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Günther, Gitta; Huschke, Wolfram; Steiner, Walter

doi:10.1007/978-3-476-02958-4_21

Cited by 5 publications

(9 citation statements)

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“…in analogy to (8). The value ρ corresponds to a rotation ofΨ E by θ corresponding to the ratio between its real and imaginary parts.…”

Section: Phase Rigidity Of the Scattering Wave Function ψ E Cmentioning

confidence: 99%

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The brachistochrone problem in open quantum systems

Rotter¹

2007

J. Phys. A: Math. Theor.

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Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al. for the transmission through microwave cavities of different shape are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can not be described in the framework of standard quantum mechanics with Hermitian Hamilton operator and consideration of S matrix poles.

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“…in analogy to (8). The value ρ corresponds to a rotation ofΨ E by θ corresponding to the ratio between its real and imaginary parts.…”

Section: Phase Rigidity Of the Scattering Wave Function ψ E Cmentioning

confidence: 99%

“…Günther et al [4] found that the passage time is reduced under the influence of exceptional points being branch points in the complex energy plane. The quantum brachistochrone problem is considered recently also by other authors [5,6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

The brachistochrone problem in open quantum systems

Rotter¹

2007

J. Phys. A: Math. Theor.

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“…The relationship between the fundamental Newton constant G N (D) ≡ κ 2 D /(2S D−1 ) in D dimensions and the effective Newton constant G N (D0) ≡ κ 2 D0 /(2S D0−1 ) in the lower dimensional subspace M D0 can be obtained from Gauss' law in D dimensions [1,2] and reads…”

Section: Introductionmentioning

confidence: 99%

“…1 In brane-world models with non-factorizable geometry, the relation between κ 0 and κ D differs from (4) [4,5]. 2 A dynamical behavior of the extra dimensions results via dimensional reduction in a variation of the effective physical constants of the resulting four-dimensional theory (see e.g. section 4 below and relation (4), where an uncompensated changing in time of V D ′ would lead to the variation of κ 0 ).…”

Section: Introductionmentioning

confidence: 99%

Remarks on Dimensional Reduction of Multidimensional Cosmological Models

Guenther

Zhuk

2006

The Tenth Marcel Grossmann Meeting

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Multidimensional cosmological models with factorizable geometry and their dimensional reduction to effective four-dimensional theories are analyzed on sensitivity to different scalings. It is shown that a noncorrect gauging of the effective four-dimensional gravitational constant within the dimensional reduction results in a non-correct rescaling of the cosmological constant and the gravexciton/radion masses. The relationship between the effective gravitational constants of theories with different dimensions is discussed for setups where the lower dimensional theory results via dimensional reduction from the higher dimensional one and where the compactified space components vary dynamically.

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“…[12] Overall, to date, there are only a handful of MRI studies of the gas phase reactions with regular non-hyperpolarized gases. [13,14] The limitation of low NMR sensitivity spurs the implementation of hyperpolarization techniques, which can potentially increase the intensity of NMR signals by up to several orders of magnitude, including spin-exchange optical pumping [15][16][17] (SEOP), dynamic nuclear polarization [18][19][20] (DNP) and parahydrogen-induced polarization [20][21][22][23][24] (PHIP) methods. SEOP relies on the polarization of noble gases, e. g., 129 Xe, [25] 3 He, [26] 83 Kr, [27] which are unreactive and very expensive.…”

mentioning

confidence: 99%

Robust In Situ Magnetic Resonance Imaging of Heterogeneous Catalytic Hydrogenation with and without Hyperpolarization

Kovtunov

Lebedev²,

Svyatova

et al. 2019

ChemCatChem

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Magnetic resonance imaging (MRI) is a powerful technique to characterize reactors during operating catalytic processes. However, MRI studies of heterogeneous catalytic reactions are particularly challenging because the low spin density of reacting and product fluids (for gas phase reactions) as well as magnetic field inhomogeneity, caused by the presence of a solid catalyst inside a reactor, exacerbate already low intrinsic sensitivity of this method. While hyperpolarization techniques such as parahydrogen induced polarization (PHIP) can substantially increase the NMR signal intensity, this general strategy to enable MR imaging of working heterogeneous catalysts to date remains underexplored. Here, we present a new type of model catalytic reactors for MRI that allow the characterization of a heterogeneous hydrogenation reaction aided by the PHIP signal enhancement, but also suitable for the imaging of regular nonpolarized gases. These catalytic systems permit exploring the complex interplay between chemistry and fluid-dynamics that are typically encountered in practical systems, but mostly absent in simple batch reactors. High stability of the model reactors at catalytic conditions and their fabrication simplicity make this approach compelling for in situ studies of heterogeneous catalytic processes by MRI.Catalytic processes (e. g., hydrogenation, reforming, oxidation, etc.) are at the cornerstone of chemical and petrochemical industry [1] and, to make these processes more sustainable, control over reaction selectivity, conversion rates, mass and heat transport inside the working reactor (that is under operando conditions) is required. Magnetic resonance imaging (MRI) is a tool applicable to operando studies that provide information for example about the distribution of liquids in the catalyst pellet during hydrogenation of α-methylstyrene [2] or heptene, [3] the coke profiles within a catalyst pellet, [4] the flow of water [5] or propane [6] through a packed bed, the structure of a porous medium and the water flow during the deposition of fines, [7] or the velocities of particles in a fluidized bed. [8][9][10] MRI of reactors utilizing gases are not as developed as studies of liquids because the spin density in the gas phase is ca. 3 orders of magnitude lower relative to the condensed phase, which significantly limits the deployment of MRI for studying gases. [11] Nevertheless, a recent report showed that the distribution of the reactants and products inside a monolith type reactor can be measured even in the gas phase during ethylene hydrogenation reaction using two different catalyst supports, thereby revealing an effect of the support on the mass and heat transport. [12] Overall, to date, there are only a handful of MRI studies of the gas phase reactions with regular non-hyperpolarized gases. [13,14] The limitation of low NMR sensitivity spurs the implementation of hyperpolarization techniques, which can potentially increase the intensity of NMR signals by up to several orders of magnitude, including spin-ex...

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U

Cited by 5 publications

References 0 publications

The brachistochrone problem in open quantum systems

The brachistochrone problem in open quantum systems

Remarks on Dimensional Reduction of Multidimensional Cosmological Models

Robust In Situ Magnetic Resonance Imaging of Heterogeneous Catalytic Hydrogenation with and without Hyperpolarization

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