucleation processes, called photoinduced domino processes, via excited electronic states are discussed theoretically for a one-dimensional arrangement of deformable molecules using a model composed of localized electrons and lattices. We show that the global structural transition by photoexcitation only at a molecule (site) is possible in the adiabatic and diabatic limits. An intermediate regime between these limits is investigated; an analytical treatment and a numerical calculation are presented taking into account the nonadiabatic electronic transition, i . e ., the Landau-Zener-type transition. In this regime, the domino dynamics can be terminated halfway ( i . e ., a finite - size domain appears) in contrast to the "all-or-nothing" domino dynamics ( i . e ., a photoinduced domain vanishes or grows up to the system size) in the adiabatic and diabatic limits.     

Stochastic and deterministic domino processes in photoinduced structural changes

The photoinduced structural change is discussed theoretically using a one-dimensional model, which is composed of localized electrons and lattices. We clarify the condition for the adiabatic and/or diabatic approximations. The global structural change by one-site excitation is possible in both cases. Under the adiabatic picture, the domain wall between the two phases moves at constant velocity, and the structural change in each site occurs nonradiatively within the time order of the lattice vibration. On the contrary, under the diabatic picture, the motion of the domain wall becomes a stochastic process because the structural change in each site occurs via the radiative transition, which takes a longer time than the lattice vibration.     

Bound-bound state quantum wave packet dynamics in the intermediate coupling range: the A1Sigma+u (0+u) and b3IIu (0+u) system in Rb2

The real-time quantum dynamics of a wave packet confined to two coupled bound states at intermediate interaction strength is probed by experiment and calculations on the A1Sigma(+)(u) approximately b (3)II(u) system in Rb2 molecules. The general dynamics consists of rapid spreading out over the whole phase space. Particular conditions exist, however, under which the initial wave packet motion separates into two mesobatic trajectories with distinct frequencies. These diabatic or adiabatic hybrid trajectories are analogous to those responsible for longevity resonances in bound-unbound systems.     

Spontaneous phase transitions in ferrite garnet films

Spontaneous phase transitions in ferrite garnet films have been studied. It has been shown that, with variations in the temperature, domain walls undergo phase transitions which cause spontaneous phase transitions in the lattice of cylindrical magnetic domains. The phase transition in a domain wall causes a spin-reorientation phase transition over the whole sample near the magnetic compensation point. The character of the phase transition in the domain wall determines the mechanism of the spin-reorientation phase transition.     

Theory for photoinduced structural phase transitions

A general concept for photoinduced structural phase transitions is developed in terms of the hidden multistability of the ground state and the proliferations of optically excited states. Taking the ionic→neutral (I - N) phase transition in the organic charge transfer crystal, TTF—CA, as a typical example for this type of transition, we, at first, theoretically show an adiabatic path of this transition, which starts from a single charge transfer exciton in the ionic phase, but finally reaches a neutral domain with a macroscopic size. In connection with this I—N transition, the concept of the initial condition sensitivity is also developed so as to clarify experimentally observed nonlinear characteristics of this material. In the next, using a more simplified model for the many-exciton system, we theoretically study the early time quantum dynamics of the exciton proliferation, which finally results in the domain formation of a large number of ex-citons. For this purpose, we derive a stepwise iterative equation to describe the exciton proliferation, and clarify the origin of the initial condition sensitivity.     

On the thickness of domain walls in ferroelectrics and ferroelastics

Ferroelastic and ferroelectric domain walls are commonly described by wall profiles of the tanh(x/w)-type. We argue that this profile is still a good approximation if higher-order gradient energies are considered. Such energies are relevant for phase transitions close to structural incommensurations and also for phase transitions with dominant elastic interactions. Their effect on the wall profile is to influence the effective wall thickness. Positive gradient energies tend to widen domain walls beyond the values predicted in classic Landau-Ginzburg theory.     

