Classical dynamics of polar diatomic molecules in external fields

In this paper, we present the study of the global classical dynamics of a rigid diatomic molecule in the presence of combined electrostatic and nonresonant polarized laser fields. In particular, we focus on the collinear field case, which is an integrable system because the z-component P_φ of the angular momentum is conserved. The study involves the complete analysis of the stability of the equilibrium points, their bifurcations and the evolution of the phase flow as a function of the field strengths and P_φ. Finally, the influence of the bifurcations on the orientation of the quantum states is studied.     

Numerical studies on boundary effects on the FPU paradox

We study numerically the dynamics of a chain of particles subjected to an on site restoring nonlinear force and a first neighbor harmonic coupling. We excite the first linear mode and investigate the distribution of the average harmonic energies at metastable regime, in the spirit of Fermi Pasta Ulam experiment. The limit distribution turns out to strongly depend on the boundary conditions. A theoretical discussion of the phenomenon is also given.     

Diffusion paths in resonantly driven Hamiltonian systems

A diffusive Hamiltonian flow triggered by a resonant drive is confined to a phase subspace determined by the resonance structure. The diffusion path is found for an arbitrary, possibly nonstationary discrete system by applying generalized Manley-Rowe relations to an extended Hamiltonian.     

Manley-Rowe relations for an arbitrary discrete system

Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as , where is an n×n integer matrix of rank r<n, and |ω〉≡T(ω₁,…,ωn) is the frequency vector, the projection of the action vector |J〉 on is an adiabatic invariant. Hence n−r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.     

The width of a chaotic layer

A model of nonlinear resonance as a periodically perturbed pendulum is considered, and a new method of analytical estimating the width of a chaotic layer near the separatrices of the resonance is derived for the case of slow perturbation (the case of adiabatic chaos). The method turns out to be successful not only in the case of adiabatic chaos, but in the case of intermediate perturbation frequencies as well.     

Bifurcations of the normal modes of the Ne?Br2 complex

We study the classical dynamics of the rare gas-dihalogen Ne?Br₂ complex in its ground electronic state. By considering the dihalogen bond frozen at its equilibrium distance, the system has two degrees of freedom and its potential energy surface presents linear and T-shape isomers. We find the nonlinear normal modes of both isomers that determine the phase space structure of the system. By means of surfaces of section and applying the numerical continuation of families of periodic orbits, we detect and identify the different bifurcations suffered by the normal modes as a function of the system energy. Finally, using the Orthogonal Fast Lyapunov Indicator (OFLI), we study the evolution of the fraction of the phase space volume occupied by regular motions.     

Stationary response of multi-degree-of-freedom vibro-impact systems to Poisson white noises

The stationary response of multi-degree-of-freedom (MDOF) vibro-impact (VI) systems to random pulse trains is studied. The system is formulated as a stochastically excited and dissipated Hamiltonian system. The constraints are modeled as non-linear springs according to the Hertz contact law. The random pulse trains are modeled as Poisson white noises. The approximate stationary probability density function (PDF) for the response of MDOF dissipated Hamiltonian systems to Poisson white noises is obtained by solving the fourth-order generalized Fokker-Planck-Kolmogorov (FPK) equation using perturbation approach. As examples, two-degree-of-freedom (2DOF) VI systems under external and parametric Poisson white noise excitations, respectively, are investigated. The validity of the proposed approach is confirmed by using the results obtained from Monte Carlo simulation. It is shown that the non-Gaussian behaviour depends on the product of the mean arrival rate of the impulses and the relaxation time of the oscillator.     

Interaction of polar molecules with a resonant RF electric field: strong deflection of a NO molecular beam

Deflection of a cold supersonic NO beam seeded in He has been observed when these molecules interact with both static and a resonant oscillating electric field. The NO beam splits into two beams each one deflecting about 0.5° towards the positive and negative direction of the Stark field when the employed resonant frequency between the two Stark levels of the NO molecule is 1515 kHz. This deflection angle is about four orders of magnitude higher than the value one would expect from the NO dipole moment and the employed RF field gradient. This phenomenon suggests the possibility of a significant translational motion perpendicular to the beam axis, which is induced by the resonant RF electric field on the cold and high-density supersonic beam.     

Entanglement dynamics in Coriolis coupled rovibrational states of formaldehyde

The entanglement dynamics of two vibrational modes of a polyatomic molecule coupled by Coriolis interaction to overall molecular rotation is studied in terms of two negativities, N(t) and N_s(t), respectively, defined by the minimum of the eigenvalues and by the sum of the negative eigenvalues of the partial transpose of a density matrix. Various initial states are the products of Dicke states and the products of coherent states of vibrations and rotations. Formaldehyde is taken as an example, and the von Neumann entropy s(t) is simulated for the comparison with both negativities. It is shown that negativity N_s(t) is positively correlated with entropy s(t), and the correlated behavior between negativity N(t) and entropy s(t) strongly depends on initial states. However, these three indicators of entanglement display a dominantly positive correlation for the coherent states with small or large parameters. In addition, for the latter state two quantities N(t) and s(t) are nearly unchanged for a long time. This time can be further increased by the increasing of vibrational quantum number so that molecular information processing and quantum computing is allowed. These results are useful in quantum information theory.     

