The correspondence between quantum and classical mechanics: an experimental demonstration of the smooth transition between the two regimes

Wu, Weimin; Noble, David; Horsewill, A.J.

doi:10.1016/j.cplett.2004.12.080

Cited by 16 publications

(34 citation statements)

References 20 publications

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“…The calculated value is C ðcalcÞ CH ¼ 1.36 Â 10 7 s À2 . The value C HH = 6.3 · 10 7 s À2 was obtained from the field-cycling 1 H NMR relaxometry study of BA in natural isotopic abundance [16].…”

Section: Resultsmentioning

confidence: 99%

“…(2) and (4) from the spectral density functions, it is assumed that the proton dynamics are stochastic hops and therefore the correlation functions are exponential decays. That this is so for concerted double proton transfer in carboxylic acids in general, and in BA in particular, has been established experimentally to a high degree of precision in previous field-cycling investigations [10,12,15,16].…”

Section: Theorymentioning

confidence: 87%

“…Expressions for the spin-lattice relaxation arising from both heteronuclear and homonuclear interactions with the protons in the hydrogen bond have been given in earlier papers for single crystal and powder samples [6,8,10,16,18,26,27]. The differential equations governing the longitudinal polarisations AEI z ae and AES z ae are given by [7] …”

Section: Theorymentioning

confidence: 99%

“…They interchange by double proton transfer within the bridging hydrogen bonds of the dimer. The mechanism underlying the motion is dominated by phonon-assisted tunnelling and this is well established as the model system for translational molecular tunnelling [5,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. We have made 99% 13 C substitution of the carboxycarbon which now acts as a Ôspy nucleusÕ monitoring the concerted motion of the two hydrogen atoms in the hydrogen bonds that bridge the BA dimer.…”

Section: Introductionmentioning

confidence: 98%

See 3 more Smart Citations

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: Dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

Noble

Owers‐Bradley

et al. 2005

Journal of Magnetic Resonance

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Section: Resultsmentioning

confidence: 99%

Section: Theorymentioning

confidence: 87%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: Dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

Noble

Owers‐Bradley

et al. 2005

Journal of Magnetic Resonance

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“…However, the two-regime assumption is a simplification and the reality is certainly more like a continuum of regimes. Nevertheless, this assumption is commonly made in order to build tractable models and describe main changes in dynamical systems; see Iglesias and Labarta (2002), van Dijk and Franses (1999), and Wu et al (2005) who discussed the two-regime (or two-state) approximation in physics, economics, and chemistry, respectively.…”

Section: The Two-regimes Assumption and Beyondmentioning

confidence: 99%

Mechanical-Statistical Modeling in Ecology: From Outbreak Detections to Pest Dynamics

2008

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Knowledge about large-scale and long-term dynamics of (natural) populations is required to assess the efficiency of control strategies, the potential for long-term persistence, and the adaptability to global changes such as habitat fragmentation and global warming. For most natural populations, such as pest populations, large-scale and long-term surveys cannot be carried out at a high resolution. For instance, for population dynamics characterized by irregular abundance explosions, i.e., outbreaks, it is common to report detected outbreaks rather than measuring the population density at every location and time event. Here, we propose a mechanical-statistical model for analyzing such outbreak occurrence data and making inference about population dynamics. This spatio-temporal model contains the main mechanisms of the dynamics and describes the observation process. This construction enables us to account for the discrepancy between the phenomenon scale and the sampling scale. We propose the Bayesian method to estimate model parameters, pest densities and hidden factors, i.e., variables involved in the dynamics but not observed. The model was specified and used to learn about the dynamics of the European pine sawfly (Neodiprion sertifer Geoffr., an insect causing major defoliation of pines in northern Europe) based on Finnish sawfly data covering the years 1961-1990. In this application, a dynamical Beverton-Holt model including a hidden regime variable was incorporated into the model to deal with large variations in the population densities. Our results gave support to the idea that pine sawfly dynamics should be studied as metapopulations with alternative equilibria. The results confirmed the importance of extreme minimum winter temperatures for the occurrence of European pine sawfly outbreaks. The strong positive connection between the ratio of lake area over total area and outbreaks was quantified for the first time.

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Concept of correlation time, autocorrelation functions, and spectral densities of the tunneling jumps through the potential barrier

Latanowicz

2012

Concepts Magnetic Resonance

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The concept of the tunneling correlation time according to Schrö dinger is presented. This tunneling jumps and the over the barrier jumps (Arrhenius type) correlation times are applied to calculate the autocorrelation functions and spectral densities of a complex motion. Complex motion means that the relaxation vector performs more than one motion. Two examples of temperature dependencies of a complex motion in a wide temperature regime are given. One example concerns the complex motion consisting of the fast hindered rotation of the methyl group which participates additionally in a slower isotropic motion. The other example concerns the complex motion consisting of the jumps of the proton-proton vector between the two sites in a double hydrogen bond as well as the jumps between other two equilibrium sites (librations of the whole molecule). The latter motion is assumed as slower than the concerted motion of two protons in a double hydrogen bond. In both examples the tunneling jumps are considered as a component of a complex motion. However, only the tunneling jumps of the faster motion are taken into account. Why the tunneling jumps of the slower motion are neglected is explained. The tunneling spectral density dominates only at low temperatures and contributes to the spectral density of the complex motion at intermediate temperatures up to T tun temperature. The sense of T tun temperature is explained. A comparison is made with the other theories of tunneling correlation time. 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40A: 66-79, 2012.

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The correspondence between quantum and classical mechanics: an experimental demonstration of the smooth transition between the two regimes

Cited by 16 publications

References 20 publications

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: Dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

A 13C field-cycling NMR relaxometry investigation of proton tunnelling in the hydrogen bond: Dynamic isotope effects, the influence of heteronuclear interactions and coupled relaxation

Mechanical-Statistical Modeling in Ecology: From Outbreak Detections to Pest Dynamics

Concept of correlation time, autocorrelation functions, and spectral densities of the tunneling jumps through the potential barrier

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