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Recent experimental and theoretical methods allowed the efficient investigation of highly excited rovibrational states of molecular systems. At these levels of excitation the correspondence principle holds, and then classical mechanics can provide intuitive views of the involved processes. In this respect, we have recently shown that for completely hyperbolic systems, homoclinic motions, which are known to organize the classical chaotic region in Hamiltonian systems, imprint a clear signature in the corresponding highly excited quantum spectra. In this Communication we show that this result also holds in mixed systems, by considering an application to the floppy LiNC/LiCN molecular system. [ABSTRACT FROM AUTHOR]

In this work, a full quantum study of the scattering of He atoms off single CO molecules, adsorbed onto the Pt(111) surface, is presented within the formalism of quantum trajectories provided by Bohmian mechanics. By means of this theory, it is shown that the underlying dynamics is strongly dominated by the existence of a transient vortitial trapping with measurable effects on the whole diffraction pattern. This kind of trapping emphasizes the key role played by quantum vortices in this scattering. Moreover, an analysis of the surface rainbow effect caused by the local corrugation that the CO molecule induces on the surface, and its manifestation in the corresponding intensity pattern, is also presented and discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The dynamics of the isomerization reaction LiNC...LiCN is considered at a quantum level. This study is performed with the aid of dynamically localized wave packets, which provide a wealth of information about the relevant parts of the molecular phase space. Three cases are considered, corresponding to energies close to the threshold for isomerization. The initial position of the packet is always localized in the LiNC well (which is the most stable), and different energies and distributions among the vibrational modes of the molecule are used. The packet will then explore phase space and, as a result of these dynamics, different time scales (including those from intramolecular energy transfer processes) exist, which appear in the low resolution features of the corresponding spectra. The characteristics of these spectra are discussed and analyzed using a variety of techniques, making extensive use of the ideas of nonlinear dynamics, and the conditions for the applicability of statistical theories to evaluate reaction rates in this case are considered. [ABSTRACT FROM AUTHOR]

A classical-quantum correspondence study of a saddle-node bifurcation in a realistic molecular system is presented. The relevant classical structures (periodic orbits and manifolds) and its origin are examined in detail. The most important conclusion of this study is that, below the bifurcation point, there exists an infinite sequence of precursor orbits, which mimic for a significant period of time the (future) saddle-node orbits. These structures have a profound influence in the quantum mechanics of the molecule and several vibrational wave functions of the system present a strong localization along the saddle-node periodic orbits. A striking result is that this scarring effect also takes place well below the bifurcation energy, which constitutes a manifestation of the so-called ‘‘ghost’’ orbits in configuration and phase space. This localization effect has been further investigated using wave packet dynamics. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 h we show how the scars result from combinations of regular wave functions. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present a calculation of the potential energy curves of the 3Σ+u states of the H2 molecule in the region R=1–30 a.u. The features of the correlation diagram are discussed, and a new series of avoided crossings in the region of R<5 a.u. is predicted. We calculate and analyze the radial couplings which are of interest in the study of the excitation process H(1s)+H(1s)→H(2s,2p)+H(1s). Finally, we introduce a simple analytical model which accounts for the 2 3Σ+u-3 3Σ+u interaction. [ABSTRACT FROM AUTHOR]

The behavior of semiclassical wave functions during adiabatic deformations of the Hamiltonian is studied. A practical technique based on Gaussian wave packet dynamics is presented which allows a semiclassical eigenstate for one Hamiltonian to be adiabatically switched into an eigenstate for a different Hamiltonian. The validity of this technique is established by studying the properties of the Hamilton–Jacobi equation during adiabatic processes. The method is shown to yield good results for several one- and two-dimensional model problems. It is shown that converged semiclassical eigenstates can be obtained even if the trajectories have become chaotic by the end of the switching process. [ABSTRACT FROM AUTHOR]

Describes an implementation of the Einstein-Brillouin-Keller (EBK) quantization method for partially destroyed tori. Background on the EBK method; Description of the system model and computational method; Qualitative picture of a destroyed invariant torus; Semiclassical quantization using gap filling orbits.