Anomalies of internal friction of ferrimagnetic spinel Li0.5Fe2.5O4 in various structural states

The results of high-temperature (20≤T≤800°C) relaxation and magnetic investigations of ferrite Li_0.5Fe_2.5O₄ in various structural states are given. Anomalies of internal friction caused by the occurrence of ferrimagnetic and structural (ordering type) second-order phase transitions and by vibrations of domain walls of ferrimagnetic and antiphase domains were revealed. It is shown that the 1: 3 ordering of Fe³⁺ and Li⁺ ions in the octahedral sublattice of the spinel leads to a decrease in the Curie temperature, a change in the character of the temperature dependence of the low-field magnetization, and a narrowing of the temperature range of the structural phase transition, as well to a substantial weakening of dissipation processes connected with vibrations of ferrimagnetic domain walls in the field of elastic stresses.     

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state S, coupled to all other intra-molecular vibrational states R of the same molecule, and also to its environment Q. Molecular states forming the first reservoir R are characterized by a discrete dense spectrum, whereas the environment reservoir Q states form a continuous spectrum. Assuming the equidistant reservoir R states we find the exact analytical solution of the quantum dynamic equations. S-Q and R-Q couplings yield to spontaneous decay of the S and R states, whereas S-R exchange leads to recurrence cycles and Loschmidt echo at frequencies of S-R transitions and double resonances at the interlevel reservoir R transitions. Due to these couplings the system S time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system S dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are possible four dynamic regimes of the evolution: (i) independent of the environment Q exponential decay suppressing backward R - S transitions, (ii) Loschmidt echo regime, (iii) incoherent dynamics with multicomponent Loschmidt echo, when the system state is exchanged its energy with many states of the reservoir, (iv) cycle mixing regime, when long time system dynamics looks as a random-like. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.     

用Sin-DVR方法求解在绝热表象下锥形交叉分子振动本征态

在波恩-奥本海默近似中,分子中原子核的运动通常采用绝热表象的基态势能面来描述,一般情况下这样是比较好的近似. 然而当势能面上存在锥形交叉时,即使体系的能量远远低于锥形交叉点,绝热基态势能面近似将不再有效. 锥形交叉的出现,使得绝热表象下描述核运动的哈密顿中出现了两个额外的附加项：对角波恩－奥本海默近似校正(DBOC)项和几何相位(GP)项. 尤其GP项,使得基态绝热势能面近似失效. 这两项在锥形交叉点处的数值是发散的,因此在绝热表象中来严格描述核运动,会使量子动力学的计算存在数值收敛的困难. 在量子分子动力学计算中,最常用的数值方法是分离变量表象方法(DVR). 本文通过在绝热表象和透热表象下求解涉及两个电子态且包含锥形交叉的二维的薛定谔方程来验证Sinc-DVR的数值收敛性. 计算结果显示,在绝热表象中采用通常格点密度分布的Sinc-DVR方法,即使在没有特别的处理DBOC和GP项时,也可以得到比较可靠的结果. 此时的数值不确定性并没有比引入任意的向量势来纠正GP效应的不确定性更差. 需要特别注意的是,纠正GP效应的任意向量势的精确形式,通常是不易得到其精确形式的.     

Constrained relativistic mean-field approach with fixed configurations

A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean-field model. As an example, the potential energy surfaces of ²⁰⁸Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. It is shown that the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to follow the evolution of single-particle orbits till the very deformed region, and to obtain several well-defined deformed excited states which can hardly be expected from the adiabatic PESs.     

Secondary ferroic properties of ferroelectric crystals

Twenty five types of structural phase transitions that are accompanied by the appearance of a spontaneous optical activity in the low-temperature phase are analyzed. A technique is proposed for describing the enantiomorphic domain structure (orientation states) in these crystals.     

