F. J. Arranz

Avoided crossings, scars, and transition to chaos

The correlation diagram of the LiNC/LiCN isomerizing system as a function of ℏ, taken as a parameter, is considered in conditions of widespread classical chaos. Two series of isolated avoided crossings of very different nature, involving states related by the same 1:8 quantum resonance condition, are characterized and the corresponding interaction matrix elements between adiabatic states analytically calculated and analyzed. One of these series has been found to separate two distinct regions: one for smaller values of ℏ (at any given energy) corresponding to regular states, i.e., with a definite nodal pattern, and the other of much more stochastic behavior. Moreover, the effect of the interaction involved in these avoided crossings is to mix the regular wave functions giving rise to wave functions strongly scarred by the periodic orbits of the associated 1:8 classical resonance. This result constitutes an interpretation of the scarring effect from a new perspective.

TRANSITION FROM ORDER TO CHAOS IN MOLECULAR WAVE FUNCTIONS AND SPECTRA

In this Communication we describe how the transition from regularity to classical chaos in molecular Hamiltonian systems shows up at the quantum level in the structure of the corresponding wave functions and spectra. By changing the value of ℏ we show how the scars result from combinations of regular wave functions.

Topology of the distribution of zeros of the Husimi function in the LiNC/LiCN molecular system

Phase space representations of quantum mechanics constitute useful tools to study vibrations in molecular systems. Among all possibilities, the Husimi function or coherent state representation is very widely used, its maxima indicating which regions of phase space are relevant in the dynamics of the system. The corresponding zeros are also a good indicator to investigate the characteristics of the eigenstates, and it has been shown how the corresponding distributions can discriminate between regular, irregular, and scarred wave functions. In this paper, we discuss how this result can be understood in terms of the overlap between coherent states and system eigenfunctions.

Maximum population transfer in a periodically driven quantum system

We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model

Poincaré-Birkhoff theorem in quantum mechanics

Quantum manifestations of the dynamics around resonant tori in perturbed hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros.

Quantum control of isomerization by robust navigation in the energy spectrum

In this paper, we present a detailed study on the application of the quantum control technique of navigation in the energy spectrum to chemical isomerization processes, namely, CN-Li⇆ Li-CN. This technique is based on the controlled time variation of a Hamiltonian parameter, an external uniform electric field in our case. The main result of our work establishes that the navigation involved in the method is robust, in the sense that quite sizable deviations from a pre-established control parameter time profile can be introduced and still get good final results. This is specially relevant thinking of a experimental implementation of the method.

Ab initio potential energy surface for the highly nonlinear dynamics of the KCN molecule

An accurate ab initio quantum chemistry study at level of quadratic configuration interaction method of the electronic ground state of the KCN molecule is presented. A fitting of the results to an analytical series expansion was performed to obtain a global potential energy surface suitable for the study of the associated vibrational dynamics. Additionally, classical Poincaré surfaces of section for different energies and quantum eigenstates were calculated, showing the highly nonlinear behavior of this system.

Above Saddle-Point Regions of Order in a Sea of Chaos in the Vibrational Dynamics of KCN

The dynamical characteristics of a region of regular vibrational motion in the sea of chaos above the saddle point corresponding to the linear C-N-K configuration is examined in detail. To explain the origin of this regularity, the associated phase space structures were characterized using suitably defined Poincaré surfaces of section, identifying the different resonances between the stretching and bending modes, as a function of excitation energy. The corresponding topology is elucidated by means of periodic orbit analysis.