Reports that the correlation diagram of the LiNC/LiCN isomerizing system as a function of h, taken as a parameter, is considered in conditions of widespread classical chaos. Characterization of series of isolated avoided crossings of different nature; Interaction matrix elements between adiabatic states analytically calculated.

We show that the adiabatic switching method can be used to find periodic orbits in nonseparable multidimensional Hamiltonian systems. It is shown that the stable periodic orbits for the fully coupled system can be found by adiabatically propagating periodic orbits from a soluble zero order reference system. A general validity criterion for the technique is presented. The method is successfully tested on several two-dimensional coupled Morse oscillator problems. The most exciting applications are to chemical reactions. We successfully locate trapped, quantized orbits for collinear and three-dimensional models of the H+MuH and H+FH reactions. [ABSTRACT FROM AUTHOR]

A method for the semiclassical quantization of multidimensional bound systems based on the adiabatic hypothesis is examined. The validity criteria for multidimensional adiabaticity is discussed. It is demonstrated that the quantizing orbits for nonseparable systems can often be obtained by propagating a single trajectory from well defined initial conditions with a time-dependent Hamiltonian for ∼100 periods. Numerical examples using systems with up to five degrees of freedom are presented and show generally excellent results. It is shown that this method can be used to quantize some states using chaotic trajectories. [ABSTRACT FROM AUTHOR]

The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware. [ABSTRACT FROM AUTHOR]

A system is said to be meritocratic if the compensation and power available to individuals is determined by their abilities and merits. A system is topocratic if the compensation and power available to an individual is determined primarily by her position in a network. Here we introduce a model that is perfectly meritocratic for fully connected networks but that becomes topocratic for sparse networks-like the ones in society. In the model, individuals produce and sell content, but also distribute the content produced by others when they belong to the shortest path connecting a buyer and a seller. The production and distribution of content defines two channels of compensation: a meritocratic channel, where individuals are compensated for the content they produce, and a topocratic channel, where individual compensation is based on the number of shortest paths that go through them in the network. We solve the model analytically and show that the distribution of payoffs is meritocratic only if the average degree of the nodes is larger than a root of the total number of nodes. We conclude that, in the light of this model, the sparsity and structure of networks represents a fundamental constraint to the meritocracy of societies. [ABSTRACT FROM AUTHOR]

Newtonian and special-relativistic predictions, based on the same model parameters and initial conditions for the trajectory of a low-speed scattering system are compared. When the scattering is chaotic, the two predictions for the trajectory can rapidly diverge completely, not only quantitatively but also qualitatively, due to an exponentially growing separation taking place in the scattering region. In contrast, when the scattering is nonchaotic, the breakdown of agreement between predictions takes a very long time, since the difference between the predictions grows only linearly. More importantly, in the case of low-speed chaotic scattering, the rapid loss of agreement between the Newtonian and special-relativistic trajectory predictions implies that special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to correctly describe the scattering dynamics. [ABSTRACT FROM AUTHOR]

Abstract: Here we analyze the relationship between quantum contextuality and decoherence in interference experiments with matter particles by means of a simple reduced quantum-trajectory model, which attempts to simulate the behavior of the projections of multi-dimensional, system-plus-environment Bohmian trajectories onto the subspace of the reduced system. This model allows us to understand the crossing of the subsystem trajectories as a combined effect of interference quenching and erasure of ‘which-way’ information, which can be of utility to interpret decoherence effects in many-dimensional systems where full Bohmian treatments become prohibitive computationally. [Copyright &y& Elsevier]

