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Institute
Die Arbeit behandelt die Messung von Photonen mit Teilchendetektoren, die auf digitalen Silizium-Pixelsensoren basieren. Diskutiert werden zwei wesentliche Schritte in den Upgrade-Programmen des ALICE-Experiments am CERN-LHC:
1. FOCAL-Detektor-Upgrade (2027): Untersuchung der Detektorantwort des elektromagnetischen Pixel-Kalorimeters EPICAL-2 und der Form elektromagnetischer Schauer durch Teststrahl-Messungen und Monte Carlo Simulationen.
2. ALICE 3-Upgrade (2035): Simulationsstudien zum Untergrund in der Messung von Photonen mit sehr kleinem Transversalimpuls.
Teil 1: Performance des elektromagnetischen Pixel-Kalorimeters EPICAL-2
Detektordesign und Testmessungen: EPICAL-2, ein SiW-Sandwich-Design-Kalorimeter mit ALPIDE Sensoren, besitzt eine Tiefe von ca. 20 Strahlungslängen und etwa 25 Millionen Pixel. Testmessungen wurden an der Universität Utrecht (kosmische Myonen) sowie am DESY und CERN-SPS (Elektronen) durchgeführt.
Simulation und Validierung: Das EPICAL-2 wird im Simulationspaket Allpix2 implementiert, um die Testmessungen zu validieren und das Detektorverhalten zu untersuchen. Systematische Variationen bestätigen die Stabilität und Reproduzierbarkeit der Simulation.
Datenaufbereitung und Schauerprofile: Im Rahmen der Datenanalyse werden fehlerhafte Pixel ausgeschlossen, Pixel-Treffer zu Clustern gruppiert, Chips kalibriert und der Strahlwinkel korrigiert. Das longitudinale Profil elektromagnetischer Schauer zeigt, dass das Schauermaximum in der Simulation etwas tiefer liegt als in den Testdaten, was auf zusätzliches Material oder eine unvollständige Beschreibung der Schauerentwicklung in der Simulation zurückzuführen sein könnte. Das laterale Profil zeigt, dass eine Schauertrennung im Millimeter-Bereich möglich ist.
Energieantwort und -auflösung: Die nicht-lineare Energieantwort wird sowohl in Testdaten als auch in Simulationen beobachtet. Die Energieauflösung des EPICAL-2 für Cluster ist besser als für Pixeltreffer und vergleichbar mit dem analogen CALICE-Prototypen. Simulationen ohne Strahlenergie-Fluktuationen zeigen eine bessere Energieauflösung als in den Testdaten.
Teil 2: Untergrund in der Messung von Photonen in ALICE 3
Simulationssetup: Die ALICE 3-Detektorgeometrie wird in GEANT4 implementiert, um den Untergrund in der Messung weicher Photonen zu untersuchen. Simulationen mit PYTHIA und GEANT4 zeigen, dass der Untergrund hauptsächlich aus Zerfallsphotonen und Photonen aus externer Bremsstrahlung besteht.
Ergebnisse der Untergrundstudien: Der Untergrund durch Photonen aus externer Bremsstrahlung dominiert und liegt im Akzeptanzbereich des FCT um einen Faktor von 5 bis 10 über dem theoretischen Signal weicher Photonen. In der Simulation wird das Material zu 8%—14% X0 in ALICE 3 bestimmt, wobei bereits bei 5% X0 der Untergrund genauso stark ist wie das erwartete Signal.
Möglichkeiten zur Untergrundreduzierung: Untersuchungen zeigen, dass ein Elektron-Veto das Signal-zu-Untergrund-Verhältnis um den Faktor 30 verbessern und eine Materialreduktion durch ein optimiertes Strahlrohr um den Faktor 7.
Die Ergebnisse des ersten Teils dieser Arbeit demonstrieren insgesamt die gute Performance des EPICAL-2 in Bezug auf die Energiemessung und die Bestimmung der Schauerform. Darüber hinaus unterstützen sie den Einsatz digitaler Kalorimeter im FOCAL-Upgrade des ALICE-Experiments und zeigen das Potenzial der digitalen Kalorimetertechnologie für zukünftige Hochenergiephysik-Experimente.
