Time-dependent local-to-normal mode transition in triatomic molecules

Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H₂O, CO₂, O₃ and NO₂ molecules in the adiabatic, sudden and linear regime are considered.     

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

Excitation of coherent correlated states in the Jaynes-Cummings model by external deterministic forces: II

In terms of excitation creation and annihilation operators of the Jaynes-Cummings model, acting in the representation of dressed states, the Hamiltonian is written which describes the character of the spectrum of excitations of two modes, representing a quantum analog of the classical behavior of two interacting one-dimensional anharmonic oscillators, namely, the field and atomic oscillators. The anharmonicity is caused by the nonlinearity of the oscillator interaction and manifests itself in the dependence of the frequencies of both modes on the number of excitations, i.e., on the energy. It is shown that an external deterministic force, acting on the system during a certain time t ₀, transfers it from a vacuum state to a coherent state or from one of the coherent states to another coherent state. The probability of the transition from the vacuum state to the coherent state with a given number of excitations represents the Poissonian distribution for the number of excitations formed in the (atom + field) system by the end of action of the external force. It was found to be proportional to the excitation time t ₀.     

Local modes of silane within the framework of stretching vibrational polyads

We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes ν₁ and ν₃ of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C_3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad.     

Theory of substitutional alloys of intermediate valence systems: Concentration and temperature dependence of the static magnetic susceptibility

The effect of alloying in intermediate valence compounds is studied within an extended version of the Anderson model which takes into account substitutional disorder of the rare earth ions. In particular, we concentrate on modifications of the conduction band, describe them by an effective shift in the Fermi energy, and consider its influence on the mixed valence behaviour. By applying the alloy analog approximation to the manyparticle Hamiltonian describing the local magnetic 4f shells, the complete effective Hamiltonian is that of a ternary alloy. This problem is solved within the coherent potential approximation and the static magnetic susceptibility is calculated as a function of temperature and disorder. Depending on the shift of the Fermi energy with respect to the 4f levels, qualitatively different behaviour is obtained which corresponds very well with magnetic measurements on different Yb alloys. The model yields an inverse proportionality between the susceptibility atT=0 and the temperatureT _M of the susceptibility maximum as functions of the disorder.Work performed within the research program of the Sonderfor-schungsbereich 125 Aachen-Jülich-Köln     

非线型三原子分子势能面的Lie代数方法

利用Lie代数方法得到三原子分子的代数Hamiltonian ,通过对光谱数据的拟合确定其展开系数 ,再用相干态得到代数Hamiltonian的经典极限 ,从而得到三原子分子的势能面 .以H2 O分子为例进行了计算 ,其理论值与实验结果一致. The algebraic Hamiltonian for a triatomic molecule can be obtained by using dynamical Lie algebra method (the expansion coefficients are obtained by fitting spectroscopic data). Triatomic molecular potential energy surface (PES) is obtained by using coherent state to take the classical limits of algebraic Hamiltonian. This PES is applied to H 2O molecule, and the deduced force constant is in good agreement with the experimental data.     

Interpretation of the IR spectral intensity anomaly of HCN by potential energy surface bifurcation along a normal mode

Stable normal IR modes vibrate in a convex basin of the potential energy surface (PES). The change to locally concave equipotential lines in a higher energy normal mode direction is interpreted as a possible reason for irreversible and rotation controlled internal vibrational energy redistribution (IVR) during excitation of that normal mode. In hydrogen cyanide (HCN) such an IVR process already occurs in the CN fundamental μ₁. The concept is proven by an explanation of the spectroscopic data: The disturbed IR absorption, the very high intensity in the neighbouring Q-branch of the bending overtone 3v¹₂, the emerging of only higher J lines in the R branch of μ₁, the intensity anomaly in the further state (1, 1¹, 0), and the nearly normal behaviour of the DCN μ₁ band.     

Many fields interaction: Beam splitters and waveguide arrays

We study the interaction of many fields. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. We show that coherent states remain coherent under the action of a quadratic Hamiltonian and by solving the eigenvalue and eigenvector problem for tridiagonal matrices we also show that a system of n interacting harmonic oscillators, initially in coherent states, remain coherent during the interaction.     

Coherent states for Smorodinsky-Winternitz potentials

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.      

利用不变量本征算符求解二维耦合量子谐振子的能级间隔

目前不变量本征算符方法已成功地解决了某些量子系统哈密顿量能级问题.对于二维耦合量子谐振子,利用这一方法可以非常简捷有效地给出其能级信息,而不需要使其哈密顿量对角化.计算结果表明,不同耦合形式的二维耦合量子谐振子的能级间隔是不同的.     

Spin Number Coherent States and the Problem of Two Coupled Oscillators

From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.     

Numerical experiment of anharmonic oscillators by using the symplectic scheme-shooting method

Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx4 and V(x)=(1/2)x2+λx2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x2+λ1x4+λ2x6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.     

Entangled chimeras in nonlocally coupled bicomponent phase oscillators: From synchronous to asynchronous chimeras

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units, have been identified in various systems and generalized to coupled nonidentical oscillators. It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states. In this work, we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring: some oscillators with natural frequency ω₁ and others with ω₂ . In this model, the heterogeneity in frequency is measured by frequency mismatch |ω₁−ω₂| between the oscillators in these two subpopulations. We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is. The bicomponent oscillators are composed of two chimera states, one supported by oscillators with natural frequency ω₁ and the other by oscillators with natural frequency ω₂. The two chimera states in two subpopulations are synchronized at weak frequency mismatch, in which the coherent oscillators in them share similar mean phase velocity, and are desynchronized at large frequency mismatch, in which the coherent oscillators in different subpopulations have distinct mean phase velocities. The synchronization–desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch. The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.     

Correlations between the Interacting Fragments of Decaying Processes

We study the correlations (and alignment as a particular case) existent between the fragments originated in a decaying process when the daughter particles interact. The interaction between the particles is modeled using the potential of coupled oscillators, which can be treated analytically. This approach can be considered as a first step towards the characterization of realistic interacting decaying systems, an archetypal process in physics. The results presented here also suggest the possibility of manipulating correlations using external fields, a technique that could be useful to provide sources of entangled massive particles.