Bright optical lattices in a longitudinal magnetic field. Experimental study of the oscillating and jumping regimes

All the bright optical lattices studied so far have been designed to obtain a circularly polarized light at the bottom of the optical potential wells. This condition minimizes the departure rate of the atoms from the fundamental adiabatic surface and permits an oscillating regime in a large range of parameters. We present here an experimental study of cesium atoms in a three-dimensional optical lattice, where the light is linearly polarized at the bottom of the potential wells. Temperature measurements and pump-probe spectroscopy give similar results for this lattice and for the conventional lin lin lattice (which have circular polarizations at the bottom of the wells) despite the fact that one lattice operates in the jumping regime and the other in the oscillating regime. We study the behaviour of the two types of lattices in a longitudinal magnetic field, with particular emphasis on the zero field and strong field regimes. The strong field situation is very simple because the eigenstates are then almost pure Zeeman substates and the adiabatic and diabatic potential surfaces are identical. The comparison between the zero-field and the high-field situations shows that the diabatic potentials are more appropriate to account for experimental observations in the novel lattice. Received: 9 October 1997 / Accepted: 6 November 1997     

Dynamics of spontaneous radiation of atoms scattered by a resonance standing light wave

The scattering of atoms by a resonance standing light wave is considered under conditions when the lower of two resonance levels is metastable, while the upper level rapidly decays due to mainly spontaneous radiative transitions to the nonresonance levels of an atom. The diffraction scattering regime is studied, when the Rabi frequency is sufficiently high and many diffraction maxima are formed due to scattering. The dynamics of spontaneous radiation of an atom is investigated. It is shown that scattering slows down substantially the radiative decay of the atom. The regions and characteristics of the power and exponential decay are determined. The adiabatic and nonadiabatic scattering regimes are studied. It is shown that the wave packets of atoms in the metastable and resonance excited states narrow down during scattering. A limiting (minimal) size of the wave packets is found, which is achieved upon nonadiabatic scattering in the case of a sufficiently long interaction time.     

Nonlinear voter models: the transition from invasion to coexistence

In nonlinear voter models the transitions between two states depend in a nonlinear manner on the frequencies of these states in the neighborhood. We investigate the role of these nonlinearities on the global outcome of the dynamics for a homogeneous network where each node is connected to m = 4 neighbors. The paper unfolds in two directions. We first develop a general stochastic framework for frequency dependent processes from which we derive the macroscopic dynamics for key variables, such as global frequencies and correlations. Explicit expressions for both the mean-field limit and the pair approximation are obtained. We then apply these equations to determine a phase diagram in the parameter space that distinguishes between different dynamic regimes. The pair approximation allows us to identify three regimes for nonlinear voter models: (i) complete invasion; (ii) random coexistence; and – most interestingly – (iii) correlated coexistence. These findings are contrasted with predictions from the mean-field phase diagram and are confirmed by extensive computer simulations of the microscopic dynamics.     

A critique of Zwaan-Stueckelberg phase integral techniques

The Zwaan-Stueckelberg technique, based on semi-classical J.W.K.B. phase integrals and their analytic continuation in the complex plane, is reviewed. Stueckelberg's derivation of Jeffreys' connection formula is discussed, as are his connection formulae for strongly coupled, non-adiabatic collisions involving adiabatic crossings or diabatic non-crossings. His choice of branch cut is clarified. Avoided adiabatic crossings are described using both physical and non-physical branch cuts. Other limitations and defects of the Stueckelberg treatment are examined in detail and most are eliminated. New formulae for the general non-crossing case are presented. They describe perturbed symmetric resonance, reducing in an exactly correct manner for the Rosen-Zener model and also for exact resonance. Within a dynamical adiabatic treatment they also describe perturbed united-atom degeneracy, giving rise to strong rotational coupling in σ-π transitions. The limitation of the Landau-Zener theory to σ-σ transitions is thus avoided.     