Die Ergebnisse des zweiten Teils dieser Arbeit liefern einen wesentliche Beitrag zum geplanten ALICE 3-Upgrade. Weiterhin veranschaulichen sie, wie ein Elektron-Veto und die Reduzierung des Materials zusammen eine vielversprechende Messstrategie bilden können.
The thermodynamic properties of the interacting particle–antiparticle boson system at high temperatures and densities were investigated within the framework of scalar and thermodynamic mean-field models. We assume isospin (charge) density conservation in the system. The equations of state and thermodynamic functions are determined after solving the self-consistent equations. We study the relationship between attractive and repulsive forces in the system and the influence of these interactions on the thermodynamic properties of the bosonic system, especially on the development of the Bose–Einstein condensate. It is shown that under “weak” attraction, the boson system has a phase transition of the second order, which occurs every time the dependence of the particle density crosses the critical curve or even touches it. It was found that with a “strong” attractive interaction, the system forms a Bose condensate during a phase transition of the first order, and, despite the finite value of the isospin density, these condensate states are characterized by a zero chemical potential. That is, such condensate states cannot be described by the grand canonical ensemble since the chemical potential is involved in the conditions of condensate formation, so it cannot be a free variable when the system is in the condensate phase.
The main focus of this thesis is the application of the nonperturbative Functional Renormalization Group (FRG) to the study of low-energies effective models for Quantum Chromodynamics (QCD). The study of effective field theories and models is crucial for our understanding of physics, especially when we deal with fundamental interaction theories like QCD. In particular, the ultimate goal is the understanding of the critical properties of these models in such a way that we can have an insight on the actual critical phenomena of QCD, with a special focus on its chiral phase transition. The choice of the FRG method derives from the fact that it belongs to the class of functional non-perturbative methods and has also the advantage of linking physics at different energy scales. These features make FRG perfectly compatible with the task of studying non-perturbative phenomena and in particular phase transitions, like the ones expected for strongly interacting matter. However, the functional nature of the FRG approach and of the Wetterich equation has a consequence that its exact resolution is hardly possible, and an ansatz for the effective action is generally needed. In this work we choose to adopt the local-potential approximation (LPA), which prescribes to stop at zeroth order in the expansion in derivative operators of the quantum effective action, including only the quantum effective potential. In this work we exploited the key observation that the FRG flow equation can be cast, for specific models and truncation schemes, in the form of an advection-diffusion, possibly with a source term. This type of equation belongs to the class of problems faced in the context of viscous hydrodynamics. Therefore, an innovative approach to the solution of the FRG flow equation consists in the choice of a method developed specifically for the resolution of this class of hydrodynamic equations. In particular, the Kurganov-Tadmor finite-volume scheme is adopted. Throughout this work we apply this scheme to the study of different physical systems, showing the reliability and the flexibility of this approach.
In the first part of the thesis, we discuss the well-known O(N) model, using the hydrodynamic formulation to solve the FRG flow equation in the LPA truncation. We focus on the study of the critical behaviour of the system and calculate the corresponding critical exponents. Particular attention is given to the error estimation in the extraction of critical exponents, which is a needed and not widely explored aspect. The results are well compatible with others in the literature, obtained with different perturbative and nonperturbative methods, which validates the procedure. In the second part of the thesis, we introduce the quark-meson model as a low-energy effective model for QCD, with a specific focus on its chiral symmetry-breaking pattern and the subsequent dynamical quark-mass generation. The LPA flow equation is of the advection-diffusion type, with an extra source contribution which is due to the inclusion of fermionic degrees of freedom. We thus adopt the developed numerical techniques to derive the phase diagram of the model, which is in agreement with the one obtained with other techniques in the literature.
