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The question of how systems respond to perturbations is ubiquitous in physics. Predicting this response for large classes of systems becomes particularly challenging if many degrees of freedom are involved and linear response theory cannot be applied. Here, we consider isolated many-body quantum systems which either start out far from equilibrium and then thermalize, or find themselves near thermal equilibrium from the outset. We show that time-periodic perturbations of moderate strength, in the sense that they do not heat up the system too quickly, give rise to the following phenomenon of stalled response: While the driving usually causes quite considerable reactions as long as the unperturbed system is far from equilibrium, the driving effects are strongly suppressed when the unperturbed system approaches thermal equilibrium. Likewise, for systems prepared near thermal equilibrium, the response to the driving is barely noticeable right from the beginning. Numerical results are complemented by a quantitatively accurate analytical description and by simple qualitative arguments.

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Laser-based directed energy deposition using metal powder (DED-LB/M) offers great potential for a flexible production mainly defined by software. To exploit this potential, knowledge of the process parameters required to achieve a specific track geometry is essential. Existing analytical, numerical, and machine-learning approaches, however, are not yet able to predict the process parameters in a satisfactory way. A trial-&-error approach is therefore usually applied to find the best process parameters. This paper presents a novel user-centric decision-making workflow, in which several combinations of process parameters that are most likely to yield the desired track geometry are proposed to the user. For this purpose, a Gaussian Process Regression (GPR) model, which has the advantage of including uncertainty quantification (UQ), was trained with experimental data to predict the geometry of single DED tracks based on the process parameters. The inherent UQ of the GPR together with the expert knowledge of the user can subsequently be leveraged for the inverse question of finding the best sets of process parameters by minimizing the expected squared deviation between target and actual track geometry. The GPR was trained and validated with a total of 379 cross sections of single tracks and the benefit of the workflow is demonstrated by two exemplary use cases.

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Although the principles behind assessment for and as learning are well-established, there can be a struggle when reforming traditional assessment of learning to a program which encompasses assessment for and as learning. When introducing and reporting reforms, tensions in faculty may arise because of differing beliefs about the relationship between assessment and learning and the rules for the validity of assessments. Traditional systems of assessment of learning privilege objective, structured quantification of learners' performances, and are done to the students. Newer systems of assessment promote assessment for learning, emphasise subjectivity, collate data from multiple sources, emphasise narrative-rich feedback to promote learner agency, and are done with the students. This contrast has implications for implementation and evaluative research. Research of assessment which is done to students typically asks, "what works", whereas assessment that is done with the students focuses on more complex questions such as "what works, for whom, in which context, and why?" We applied such a critical realist perspective drawing on the interplay between structure and agency, and a systems approach to explore what theory says about introducing programmatic assessment in the context of pre-existing traditional approaches. Using a reflective technique, the internal conversation, we developed four factors that can assist educators considering major change to assessment practice in their own contexts. These include enabling positive learner agency and engagement; establishing argument-based validity frameworks; designing purposeful and eclectic evidence-based assessment tasks; and developing a shared narrative that promotes reflexivity in appreciating the complex relationships between assessment and learning.

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The groundbreaking investigation by Deutsch [Phys. Rev. A 43, 2046 (1991)PLRAAN1050-294710.1103/PhysRevA.43.2046] of how a closed many-body quantum system approaches thermal equilibrium is revisited. It is shown how to carry out some important steps that were missing in that paper. Moreover, the class of admitted systems is extended considerably.

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An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal longtime limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case whose temporal relaxation is known. This is achieved within the conceptual framework of a typicality approach by showing and exploiting that the time-dependent expectation values behave very similarly for most members of a suitably chosen ensemble of perturbations. The predictions are validated by comparison with various numerical and experimental results from the literature.

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Prethermalization refers to the remarkable relaxation behavior which an integrable many-body system in the presence of a weak integrability-breaking perturbation may exhibit: After initial transients have died out, it stays for a long time close to some nonthermal steady state, but on even much larger time scales, it ultimately switches over to the proper thermal equilibrium behavior. By extending Deutsch's conceptual framework from Phys. Rev. A 43, 2046 (1991)PLRAAN1050-294710.1103/PhysRevA.43.2046, we analytically predict that prethermalization is a typical feature for a very general class of such weakly perturbed systems.

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We explore how the expectation values 〈ψ|A|ψ〉 of a largely arbitrary observable A are distributed when normalized vectors |ψ〉 are randomly sampled from a high-dimensional Hilbert space. Our analytical results predict that the distribution exhibits a very narrow peak of approximately Gaussian shape, while the tails significantly deviate from a Gaussian behavior. In the important special case that the eigenvalues of A satisfy Wigner's semicircle law, the expectation-value distribution for asymptotically large dimensions is explicitly obtained in terms of a large deviation function, which exhibits two symmetric nonanalyticities akin to critical points in thermodynamics.

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Dynamical typicality refers to the property that two pure states, which initially exhibit (almost) the same expectation value for some given observable A, are very likely to exhibit also very similar expectation values when evolving in time according to the pertinent Schrödinger equation. We unify and generalize a variety of previous findings of this type for sufficiently high-dimensional quantum mechanical model systems. Particular emphasis is put on the necessary and sufficient conditions, which the initial expectation value and the spectrum of A have to fulfill.

