DOI: 10.1016/j.physleta.2022.128548
Abstract:

Among the numerous concepts of time in quantum scattering, Smith’s dwell time [F. T. Smith, Phys. Rev. 118, 349–356 (1960)] and Eisenbud & Wigner’s time delay [E. P. Wigner, Phys. Rev. 98, 145 (1955)] are the most well established. The dwell time represents the amount of time spent by the particle inside a given coordinate range (typically a potential barrier interaction region), while the time delay measures the excess time spent in the interaction region because of the potential. In this paper, we use the exact trajectory-ensemble reformulation of quantum mechanics, recently proposed by one of the authors (Poirier), to study how tunneling and reflection unfold over time, in a one-dimensional rectangular potential barrier. Among other dynamical details, the quantum trajectory approach provides an extremely robust, accurate, and straightforward method for directly computing the dwell time and time delay, from a single quantum trajectory. The resultant numerical method is highly efficient, and in the case of the time delay, completely obviates the traditional need to energy-differentiate the scattering phase shift. In particular, the trajectory variables provide a simple expression for the time delay that disentangles the contribution of the self-interference delay. More generally, quantum trajectories provide interesting physical insight into the tunneling process.

Abstract:

In this work we propose an exact derivation of the Hamilton formulation of quantum mechanical stationary scattering in one-dimensional curved space.

DOI: 10.1016/j.cplett.2021.139241
Abstract:

In this work, we present the efficient combination of Smolyak representations with time indepen- dent quantum mechanical approach using absorbing boundary conditions for the cumulative reac- tion probability calculations of a multidimensional reactive scattering problem. Our approach uses both kinds of Smolyak representations (finite basis and grid) which drastically reduces the size of the basis representation for the cumulative reaction operator. The cumulative reaction probability is thus obtained by solving the eigenvalue problem within the context of reaction path Hamiltonian using the compact Smolyak basis combined with an iterative Lanczos algorithm. Benchmark cal- culations are presented for reactive scattering models with a linear reaction coordinate and applied to a 25D model highlighting the efficiency of the present approach for multidimensional reactive processes.

Abstract:

We present recent progress on quantum trajectories method for one dimensional resonant reactive scattering processes.

Abstract:

Cumulative reaction probability plays a central role in the calculation of reaction rate constant of any bimolecular chemical reaction of interest. In order to give meaningful results, these calculations should be performed for chemical systems with a large number of degrees of freedom leadingto expensive and often infeasible simulations. In this work, a new computational scheme is proposed to allow high dimensional quantum reactive simulations. This scheme is based on the Green’s function operator technics combined to absorbing boundary conditions, a powerful approach introduced by W.H. Miller, T. Seideman and U. Manthe many years ago [1,2]. The new implementation takes benefit that the initial quantum reactive scattering problem can be cast into an eigenvalue problem [2] and uses the high efficiency and accuracy of Smolyak algorithm [3] to build very compact basis for eigenvalue problems [4]. Using this new computational framework, it is now possible to perform quantum dynamics simulations for multidimensional systems pushing away the curse of dimensionality problem. Some preliminary results will be presented [5] using this new powerful scheme

Abstract:

In Bohmian quantum mechanics, both Schrödinger's wavefunction and an ensemble of quantum trajectories are propagated together to describe the evolution of a given system. Said trajectories are driven by anadditional, fully quantum potential deduced from the "pilot" wave function. Displacement of the trajectory ensemble symmetrically dictates the evolution of the wave function. However a recent reformulation allows the exclusive use of the trajectory ensemble to modelize the scattering process. The resulting equations of motion for the trajectories can be put in an Hamiltonian form, with coupled first order ODEs describing exactly the behaviour of a 1D time-independent process. In this case, propagation of a single trajectory is sucient to completely characterize the system. This ecient procedure ( great stability and accuracy ) was applied to scattering processes through simple potential barrier model and more recently in a quantum capture model of ultra-cold chemical reaction. I will highlight the virtues of this approach when applied to scattering through multiple potential barriers. In this more complex situation often encountered in chemistry, coupling with metastable states breaks themonotonicity of the cumulated reaction probability prole through the presence of resonance peaks. Strong interference patterns are observed inbetween the barrier and necessitate the use of an adaptative ODE solving procedure. Numerical simulations will be presented both on system models and on a 1D-reaction path hamiltonian model of ketene izomerisation for which conventional quantum mechanical calculations (using grid methods and absorbing boundary conditions) are available. I will also present how Hamiltonianform allows for a straightforward extension of the one-dimensional quantum formalism to multidimensional processes through the use of hybrid quantum-classical trajectories. The efficiency of this dual-level theorywill be illustrated on the ketene isomerization process.

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