We also follow another possible way for the study of the critical properties of the quark-meson model: the so-called thermodynamic geometry. This approach is based on the interpretation of the parameter space of the system as a differential manifold. One can then obtain relevant information about the phase transitions from the Ricci scalar. We studied the chiral crossover investigating the behavior of the Ricci scalar up to the critical point, featuring a peaking behavior in the presence of the crossover. We then repeated this analysis in the chiral limit, where the phase transition is expected to be of second order. Via this geometric technique it is possible to have a different view on the chiral phase transition of QCD. This is the case since this approach is based on the calculation of quantities which are influenced by higher-order momenta of the thermodynamic potential, thus allowing for a more comprehensive analysis of the phase transition.
Finally, we exploit the numerical advancement to face the issue of the regulator choice in the FRG calculations. This is one of the most delicate issues which arise when using approximations to solve the FRG flow equation and deserves extensive investigation. In particular, we performed a vacuum parameter study and used the RG consistency requirement to determine the impact of the choice of the regulator on the physical observables and on the phase diagram of the model. Via this study we develop a systematic method to comparison the results obtained via different regulators. We show the importance of the choice of an appropriate UV cutoff in the determination of UV-independent IR observables and, consequently, the impact on the latter that the truncation of the effective average action and the choice of the regulator have.
Alternating acquisition of background and sample spectra is often employed in conventional Fourier-transform infrared spectroscopy or ultraviolet–visible spectroscopy for accurate background subtraction. For example, for solvent background correction, typically a spectrum of a cuvette with solvent is measured and subtracted from a spectrum of a cuvette with solvent and solute. Ultrafast spectroscopies, though, come with many peculiarities that make the collection of well-matched, subtractable background and sample spectra challenging. Here, we present a demountable split-sample cell in combination with a modified Lissajous scanner to overcome these challenges. It allows for quasi-simultaneous measurements of background and sample spectra, mitigating the effects of drifts of the setup and maintaining the beam and sample geometry when swapping between background and sample measurements. The cell is moving between subsequent laser shots to refresh the excited sample volume. With less than 45 μl of solution for 150 μm optical thickness, sample usage is economical. Cell assembly is a key step and covered in an illustrated protocol.
This thesis is concerned with the investigation of static and dynamic properties of quantum Heisenberg paramagnets in the absence of a magnetic field and therefore for vanishing magnetization. For this purpose a new formulation of the spin functional renormalization group (SFRG) is employed. The first manifestations of the SFRG were developed by Krieg and Kopietz, motivated by the FRG approach to ordinary field theories and the older works of Vaks, Larkin and Pikin on diagrammatic methods for spin operators.
The main idea is to study quantum spin systems by considering the evolution of correlation functions under a continuous deformation of the interaction between magnetic moments, starting from a solvable limit. This leads to nonperturbative results for quantities like the spin-spin correlation function. After a basic introduction to the phenomena and concomitant problems discussed in this thesis, a detailed description of the SFRG method in its initial formulation is given in the second chapter. We start with the generating functional of connected imaginary-time spin-correlation functions GΛ [h], for which an exact flow equation is derived. A particular issue, already pointed out by Krieg and Kopietz, arises here, namely the singular non-interacting limit of its subtracted Legendre transform ΓΛ [m]. As a consequence the initial condition of that functional does not have a proper series expansion in powers of m. This prevents us from working directly within a pure one-particle irreducible (1-PI) parametrization of the correlation functions, as is often done in the context of field theories. Thus motivated, we develop a workaround explicitly tailored to paramagnets, which provides us with a functional that has a well-behaved Legendre transform. The new approach is based on a different treatment of fluctuations at zero and finite frequencies, analogous to a previous hybrid formulation for the symmetry-broken phase. Certain properties, considered to be highly relevant for isotropic paramagnets, as well as previous observations, already made in the study of simpler spin systems like the Ising model, serve as additional justifications for choosing this construction.
