Discretization of the electron continuum in the non-local theory of inelastic electron - molecule collisions

Kazansky, A K

doi:10.1088/0953-4075/29/20/023

Cited by 17 publications

(4 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a more recent review, see, e.g., Morrison ͓14͔. From recent works we mention the calculations based on the frame-transformation theory by Robicheaux ͓15͔ and Gao ͓16͔, the nonlocal resonance theory of Bardsley and Wadehra ͓17͔, the ab initio calculation of Rescigno et al ͓12͔, the semiclassical approach of Kazansky and Yelets ͓18,19͔, the nonadiabatic phase matrix method of Mazevet et al ͓20,21͔, the body-frame vibrational close coupling approach of Lee and Mazon ͓22͔, and the Faddeev equation approach by Pozdneev ͓23͔. All calculations presented in this paper are based on the improved nonlocal resonance model developed by Čížek,Horáček,and Domcke ͓24͔. The process of dissociative attachment ͑DA͒ has in detail been studied in the first part of this paper ͓25͔ which we will cite in the following text as paper I.…”

Section: Introductionmentioning

confidence: 99%

Dissociative electron attachment and vibrational excitation ofH2by low-energy electrons: Calculations based on an improved nonlocal resonance model. II. Vibrational excitation

et al. 2006

View full text Add to dashboard Cite

We treat vibrational excitation of hydrogen by low-energy electrons using an improved nonlocal resonance model. The model is based on accurate ab initio data for the 2 ⌺ u + shape resonance and takes full account of the nonlocality of the effective potential for nuclear motion. Integral vibrational excitation cross sections were calculated for numerous initial and final rovibrational states of the hydrogen molecule, and the dependence of the vibrational excitation cross section on the rovibrational initial target state has been investigated. The vibrational excitation cross sections are in very good agreement with measurements for the transitions v =0 → 1 and v =0→ 2, while for higher vibrational channels the agreement is less satisfactory. However, the oscillatory structures in v =0→ 4 vibrational excitation and higher channels predicted by Domcke and collaborators and measured by Allan are described by the present calculation, in very good agreement with the experimental data. A detailed analysis of the origin of the oscillations has been performed. It is shown that the oscillations can be qualitatively understood within the so-called boomerang model of Herzenberg. The resonance contribution to the vibrationally elastic scattering ͑v → v͒ is also discussed. It is found that this cross section is dominated at low energies by the resonance contribution, as predicted by Schulz. The calculated integral vibrational excitation cross sections generally are in good agreement with other theoretical data obtained by different approaches. A comprehensive study of the effect of isotopic substitution has been performed, and an inverse isotope effect in vibrational excitation has been found for certain vibrational levels of the target.

show abstract

Section: Introductionmentioning

confidence: 99%

Dissociative electron attachment and vibrational excitation ofH2by low-energy electrons: Calculations based on an improved nonlocal resonance model. II. Vibrational excitation

et al. 2006

View full text Add to dashboard Cite

show abstract

“…In this figure, n = 0 curve corresponds to the approximation when all the virtual quanta are neglected (discarded all the operators b (t), b † (t)) in Eq. (12). We see that in this case, when there is only the observable quantum field, the system reaches the steady state, and no revivals are present.…”

Section: E Problem Of Memory Tails For the Virtual Quantamentioning

confidence: 70%

“…The continuum acquires a memory about the past subsystem behaviour. In other words, there is non-zero amplitude that the particles (bath excitations) will return back from the contuum to the subsystem: the emitted virtual photons can be reabsorbed by the atom [1]; the reaction fragments can temporarily return to the interacting region during a reative collision [10][11][12][13][14]. Moreover, the memory of the continuum is long-range: no matter how far the particles fly into the continuum, the return amplitude decays only as inverse power law.…”

Section: Introductionmentioning

confidence: 99%

Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System

Polyakov,

Rubtsov

2018

Preprint

View full text Add to dashboard Cite

In the non-Markovian regime, the bath has the memory about the past behaviour of the open quantum system. This memory has slowly-decaying power-law tails. Such a long-range character of the memory complicates the description of the resulting real-time dynamics on large time scales. In a numerical simulation, this problem manifests itself in a "revival", a spurious reflected signal which appears after a finite time thus invalidating the simulation. In the present work, we approach this problem and develop a numerical discretization of the bath without revivals. We find that a crucial role is played by the singularities of the bath spectral density (e.g. edges of bands): the memory about the (spectral) behaviour of the open system in the remote past is completely averaged out (forgotten), except an increasingly small vicinity of these singular frequencies. Therefore, we introduce the concept of memory channel, to denote such an irreversible information loss proccess around a particular singular frequency. On a technical side, we begin the treatment by noting that with respect to the memory loss, the quantum field of the bath should be divided into the following two different parts: the observable and the virtual quanta. Information about the former is never lost: they contribute to the trace over the bath degrees of freedom. The only way to avoid the revival from the observable quanta is to calculate their dynamics exactly. We do this by employing a stochastic sampling of the Husimi function of the bath. The other part, the virtual quanta, are always annihilated after a certain delay time. We construct a dedicated quantum representation for the virtual states by assinging amplitudes to the delay times before annihilation. It is in this representation we rigorously define the concept of memory channels.

show abstract

“…In the numerical calculations reported below, the electronic continuum is represented by a finite number of states, N el . Thereby, a discretization scheme developed by Kazansky 100 is used, which employs an analytic continuation technique to minimize the number of states, N el , required to represent the continuum. It is noted that formally equivalent models have been used recently to describe the similar process of electronic resonance decay in the presence of a vibrational bath in the context of electron scattering from large molecules.…”

Section: Modelmentioning

confidence: 99%

Self‐consistent hybrid approach for simulating electron transfer reactions in condensed phases

Wang¹,

Thoss²

2002

Israel Journal of Chemistry

View full text Add to dashboard Cite

The recently proposed self‐consistent hybrid method is presented as a numerical tool for simulating quantum dynamics in complex systems. This method is based on an iterative convergence procedure for a dynamical hybrid approach. In this approach the overall system is partitioned into a core and a reservoir. The former is treated via a numerically exact quantum mechanical method, and the latter is treated via a more approximate method. Self‐consistent iterations are then carried out, with the number of core degrees of freedom and other variational parameters increased systematically to achieve numerical convergence for the overall quantum dynamics. The details of treating the core and the reservoir, as well as the convergence procedure, are discussed for several examples of electron transfer reactions in condensed phases. It is shown that the self‐consistent hybrid method provides an accurate and practical way of simulating quantum dissipative dynamics in a wide range of physical regimes.

show abstract

Discretization of the electron continuum in the non-local theory of inelastic electron - molecule collisions

Cited by 17 publications

References 42 publications

Dissociative electron attachment and vibrational excitation ofH2by low-energy electrons: Calculations based on an improved nonlocal resonance model. II. Vibrational excitation

Dissociative electron attachment and vibrational excitation ofH2by low-energy electrons: Calculations based on an improved nonlocal resonance model. II. Vibrational excitation

Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System

Self‐consistent hybrid approach for simulating electron transfer reactions in condensed phases

Contact Info

Product

Resources

About