Noether symmetries of discrete nonholonomic dynamical systems

In this letter, we investigate Noether symmetries and conservation laws of discrete dynamical systems on an uniform lattice with the nonholonomic constraints. Based on the quasi-invariance of discrete Hamiltonian action of the systems under the infinitesimal transformation with respect to the time and generalized coordinates, we give the discrete analogue of generalized variational formula of the systems. From this formula we derive the discrete analogue of generalized Noether-type identity, and then we present the generalized quasi-extremal equations of the systems. We also obtain the discrete analogue of Noether theorems and the discrete analogue of Noether conservation laws of the systems. Finally, an example is discussed to illustrate these results.     

Integrable discrete static Hamiltonian with a parametric double-well potential

A one-dimensional discrete conservative Hamiltonian with a generalized form of the Schmidt potential, is constructed with the help of a non-integrable discrete Hamiltonian whose parametrized double-well potential can be reduced to the ?⁴ potential. The new conservative Hamiltonian is completely integrable in the discrete static regime, and the associate exact nonlinear solution is shown to coincide with the continuum nonlinear periodic solution of the non-integrable Hamiltonian. Numerical simulations and nonlinear stability analysis suggest that the discrete mapping derived from the completely integrable Hamiltonian undergoes a bifurcation which does not leads to the chaotic phase with randomly pinned states, but instead to a phase where real solutions become rare forming a cluster of periodic points around an elliptic fixed point.     

Improvement of the Hopfield Neural Network by MC-Adaptation Rule

We show that the performance of the Hopfield neural networks, especially the quality of the recall and the capacity of the effective storing, can be greatly improved by making use of a recently presented neural network designing method without altering the whole structure of the network. In the improved neural network, a memory pattern is recalled exactly from initial states having a given degree of similarity with the memory pattern, and thus one can avoids to apply the overlap criterion as carried out in the Hopfield neural networks.     

Rovibrational dynamics of the RbCs molecule in static electric fields. Classical study

We study the classical dynamics of the RbCs molecule in the presence of a static electric field. Under the Born–Oppenheimer approximation, we perform a rovibrational investigation which includes the interaction of the field with the molecular polarizability. The stability of the equilibrium points and the phase space structure of the system are explored in detail. We find that, for strong electric fields or for energies close to the dissociation threshold, the molecular polarizability causes relevant effects on the system dynamics.     

Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields

The scaling properties of various composite information-theoretic measures (Shannon and Rényi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in position and momentum spaces for the non-relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields. Such measures are found to be invariant at the fixed values of the scaling parameters given by and . Numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity. Physical significance of the resulting scaling behavior is discussed.     

Superradiant transitions between high-lying levels of Sr in an external electric field

Superradiant transitions were observed between high lying levels in Sr. The transitions react very sensitively to an external electric field. Superradiant cascades or one transition in a superradiant branching can be suppressed. The square root of the high of a superradiant pulse decreases with the second power of the electric field strength. This behaviour can be explained by calculations.Dedicated to Prof. Dr. Herbert Welling on the occasion of his 60th birthday     

Photodetachment of H- in a static electric field

We derive a formula using closed-orbit theory for the photodetachment cross-section of H^- in the presence of a static electric field when there is an arbitrary angle θ_L between the laser polarization direction and the static electric field. This formula generalizes the previous result for laser polarization parallel to the static electric field, the effect of laser polarization direction appears as a factor cos²(θ_L) in the amplitude of the oscillation. A photodetachment cross-section formula valid above and below detachment threshold is proposed.     

High-resolution selective reflection spectroscopy in intermediate magnetic fields

We have measured the modifications of frequency-modulated selective reflection spectra of the CsD ₂ line recorded with circularly polarized light by a longitudinal magnetic field in the range 120–280 G. The spectra recorded with ⁺ and ^– polarizations were found to be qualitatively different, but are well described by a theoretical model based on the diagonalization of the hyperfine-Zeeman Hamiltonian. The technique presented here is a simple way for investigating fully resolved complex Zeeman spectra in moderate magnetic fields and may find applications in the investigation of anisotropies in long-range atom-surface interactions.     

Special Lie Symmetry and Hojman Conserved Quantity of Appell Equations for a Holonomic System

Special Lie symmetry and Hojman conserved quantity of Appell equations for a holonomic system are studied. Appell equations and differential equations of motion for holonomic mechanic systems are established. Under special Lie infinitesimal transformations in which the time is invariable, the determining equation of the special Lie symmetry and the expressions of Hojman conserved quantity for Appell equations of holonomic systems are presented. Finally, an example is given to illustrate the application of the results.     

Dynamics of the Langevin model subjected to colored noise: Functional-integral method

We have discussed the dynamics of Langevin model subjected to colored noise, by using the functional-integral method (FIM) combined with equations of motion for mean and variance of the state variable. Two sets of colored noise have been investigated: (a) one additive and one multiplicative colored noise, and (b) one additive and two multiplicative colored noise. The case (b) is examined with relevance to a recent controversy on the stationary subthreshold voltage distribution of an integrate-and-fire model including stochastic excitatory and inhibitory synapses and a noisy input. We have studied the stationary probability distribution and dynamical responses to time-dependent (pulse and sinusoidal) inputs of the linear Langevin model. Model calculations have shown that results of the FIM are in good agreement with those of direct simulations (DSs). A comparison is made among various approximate analytic solutions such as the universal colored noise approximation (UCNA). It has been pointed out that dynamical responses to pulse and sinusoidal inputs calculated by the UCNA are rather different from those of DS and the FIM, although they yield the same stationary distribution.