In the third chapter our new method is assessed by calculating the dynamic susceptibility G(k, iω) and thus the dynamic structure factor S(k, ω) in the symmetric phase. For this purpose an approximate integral equation for the dynamic polarization function Π̃(k, iω) was derived. This equation results from a truncation of the hierarchy of flow equations and contains static quantities, that are assumed to be known from another source. Our first application is the high-temperature limit T → ∞ in d ≤ 3 dimensions. Salient features, believed to be part of the spin dynamics in isotropic Heisenberg magnets are also exhibited by our solution, like (anomalous) diffusion in a suitable hydrodynamic limit. Moreover we obtain the same order of magnitude for the diffusion coefficient D as in experiments and other theoretical calculations. Other aspects do not entirely agree with previous approaches.
Afterwards we continue by investigating systems close to the critical point Tc. Dynamic scaling forms for Π̃(k, iω) and S(k, ω), which, like spin diffusion, are postulated on the basis of quite general physical arguments, are reproduced. Agreement of the line-shapes 2with neutron scattering experiments at T = Tc is found to be satisfying, with deviations for ω → 0, that may be attributed to the simplicity of the approximation, like at infinite temperature.
Finally, we focus our attention on the thermodynamic properties of isotropic Heisenberg paramagnets by calculating the static susceptibility G(k). For this purpose we employ simple truncation schemes of the flow equations for the static self-energy ΣΛ (k) and four-spin vertex ΓΛ , together with a basic ansatz for the dynamic polarization Π̃(k, iω) in quantum systems. As a result we obtain transition temperatures Tc of three-dimensional nonfrustrated magnets within an accuracy of 5 percent compared to established benchmark values from Quantum Monte Carlo and high temperature expansion series. We conclude this chapter by giving an outlook on the application of our method to frustrated systems, which may require a combined non-trivial calculation of static and dynamic properties.
Efficient modeling and mitigation of quadrupole errors in synchrotrons and their beam transfer lines
(2023)
This thesis investigates the problem of estimating quadrupole errors on synchrotrons as well as how to minimize the influence of quadrupole errors for beam transfer lines (beamlines). It emphasizes the importance to treat possible error sources in all parts of an accelerator in order to provide constantly high beam quality to the experimental stations. While the presented methods have been investigated by using the example of the SIS18 synchrotron and the HEST beamlines at GSI Helmholtz Centre for Heavy Ion Research, they are equally relevant for the future synchrotrons and beamlines of the Facility for Antiproton and Ion Research in Europe (FAIR).
Part 1 discusses the problem of estimating quadrupole errors via orbit response measurements at synchrotrons. An emphasis is put on investigating the influence of the availability of steerer magnets and beam position monitors (BPMs) on the solvability of the inverse problem as well as on the propagation of measurement uncertainty for the estimation of quadrupole errors. The problem is approached via analytical considerations as well as via dedicated simulation studies. By developing an analytical expression for the Jacobian matrix, the theoretical boundaries for the solvability of the inverse problem are derived. Moreover, it is shown that the analytical expressions for the Jacobian matrix can be used during the fitting procedure to achieve a significant improvement in the computational efficiency by a factor $N_{steerers} \times N_{quadrupoles}$, where $N$ denotes the number of lattice elements of the respective type. The presented results are tested via dedicated measurements at the SIS18 synchrotron.
Part 2 discusses – complementary to part 1 – the influence of quadrupole errors in beam transfer lines with respect to the beam quality requirements given by the experimental stations. A preventive approach is presented which allows to minimize the influence of possible quadrupole errors on the degradation of beam quality. By identifying and selecting robust quadrupole configurations, a stable operation of the beamline can be enabled and the time needed by operators to readjust the beamline parameters can be reduced. The concept of beamline robustness is developed and is studied with the help of dedicated simulations. The simulation results are used to identify certain properties that distinguish robust from nonrobust quadrupole configurations. Also, various methods for improving the computational process of identifying robust quadrupole configurations are presented. The methods and results are tested via dedicated measurements at two different beamlines at GSI Helmholtz Centre for Heavy Ion Research and at Forschungszentrum Jülich.
