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It is well-known that if one assumes quantum theory to hold locally, then processes with indefinite causal order and cyclic causal structures become feasible. Here, we study qualitative limitations on causal structures and correlations…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
Modeling the atomic structure of amorphous materials has long been a critical challenge in materials science. Recent advances in monolayer amorphous materials enable direct observation of their atomic structures, paving the way for a better…
We have adapted classical molecular dynamics to study the structural and dynamical properties of amorphous silica surfaces. Concerning the structure, the density profile exhibits oscillations perpendicularly to the surface as observed in…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we…
We analyze the final state sensitivity of nonlocal networks with respect to initial conditions of their units. By changing the initial conditions of a single network unit, we perturb an initially synchronized state. Depending on the…
Localized waves in disordered one-dimensional materials have been studied for decades, including white-noise and correlated disorder, as well as quasi-periodic disorder. How these wave phenomena relate to those in crystalline (periodic…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
We present a computational study of small-angle X-ray scattering (SAXS) in amorphous silicon ($a$-Si) with particular emphasis on the morphology and microstructure of voids. The relationship between the scattering intensity in SAXS and the…
The negatively charged silicon vacancy [V$_\text{Si}(-)$] in silicon carbide (SiC) is a paramagnetic and optically active defect in hexagonal SiC. V$_\text{Si}(-)$ defect possesses $S = 3/2$ spin with long spin coherence time and can be…
In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
Atomistic simulations have become a powerful tool in materials research due to the extremely fine spatial and temporal resolution provided by such techniques. In order to understand the fundamental principles which govern material behavior…
This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
Signed networks provide a principled framework for representing systems in which interactions are not merely present or absent but qualitatively distinct: friendly or antagonistic, supportive or conflicting, excitatory or inhibitory. This…
Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…
We present the results of atomistic and ab initio simulation of several different tilt grain boundaries (GB) in silicon. The boundary structures obtained with genetic algorithm turned out to have no coordination defects, i.e. all silicon…
We present linear ensembles of dangling bond chains on a hydrogen terminated Si(100) surface, patterned in the closest spaced arrangement allowed by the surface lattice. Local density of states maps over a range of voltages extending…