A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of degrees of freedom, this making the problem numerically intractable from a purely quantum-mechanical point of view. To overcome this drawback, a new class of quantum trajectories is proposed. These trajectories, based on the same grounds as Bohmian ones, are solely associated to the system reduced density matrix, since the evolution of the environment degrees of freedom is not considered explicitly. Within this approach, environment effects come into play through a time-dependent damping factor that appears in the system equations of motion. Apart from their evident computational advantage, this type of trajectories also results very insightful to understand the system decoherence. In particular, here we show the usefulness of these trajectories analyzing decoherence effects in interference phenomena, taking as a working model the well-known double-slit experiment. [ABSTRACT FROM AUTHOR]

A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of degrees of freedom, this making the problem numerically intractable from a purely quantum-mechanical point of view. To overcome this drawback, a new class of quantum trajectories is proposed. These trajectories, based on the same grounds as Bohmian ones, are solely associated to the system reduced density matrix, since the evolution of the environment degrees of freedom is not considered explicitly. Within this approach, environment effects come into play through a time-dependent damping factor that appears in the system equations of motion. Apart from their evident computational advantage, this type of trajectories also results very insightful to understand the system decoherence. In particular, here we show the usefulness of these trajectories analyzing decoherence effects in interference phenomena, taking as a working model the well-known double-slit experiment. [ABSTRACT FROM AUTHOR]

Reservoir computing is a machine learning algorithm that excels at predicting the evolution of time series, in particular, dynamical systems. Moreover, it has also shown superb performance at solving partial differential equations. In this work, we adapt this methodology to integrate the time-dependent Schrödinger equation, propagating an initial wavefunction in time. Since such wavefunctions are complex-valued high-dimensional arrays, the reservoir computing formalism needs to be extended to cope with complex-valued data. Furthermore, we propose a multi-step learning strategy that avoids overfitting the training data. We illustrate the performance of our adapted reservoir computing method by application to four standard problems in molecular vibrational dynamics. [ABSTRACT FROM AUTHOR]

The reaction rate rises and falls with increasing density or friction when a molecule is activated by collisions with the solvent particles. This so-called Kramers turnover has recently been observed in the isomerization reaction of LiCN in an argon bath. In this paper, we demonstrate by direct comparison with those results that a reduced-dimensional (generalized) Langevin description gives rise to similar reaction dynamics as the corresponding (computationally expensive) full molecular dynamics calculations. We show that the density distributions within the Langevin description are in direct agreement with the full molecular dynamics results and that the turnover in the reaction rates is reproduced qualitatively and quantitatively at different temperatures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recent advances in vibrational spectroscopy have greatly enhanced the possibilities of research of highly excited states in molecular systems of moderate size. At sufficiently high level of excitation the correspondence principle holds, and classical mechanical arguments constitute a useful interpretative tool. The corresponding dynamics often become very complex specially in systems with floppy degrees of freedom, and periodic motion plays an important role for its understanding. In this paper, we present a computational procedure to systematically calculate periodic orbits of LiNC/LiCN with a given symmetry, that has the additional advantage of providing a useful insight into the onset of chaos in this system. [ABSTRACT FROM AUTHOR]

Modern spectroscopical techniques allow the efficient experimental investigation of highly excited vibrational states in molecular systems. On the theoretical side, powerful computational methods have also been developed for the calculation of the corresponding energy levels and wave functions, and their interpretation. In this paper we use a combination of two such methods, namely, the distribution of zeroes in the Husimi function and energy-level correlation diagrams, to discuss a classification scheme, for the lowest hundred vibrational levels of the LiNC/LiCN floppy molecular system, based on their dynamical characteristics. [ABSTRACT FROM AUTHOR]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Central in drug design is the identification of biomolecules that uniquely and robustly bind to a target protein, while minimizing their interactions with others. Accordingly, precise binding affinity prediction, enabling the accurate selection of suitable candidates from an extensive pool of potential compounds, can greatly reduce the expenses associated to practical experimental protocols. In this respect, recent advances revealed that deep learning methods show superior performance compared to other traditional computational methods, especially with the advent of large datasets. These methods, however, are complex and very time-intensive, thus representing an important clear bottleneck for their development and practical application. In this context, the emerging realm of quantum machine learning holds promise for enhancing numerous classical machine learning algorithms. In this work, we take one step forward and present a hybrid quantum-classical convolutional neural network, which is able to reduce by 20% the complexity of the classical counterpart while still maintaining optimal performance in the predictions. Additionally, this results in a significant cost and time savings of up to 40% in the training stage, which means a substantial speed-up of the drug design process. [ABSTRACT FROM AUTHOR]