The gas-phase reaction of O + H₃⁺ has two exothermic product channels: OH+ + H2 and H2O+ + H. In the present study, we analyze experimental data from a merged-beams measurement to derive thermal rate coefficients resolved by product channel for the temperature range from 10 to 1000 K. Published astrochemical models either ignore the second product channel or apply a temperature-independent branching ratio of 70% versus 30% for the formation of OH+ + H2 versus H2O+ + H, respectively, which originates from a single experimental data point measured at 295 K. Our results are consistent with this data point, but show a branching ratio that varies with temperature reaching 58% versus 42% at 10 K. We provide recommended rate coefficients for the two product channels for two cases, one where the initial fine-structure population of the O(3PJ) reactant is in its J = 2 ground state and the other one where it is in thermal equilibrium.
The time-dependent Schrödinger equation for quadratic Hamiltonians has Gaussian wave packets as exact solutions. For the parametric oscillator with frequency ω(t), the width of these wave packets must be time-dependent. This time-dependence can be determined by solving a complex nonlinear Riccati equation or an equivalent real nonlinear Ermakov equation. All quantum dynamical properties of the system can easily be constructed from these solutions, e.g., uncertainties of position and momentum, their correlations, ground state energies, etc. In addition, the link to the corresponding classical dynamics is supplied by linearizing the Riccati equation to a complex Newtonian equation, actually representing two equations of the same kind: one for the real and one for the imaginary part. If the solution of one part is known, the missing (linear independent) solution of the other can be obtained via a conservation law for the motion in the complex plane. Knowing these two solutions, the solution of the Ermakov equation can be determined immediately plus the explicit expressions for all the quantum dynamical properties mentioned above. The effect of a dissipative, linear velocity dependent friction force on these systems is discussed.
The theoretical and experimental investigation of exotic hadrons like tetraquarks is an important branch of modern elementary particle physics. In this thesis I investigate different four-quark systems using lattice QCD and search for evidence of stable tetraquark states or resonances.
Lattice QCD as a non-perturbative approach to QCD allows an accurate and reliable determination of the masses of strongly bound hadrons.
However, most tetraquarks appear as weakly bound states or resonances, which makes a theoretical investigation using lattice QCD difficult due to the finite spatial volume. A rigorous treatment of such systems is feasible using the so-called Lüscher method. This allows to calculate the scattering amplitude based on the finite-volume energy spectrum determined in a lattice QCD calculation. Similarly to the analysis of experimental data, this scattering amplitude can be used to determine the binding energies of bound states or the masses and decay widths of resonances in the infinite volume.
In my work I calculate the low-energy energy spectra of different four-quark systems and use - if necessary - the Lüscher method to determine the masses of potential tetraquark states.
I focus on systems consisting of two heavy antiquarks and two light quarks, where at least one of the heavy antiquarks is a bottom quark.
Even though such tetraquarks have not yet been experimentally detected, they are considered promising candidates for particles that are stable with respect to the strong interaction.
A decisive step for successfully calculating low-lying energy levels for such four-quark systems is a carefully chosen set of creation operators, which represent the physical states most accurately. In addition to operators that generate a local structure where all four quarks are located at the same space-time point, I also use so-called scattering operators that resemble two spatially separated mesons. These scattering operators turned out to be relevant for successfully determining the lowest energy levels and are therefore essential, especially if a Lüscher analysis is carried out.
In my work, I considered two different lattice setups to study the four-quark systems $\bar{b}\bar{b}ud$ with $I(J^P)=0(1^+) $, $\bar{b}\bar{b}us$ with $J^P=1^+ $ and $\bar{b}\bar{c}ud$ with $I(J^P)=0(0^+) $ and $I(J^P)=0(1^+) $ and to predict potential tetraquark states. In both setups, I considered scattering operators. While in the first setup I used them only as annihilation operators, in the second setup they were included both as creation and annihilation operators. Additionally, in the second lattice setup, I performed a simplified investigation of the $\bar{b}\bar{b}ud$ system with $I(J^P)=0(1^-) $, which is a potential candidate for a tetraquark resonance. The results of the investigation of the mentioned four-quark systems can be summarized as follows:
For the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^+) $ I found a deeply bound ground state slightly more than $ 100\,\textrm{MeV} $ below the lowest meson-meson threshold. The existence of a corresponding $\bar{b}\bar{b}ud$ tetraquark in the infinite volume was confirmed using a Lüscher analysis and possible systematic errors due to the use of lattice QCD were taken into account.
