Deviations from Thermal Equilibrium in Shock Waves

Bethe, H. A.; Teller, E.

doi:10.1142/9789812795755_0014

Cited by 10 publications

(12 citation statements)

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“…The VR rates are calculated from relaxation time parameter (pt vib ) using the Bethe-Teller model. 41,43 Here, global PESs have been constructed for the 3 A 0 and 3 A 00 electronic states for the reactive [NNO] system using RKHS interpolation from a large number (410 000) of MRCI+Q/augcc-pVTZ energies for each state. The present RKHS PESs are constructed using B3 times more ab initio energies than the previous PESs 27 and cover a wide range of configurations explored in the QCT simulations.…”

Section: Introductionmentioning

confidence: 99%

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N₂O and dynamics for the N + NO ↔ O + N₂and N₂+ O → 2N + O reactions

Koner

Veliz

Bemish

et al. 2020

Phys. Chem. Chem. Phys.

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Section: Introductionmentioning

confidence: 99%

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N₂O and dynamics for the N + NO ↔ O + N₂and N₂+ O → 2N + O reactions

Koner

Veliz

Bemish

et al. 2020

Phys. Chem. Chem. Phys.

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“…In an important investigation of deviations from thermal equilibrium in shock waves, 46 Bethe and Teller found that the average energy E(t) of a molecule in a reservoir would relax exponentially from its initial value E(0) to the thermal value E th = (Ω/2)coth(θ/2) according to…”

Section: Study Of the Validity Of The Bethe-teller Results In The Cohementioning

confidence: 99%

“…An explicit solution is obtained in the Laplace domain for initial Boltzmann conditions at a temperature different from that of the bath and a query is made into the so-called canonical evolution. 32,33 Moments are calculated and a result obtained previously by Bethe and Teller 46 for long times for the evolution of the average energy of the relaxing molecule is generalized for short times during which decoherence occurs. These should have relevance to time-resolved ultrafast observations made by Zewail and collaborators.…”

Section: Introductionmentioning

confidence: 95%

Approach to equilibrium of a quantum system and generalization of the Montroll–Shuler equation for vibrational relaxation of a molecular oscillator

Kenkre

Chase

2017

Int. J. Mod. Phys. B

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The approach to equilibrium of a quantum mechanical system in interaction with a bath is studied from a practical as well as a conceptual point of view. Explicit memory functions are derived for given models of bath couplings. If the system is a harmonic oscillator representing a molecule in interaction with a reservoir, the generalized master equation derived becomes an extension into the coherent domain of the well-known Montroll–Shuler equation for vibrational relaxation and unimolecular dissociation. A generalization of the Bethe–Teller result regarding energy relaxation is found for short times. The theory has obvious applications to relaxation dynamics at ultra-short times as in observations on the femtosecond time scale and to the investigation of quantum coherence at those short times. While vibrational relaxation in chemical physics is a primary target of the study, another system of interest in condensed matter physics, an electron or hole in a lattice subjected to a strong DC electric field that gives rise to well-known Wannier–Stark ladders, is naturally addressed with the theory. Specific system–bath interactions are explored to obtain explicit details of the dynamics. General phenomenological descriptions of the reservoir are considered rather than specific microscopic realizations.

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“…135 perimental data [136][137][138] are extracted from the vibrational relaxation time parameters (pτ vib ) following the Bethe-Teller model. 139 In a recent study, 134 QCT calculated VR rates are found to significantly underestimate the experimental results. The VR rates calculated from QCT simulations in this work using the HB and GB schemes are shown in Figure 5.…”

Section: Statementioning

confidence: 94%

Dynamics on Multiple Potential Energy Surfaces: Quantitative Studies of Elementary Processes Relevant to Hypersonics

Koner,

Bemish,

Meuwly

2020

Preprint

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The determination of thermal and vibrational relaxation rates of triatomic systems suitable for application in hypersonic model calculations is discussed. For this, potential energy surfaces for ground and electronically excited state species need to be computed and represented with high accuracy and quasiclassical or quantum nuclear dynamics simulations provide the basis for determining the relevant rates. These include thermal reaction rates, state-to-state cross sections, or vibrational relaxation rates. For exemplary systems -[NNO], [NOO], and [CNO] -all individual steps are described and a literature overview for them is provided. Finally, as some of these quantities involve considerable computational expense, for the example of state-to-state cross sections the construction of an efficient model based on neural networks is discussed. All such data is required and being used in more coarse-grained computational fluid dynamics simulations.

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Deviations from Thermal Equilibrium in Shock Waves

Cited by 10 publications

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Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N₂O and dynamics for the N + NO ↔ O + N₂and N₂+ O → 2N + O reactions

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N₂O and dynamics for the N + NO ↔ O + N₂and N₂+ O → 2N + O reactions

Approach to equilibrium of a quantum system and generalization of the Montroll–Shuler equation for vibrational relaxation of a molecular oscillator

Dynamics on Multiple Potential Energy Surfaces: Quantitative Studies of Elementary Processes Relevant to Hypersonics

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Deviations from Thermal Equilibrium in Shock Waves

Cited by 10 publications

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Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2and N2+ O → 2N + O reactions

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2and N2+ O → 2N + O reactions

Approach to equilibrium of a quantum system and generalization of the Montroll–Shuler equation for vibrational relaxation of a molecular oscillator

Dynamics on Multiple Potential Energy Surfaces: Quantitative Studies of Elementary Processes Relevant to Hypersonics

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Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N₂O and dynamics for the N + NO ↔ O + N₂and N₂+ O → 2N + O reactions

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N₂O and dynamics for the N + NO ↔ O + N₂and N₂+ O → 2N + O reactions