Classical transition state theory has been extended to address chemical reactions across barriers that are driven and anharmonic. This resolves a challenge to the naive theory that necessarily leads to recrossings and approximate rates because it relies on a fixed dividing surface. We develop both perturbative and numerical methods for the computation of a time-dependent recrossing-free dividing surface for a model anharmonic system in a solvated environment that interacts strongly with an oscillatory external field. We extend our previous work, which relied either on a harmonic approximation or on periodic force driving. We demonstrate that the reaction rate, expressed as the long-time flux of reactive trajectories, can be extracted directly from the stability exponents, namely, Lyapunov exponents, of the moving dividing surface. Comparison to numerical results demonstrates the accuracy and robustness of this approach for the computation of optimal (recrossing-free) dividing surfaces and reaction rates in systems with Markovian solvation forces. The resulting reaction rates are in strong agreement with those determined from the long-time flux of reactive trajectories. [ABSTRACT FROM AUTHOR]

We present a method to efficiently compute the eigenfunctions of classically chaotic systems. The key point is the definition of a modified Gram-Schmidt procedure which selects the most suitable elements from a basis set of scar functions localized along the shortest periodic orbits of the system. In this way, one benefits from the semiclassical dynamical properties of such functions. The performance of the method is assessed by presenting an application to a quartic two-dimensional oscillator whose classical dynamics are highly chaotic. We have been able to compute the eigenfunctions of the system using a small basis set. An estimate of the basis size is obtained from the mean participation ratio. A thorough analysis of the results using different indicators, such as eigenstate reconstruction in the local representation, scar intensities, participation ratios, and error bounds, is also presented. [ABSTRACT FROM AUTHOR]

The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite ħ, we identify a strong dependence of the current on the structure of the chaotic region. Moreover, we have determined the robustness of the current against thermal fluctuations in the very weak coupling regime. In the case of strong forcing, the current is determined by the shape of a chaotic attractor. In both cases the temperature quickly stabilizes the ratchet, but in the latter. it also destroys the asymmetry responsible for the current generation. Finally, applications to isomerization reactions are discussed. [ABSTRACT FROM AUTHOR]

Demonstrated that deterministic diffusion processes can also occurs in systems with zero entropy that mimic chaos with any precision without being mathematically chaotic. Link of diffusion processes with randomness in system; Using random walk model to predict the behavior of the diffusion coefficient.

The isomerization between CN-Li and Li-CN in an argon bath provides a paradigmatic example of a reaction in a solvent with tunable coupling. In previous work, we found that the rates exhibited a turnover with the density of the argon bath in the limit that the CN bond was held fixed [P. L. Garcia- Muller, R. Hernandez, R. M. Benito, and F. Borondo, J. Chem. Phys. 137, 204301 (2012)]. Here, we report the effect of the CN bond vibration on the dynamics and the persistence of the turnover. As hypothesized earlier, the CN bond is indeed weakly coupled with the reaction path despite the presence of the argon cage. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