Domain-Wall Dynamics After Photoexcitations Near neutral-Ionic Phase Transitions

Real-time dynamics of domain walls between the neutral and ionic phases just after photoexcitations is studied by fully solving the time-dependent Schrödinger equation for a one-dimensional extended Peierls-Hubbard (PH) model, not by relying on the adiabatic approximation. The unrestricted Hartree-Fock (HF) approximation is used for electrons, and the lattice displacements are treated classically. Three characteristic time scales are observed: rapid oscillation of ionicity owing to the local charge transfer; slow oscillation of lattice displacements; and even slower and collective motion of domain walls. Steady growth of a metastable domain is achieved after complicated competition of micro domains. The relevance to recently measured, time-resolved photoreflectance spectra in TTF-CA is discussed.     

Dynamics of Bec Mixtures Loaded into the Optical Lattice in the Presence of Linear Inter-Component Coupling

We consider dynamics of a two-component Bose–Einstein condensate, where the components correspond to different hyperfine states of the same sort of atoms. External microwave radiation leads to resonant transitions between the states. The condensate is loaded into the optical lattice. We invoke the tight-binding approximation and examine the interplay of spatial and internal dynamics of the mixture. We show that internal dynamics qualitatively depends on the intra-component interaction strength and the phase configuration of the initial state. We focus attention on two intriguing phenomena occurring at certain values of the parameters. The first phenomenon is the spontaneous synchronization of Rabi oscillations running inside neighboring lattice sites. The other one is demixing of the condensate with formation of immiscible solitons at sufficiently strong nonlinearity. Demixing is preceded by the transient regime with highly irregular behavior of the mixture.     

Predissociation resonances in CO and IBr. Smooth exterior scaling combined with the discrete variable representation

Smooth exterior scaling (SES) and the discrete variable representation (DVR) are combined to accurately compute predissociation resonances of a bound state non-adiabatically coupled to a dissociative state. For the CO( predissociation interaction good agreement is found with approaches based on optical potentials and complex scaling. The comparison is done both in the diabatic and the adiabatic representation. The effect of the coupling strength in the IBr predissociation interaction and the transition from the diabatic to the adiabatic picture was studied by computing resonances for coupling strengths from up to . The transition from weak (diabatic) to strong (adiabatic) coupling was clearly seen. The intermediate case leads to a complicated resonance distribution. Comparison was made with recent studies using pump-probe spectroscopy [M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110, 2465 (1999)]. It was found that the overall features of the experiment could be explained from the resonance distribution, but for a detailed comparison more accurate potential energy surfaces and couplings are needed. Received 12 July 1999 and Received in final form 6 December 1999     

Theoretical Investigation of Femtosecond-Resolved Photoelectron Spectrum of NaI Molecules

The time-resolved photoelectron spectra （TRPES） of NaI molecules are calculated by using the time-dependent wave packet method. Two different potential energy curves （adiabatic and diabatic） are adopted in the simulation. The third peak of the photoelectron spectra presented in the adiabatic calculation is induced by the reflection of the wave packet. The oscillating of the wave packet onto the diabatic energy curve is a decreasing process. The comparison of the photoelectron spectra between the two different calculations （adiabatic and diabatic） is presented.     

Phase transitions in two-dimensional uniformly frustratedXY models. II. General scheme

For two-dimensional uniformly frustratedXY models the group of symmetry spontaneously broken in the ground state is a cross product of the group of two-dimensional rotations by some discrete group of finite order. Different possibilities of phase transitions in such systems are investigated. The transition to the Coulomb gas with noninteger charges is widely used when analyzing the properties of relevant topological excitations. The number of these excitations includes not only domain walls and traditional (integer) vortices, but also vortices with a fractional number of circulation quanta which are to be localized at bends and intersections of domain walls. The types of possible phase transitions prove to be dependent on their relative sequence: in the case the vanishing of domain wall free energy occurs earlier (at increasing temperature) than the dissociation of pairs of ordinary vortices, the second phase transition is to be associated with dissociation of pairs of fractional vortices. The general statements are illustrated with a number of examples.