Similar results were obtained for the $ \bar{b}\bar{b}us $ four-quark system with $ J^P=1^+ $. Again, I found a ground state well below the lowest meson-meson threshold, but slightly weaker bound than for the $ \bar{b}\bar{b}ud $ system. Effects due to the finite volume turned out to be negligible for this system, as already predicted for the $ \bar{b}\bar{b}ud $ system. \item For the $ \bar{b}\bar{c}ud $ four-quark systems with $ (J^P)=0(0^+) $ and $ (J^P)=0(1^+) $ I was able to rule out the existence of a deeply bound tetraquark states based on the energy spectrum in the finite volume. However, by means of a scattering analysis using the Lüscher method, I found evidence a broad resonance for both channels.
In the case of the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^-) $, I could neither confirm the existence of a resonance, nor rule out its existence with certainty.
In particular, my investigations showed that the results of the two different lattice simulations are consistent. The theoretical prediction of the bound tetraquark states $\bar{b}\bar{b}ud$ and $\bar{b}\bar{b}us$ as well as the tetraquark resonances in the $\bar{b}\bar{c}ud$ system in this work represent an important contribution to the future experimental search for exotic hadrons and can support the discovery of previously unobserved particles.
ATP-binding cassette (ABC) transporters shuttle diverse substrates across biological membranes. They play a role in many physiological processes but are also the reason for antibiotic resistance of microbes and multi drug resistance in cancer, and their dysfunction can lead to serious diseases. Transport is achieved through an ATP-driven closure of the two nucleotide binding sites (NBSs) which induces a transition between an inward-facing (IF) and an outward-facing (OF) conformation of the connected transmembrane domains (TMDs). In contrast to this forward transition, the reverse transition (OF-to-IF) that involves Mg2+-dependent ATP hydrolysis and release is less understood. This is particularly relevant for heterodimeric ABC transporters with asymmetric NBSs. These transporters possess an ATPase active consensus NBS (c-NBS) and a degenerate NBS (d-NBS) with little or no ATPase activity.
Crucial details regarding function and mechanism of the transport cycle remain elusive.
Here, these open questions were addressed using pulse electron-electron double resonance (PELDOR or DEER) spectroscopy of the heterodimeric ABC exporter TmrAB.
To better understand the transport cycle, the underlying kinetics of the conformational transitions need to be elucidated. By introducing paramagnetic nitroxide (NO) spin probes at key positions of TmrAB and employing time-resolved PELDOR spectroscopy, the forward transition could be followed over time and the rate constants for the conformational transition at the TMDs and NBSs were characterized.
The temperature dependence of these rate constants was further analyzed to determine for the first time the activation energy of conformational changes in a large membrane protein. For TMD opening and c-NBS dimerization, values of 75 ± 27 kJ/mol and 56 ± 3 kJ/mol, respectively were found. These values agree with reported activation energies of peptide transport and peptide dissociation in other ABC transporters, suggesting that the forward transition may be the rate-limiting step for substrate translocation.
The functional relevance of asymmetric NBSs is so far not well understood. By combining Mg2+-to-Mn2+ substitution with Mn2+-NO and NO-NO PELDOR spectroscopy, the binding of ATP-Mn2+, the conformation of the NBSs, and the conformation of the TMDs could be simultaneously monitored for the first time. These results reveal an asymmetric post-hydrolytic state. Time-resolved investigation showed that ATP hydrolysis at the active c-NBS triggers the reverse transition, whereas opening of the impaired d-NBS regulates the return to the IF conformation.