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We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit an arbitrary but fixed nonequilibrium expectation value for some given observable A. On the condition that this set is not too small, it is shown by means of a dynamical typicality approach that most such initial states exhibit thermalization if and only if A satisfies the so-called weak eigenstate thermalization hypothesis (wETH). Here, thermalization means that the expectation value of A spends most of its time close to the microcanonical value after initial transients have died out. The wETH means that, within the energy shell, most eigenstates of the pertinent system Hamiltonian exhibit very similar expectation values of A.

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The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.

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We consider isolated many-body quantum systems which do not thermalize; i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and XXZ models.

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We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably rare in time. Measuring the distinguishability in terms of quantum mechanical expectation values, results of this type have been previously established under increasingly weak assumptions about the initial disequilibrium, the many-body Hamiltonian, and the considered observables. Here, we further extend these results with respect to generalized distinguishability measures which fully take into account the fact that the actually observed, primary data are not expectation values but rather the probabilistic occurrence of different possible measurement outcomes.

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The lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. However, far from equilibrium, only very few quantitative and comparably universal results are known. Here a quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium.

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The structure of metallic glasses is a long-standing question because the lack of long-range order makes diffraction based techniques difficult to be applied. Here, we used scanning tunneling microscopy with large tunneling resistance of 6 GΩ at low temperature in order to minimize forces between probe and sample and reduce thermal fluctuations of metastable structures. Under these extremely gentle conditions, atomic structures of Ni40Ta60 metallic glasses are revealed with unprecedented lateral resolution. In agreement with previous models and experiments, icosahedral-like clusters are observed. The clusters show a high degree of mobility, which explains the need of low temperatures for stable imaging. In addition to icosahedrons, chain-like structures are resolved and comparative density functional theory (DFT) calculations confirm that these structures are meta-stable. The co-existence of icosahedral and chain-like structures might be an key ingredient for the understanding of the mechanical properties of metallic glasses.

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Thermalization of isolated many-body systems is demonstrated by generalizing an approach originally due to von Neumann: For arbitrary initial states with a macroscopically well-defined energy, quantum mechanical expectation values become indistinguishable from the corresponding microcanonical expectation values for the overwhelming majority of all sufficiently late times. As in von Neumann's work, the eigenvectors of the Hamiltonian and of the considered observable are required to not exhibit any specially tailored (untypical) orientation relative to each other. But all of von Neumann's further assumptions about the admitted observables are abandoned.

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We investigated experimentally and theoretically the translocation forces when a charged polymer is threaded through a solid-state nanopore and found distinct dependencies on the nanopore diameter as well as on the nano membrane material chemistry. For this purpose we utilized dedicated optical tweezers force mechanics capable of probing the insertion of negatively charged double-stranded DNA inside a helium-ion drilled nanopore. We found that both the diameter of the nanopore and the membrane material itself have significant influences on the electroosmotic flow through the nanopore and thus on the threading force. Compared to a bare silicon-nitride membrane, the threading of DNA through only 3 nm thin carbon nano membranes as well as lipid bilayer-coated nanopores increased the threading force by 15% or 85%, respectively. This finding was quantitatively described by our recently developed theoretical model that also incorporates hydrodynamic slip effects on the translocating DNA molecule and the force dependence on the membrane thickness. The additional measurements presented in this paper further support our model.

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We use optical tweezers to investigate the threading force on a single dsDNA molecule inside silicon-nitride nanopores between 6 and 70 nm in diameter, as well as lipid-coated solid-state nanopores. We observe a strong increase of the threading force for decreasing nanopore size that can be attributed to a significant reduction in the electroosmotic flow (EOF), which opposes the electrophoresis. Additionally, we show that the EOF can also be reduced by coating the nanopore wall with an electrically neutral lipid bilayer, resulting in an 85% increase in threading force. All experimental findings can be described by a quantitative theoretical model that incorporates a hydrodynamic slip effect on the DNA surface with a slip length of 0.5 nm.

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Focusing on isolated macroscopic systems, described in terms of either a quantum mechanical or a classical model, our two key questions are how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior (equilibration) and how far is this steady state in agreement with the microcanonical ensemble as predicted by statistical mechanics (thermalization). A recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and nonequilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. An analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.

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We consider the translocation of a neutral (uncharged) nanoparticle through a pore in a thin membrane with constant surface charge density. If the concomitant Debye screening layer is sufficiently thin, the resulting forces experienced by the particle on its way through the pore are negligible. But when the Debye length becomes comparable to the pore diameter, the particle encounters a quite significant potential barrier while approaching and entering the pore, and symmetrically upon exiting the pore. The main reason is an increasing pressure, which acts on the particle when it intrudes into the counter ion cloud of the Debye screening layer. In case the polarizability of the particle is different (usually smaller) than that of the ambient fluid, a second, much smaller contribution to the potential barrier is due to self-energy effects. Our numerical treatment of the problem is complemented by analytical approximations for sufficiently long cylindrical particles and pores, which agree very well with the numerics.

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We consider elongated cylindrical particles, modeling, e.g., DNA fragments or nanorods, while they translocate under the action of an externally applied voltage through a solid state nanopore. Particular emphasis is put on the concomitant potential energy landscape encountered by the particle on its passage through the pore due to the complex interplay of various electrohydrodynamic effects beyond the realm of small Debye lengths. We find that the net potential energy difference across the membrane may be of opposite sign for short and long particles of equal diameters and charge densities (e.g., oligomers). Thermal noise thus leads to biased diffusion through the pore in opposite directions. By means of an additional membrane gate electrode it is even possible to control the specific particle length at which this transport inversion occurs.

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