According to Kramers, rates of molecular process are expected to follow a rise and fall from low friction (at little to no interaction with the environment) to high friction (at typical liquid densities and above). This so-called Kramers turnover was recently observed and delineated in the case of the LiNC<=>LiCN isomerization reaction in the presence of an argon bath [P. García-Müller, R. Hernandez, R. M. Benito, and F. Borondo, Phys. Rev. Lett. 101, 178302 (2008)]. The rates were obtained using direct molecular dynamics of an all-atom representation and the Langevin dynamics of a projected representation. We now provide further evidence that the forward and backward rates are indeed exhibiting the turnover. The rates are also seen to agree remarkably well with the Pollak-Grabert-Hänggi rate formulas in regimes satisfying the theory underlying assumptions. At higher temperatures, when the theory is expected to fail, the solvated LiCN isomerization continues to exhibit activated dynamics following the turnover. [ABSTRACT FROM AUTHOR]

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories. The location of these invariant manifolds depends both on time and on the realization of the driving force exerted by the bath. These manifolds allow the identification of reactive trajectories simply from their initial conditions, without the need of any further simulation. In this paper, we show how these invariant manifolds can be calculated, and used in a formally exact reaction rate calculation based on perturbation theory for any multidimensional potential coupled to a noisy environment. [ABSTRACT FROM AUTHOR]

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact. [ABSTRACT FROM AUTHOR]

The effect of geometrical irregularities in the work function and emitting properties of metallic surfaces at low potentials is studied. For this purpose, we propose a simplified model consisting of rectangular fractures and a classical formalism for the work function determination. The dependence of the work function with the fractures size is determined by using the electrostatic image potential method. The emission current density properties when an external electric field is applied are also analyzed. [ABSTRACT FROM AUTHOR]

Relevant aspects of the phase space structure corresponding to the vibrational dynamics of a two-dimensional model of the HCP molecule are studied in detail using a frequency analysis method. By performing this analysis locally for reduced periods of time, the underlying chaotic structure and the main resonances have been determined. [ABSTRACT FROM AUTHOR]

Shannon entropy is studied for the series of avoided crossings that characterize the transition from order to chaos in quantum mechanics. In order to be able to study jointly this entropy for discrete and continuous probability, calculations have been performed on a quantized map, the kicked Harper map, resulting in a different behavior, as order-chaos transition takes place, for the discrete (position representation) and continuous (coherent state representation) cases. This different behavior is analyzed in terms of the distribution of zeros of the Husimi function. [ABSTRACT FROM AUTHOR]

We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Mancho et al., Commun. Nonlinear Sci. Numer. Simul. 18, 3530 (2013)] to unveil the usually rich dynamics taking place in the vibrations of molecular systems, especially if they are floppy. The principal novelty of our work is the inclusion of p norms in the definition of the descriptors in this kind of system, which greatly enhances their power to discern among the different structures existing in the phase space. As an illustration we use the LiCN molecule described by realistic potentials in two and three dimensions, which exhibits chaotic motion within a mixed phase space in the isomerization between the two wells corresponding to the linear isomer stable configurations, LiNC and LiCN. In particular, we pay special attention to the manifolds emerging from the unstable fixed point between the corresponding isomer wells, and also to the marginally stable structures around a parabolic point existing near the LiNC well. [ABSTRACT FROM AUTHOR]

By constructing continuation/bifurcation diagrams of families of periodic orbits of LiNC/LiCN system the spectroscopy and dynamics for this species are deduced and compared with accurate quantum mechanical calculations up to 13 000 cm-1. The interesting phenomenon of the appearance of gaps in the continuation diagram of the principal family that corresponds to the bend motion is shown to occur in both isomers, LiNC and LiCN. Through semiclassical quantization a one to one correspondence of specific periodic orbits to certain eigenstates is demonstrated. One interesting example is the case of periodic orbits that are generated from a saddle-node bifurcation and describe rotations of the Li+ ion around the CN- fragment. The correspondence of these periodic orbits to regular rotating type eigenfunctions is shown, thus, demonstrating in a clear way the importance of the saddle-node bifurcations in locating localized wavefunctions in highly energized molecules. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]