Space-time approach to scattering from many-body systems

Gähler, R.; Felber, J.; Mezei, F.; Golub, R.

doi:10.1103/physreva.58.280

Cited by 44 publications

(29 citation statements)

References 22 publications

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“…[25]) is used to split the two states [40] by a relative time delay τ , the so-called spin-echo time. The spin states scatter at the sample at times t and t + τ , where τ is identical to the van-Hove correlation time [41]. In a second, reversed precession region after the sample the time delay is canceled out and the states interfere at the detector.…”

Section: Experiment: Neutron Spin-echo Spectroscopymentioning

confidence: 99%

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Time-dependent correlations in quantum magnets at finite temperature

et al. 2016

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In this Rapid Communication we investigate the time dependence of the gap mode of copper nitrate at various temperatures. We combine state-of-the-art theoretical calculations with high precision neutron resonance spin-echo measurements to understand the anomalous decoherence effects found previously in this material. It is shown that the time domain offers a complementary view on this phenomenon, which allows us to directly compare experimental data and theoretical predictions without the need of further intensive data analysis, such as (de)convolution.

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Section: Experiment: Neutron Spin-echo Spectroscopymentioning

confidence: 99%

“…For the sake of brevity only a brief introduction will be given to the method itself, and we refer for the detailed description to the literature [25,[38][39][40][41][42][43]. Neutron spin-echo measures the polarization of the neutron beam P = σ x , which is called the echo amplitude.…”

Section: Experiment: Neutron Spin-echo Spectroscopymentioning

confidence: 99%

Time-dependent correlations in quantum magnets at finite temperature

et al. 2016

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“…There is no separation into a sharp line and a broad homogeneous band. (iv) The neutrons act as de Broglie wave packets, shaped by the neutron source (13)(14)(15)(16)(17)(18)(19). Each wave packet contains one neutron.…”

Section: Significancementioning

confidence: 99%

The role of momentum transfer during incoherent neutron scattering is explained by the energy landscape model

Frauenfelder

Young

Fenimore

2017

Proc. Natl. Acad. Sci. U.S.A.

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We recently introduced a model of incoherent quasielastic neutron scattering (QENS) that treats the neutrons as wave packets of finite length and the protein as a random walker in the free energy landscape. We call the model ELM for "energy landscape model." In ELM, the interaction of the wave packet with a proton in a protein provides the dynamic information. During the scattering event, the momentum Q(t) is transferred by the wave packet to the struck proton and its moiety, exerting the force F(t) = dQ(t)/dt. The resultant energy E is stored elastically and returned to the neutron as it exits. The energy is given by E = k B (T 0 + χQ), where T 0 is the ambient temperature and χ (≈ 91 KÅ) is a new elastobaric coefficient. Experiments yield the scattering intensity (dynamic structure factor) S(Q; T) as a function of Q and T. To test our model, we use published data on proteins where only thermal vibrations are active. ELM competes with the currently accepted theory, here called the spatial motion model (SMM), which explains S(Q, T) by motions in real space. ELM is superior to SMM: It can explain the experimental angular and temperature dependence, whereas SMM cannot do so.QENS | de Broglie neutron wave packet | pressure-temperature equivalence | transient energy transfer I ncoherent quasielastic neutron scattering (QENS) is used to study, for instance, the dynamics of complex systems (1, 2). In these experiments, the scattering intensity S (Q, ω, T ) is measured as function of temperature T , momentum transfer Q, and energy transfer ω. "Incoherent" essentially means that the neutron scatters from only one proton, and thus interference from different protons does not contribute. To extract the information from the data, a model is needed. The currently accepted model, used for > 50 y, assumes that the observed effects are due to spatial motions. We call it the spatial motion model (SMM). We recently introduced a model in which S (Q, ω, T ) is based on motions in the conformational free energy landscape (FEL) (3, 4). We call the model ELM, for energy landscape model. ELM assumes that the effects observed in QENS are predominantly due to changes in the population of the FEL. ELM as introduced in ref. 4 explained the neutron scattering from proteins, but left the role of the momentum transfer Q in limbo. The Q dependence is noteworthy because, although the physics of n-p scattering at low energies is s-wave (isotropic), the observed scattering from proteins is Q-dependent (see Fig. 3A), meaning anisotropic. We have now found that Q plays an important role: It creates an inhomogeneity in the target during the passage of the neutron.Consider a neutron with wave vector q that hits a proton in a protein. S (Q, ω, T ) is measured as a function of the temperature T at different scattering angles, characterized by their wave vectors q . The wave vectors q and q determine the transferred wave vector, Q = q − q. Q is related to the momentum by P = Q. E = ω is the energy change of the neutron when it has completed its scatter...

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“…In experiment it is more correct to use the concept of the "correlation volume" of the neutron beam described in detail in Ref. [8]. The correlation volume may be intuitively defined as those regions where coherent properties of the neutrons are significant.…”

Section: Introductionmentioning

confidence: 99%

“…The spin precession, which is equivalent to a splitting of the initial plane wave into two plane waves, accumulates a phase shift until the end of this SE arm. This phase shift corresponds to a distance R 1 between the fronts of the split waves (or time t 1 in inelastic processes) [7,8]. The neutron thus prepared as a probe passes through the sample to test its properties on a length scale R 1 (or time scale t 1 ).…”

Section: Introductionmentioning

confidence: 99%

Four-wave neutron-resonance spin echo

2004

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We develop a technique of scattering from many-body systems. It is based on the principle of the neutron spin echo (SE), where a neutron wave in the magnetic field splits into two waves, which are separated in space or in time after propagation in this field. The neutron thus prepared as a probe passes through the sample to test its properties on a space R or time t scale. This separation in space or in time can be measured using coherence of these two waves as a phase shift between them. These two waves are collected or focused and compensated by the SE technique in order to compare their phases after interaction with the sample. In this way one studies interference between these waves and thus can directly measure the pair-correlation function in space or in time. Instead of two-wave SE we propose to realize the four-wave neutron-resonance spin-echo (NRSE). In our experiments, spin precession produced by a couple of the neutron-resonance coils in one arm is compensated by an identical couple of other NR coils in a second arm of a spin-echo machine. The neutron spin-flip probability in the resonance coils is a key parameter of the NRSE arm. The limiting cases, = 0 and = 1, provide, in quantum terms, a two-level-two-wave k splitting of the neutron and result in the separation of the split waves into two different lengths in space ͑R 1 , R 2 ͒ or in time ͑t 1 , t 2 ͒. These two cases correspond to Larmor precession with phase 1 in the static magnetic fields of the NR flippers or to NRSE precession with 2 , respectively. The intermediate case, 0 Ͻ Ͻ 1, provides a four-level-four-wave k splitting of the neutron with the corresponding separations in space ͑R 1 , R 2 , R 3 ͒ or in time ͑t 1 , t 2 , t 3 ͒. The interference of each pair of waves after compensation results in three different echos with phases 1 , 2 , and 3 = ͑ 1 + 2 ͒ / 2. Focusing or compensating all four waves into a single point of the phase-of-waves diagram produces quantum interference of all newly created waves. This task of focusing is experimentally performed. Different options for the compensation are discussed. The experiment opens the possibility to measure a composite correlation function, combined from several pair-correlation functions.

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Space-time approach to scattering from many-body systems

Cited by 44 publications

References 22 publications

Time-dependent correlations in quantum magnets at finite temperature

Time-dependent correlations in quantum magnets at finite temperature

The role of momentum transfer during incoherent neutron scattering is explained by the energy landscape model

Four-wave neutron-resonance spin echo

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