Related papers: Locality and Computational Reliability of Linear R…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
We study localized modes on a single Ablowitz-Ladik impurity embedded in the bulk or at the surface of a one-dimensional linear lattice. Exact expressions are obtained for the bound state profile and energy. Dynamical excitation of the…
Reporting extensions of a recently developed approach to density functional theory with correct long-range be-havior (Phys. Rev. Lett. 94, 043002 (2005)). The central quantities are a splitting functional gamma[n] and a complementary…
This paper concerns the numerical approximation of low-energy eigenstates of the linear random Schr\"odinger operator. Under oscillatory high-amplitude potentials with a sufficient degree of disorder it is known that these eigenstates…
We report a first-principles description of the induced wake potential and density in real solids. The linear-response formalism is used to obtain the potential and density induced by an external charge penetrating through an inhomogeneous…
Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally…
We introduce a series of quantities which characterizes a given local operator in conformal field theories from the viewpoint of quantum entanglement. It is defined by the increased amount of (Renyi) entanglement entropy at late time for an…
The local field potential (LFP) is as a measure of the combined activity of neurons within a region of brain tissue. While biophysical modeling schemes for LFP in cortical circuits are well established, there is a paramount lack of…
Simplifying expressions is important to make numerical integration of large expressions from High Energy Physics tractable. To this end, Horner's method can be used. Finding suitable Horner schemes is assumed to be hard, due to the lack of…
The dynamics of molecular electron excitation and ionisation is studied in real-time for ultra-short IR laser pulses of intensity I>10^{13} W/cm^{2}. The multi-electron molecule is modeled by a system of two active electrons moving in a…
Within the Local Unitarity formalism, any physical cross-section is re-written in such a way that cancellations of infrared singularities between real and virtual contributions are realised locally. Consequently, phase-space and loop…
The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet…
Two-color laser fields offer significantly enhanced control over electron excitation dynamics under ultrashort intense laser pulses compared to monochromatic fields. However, their strong nonlinearity necessitates computationally expensive…
We study the local stability of nonlinear systems in the Lur'e form with static nonlinear feedback realized by feedforward neural networks (FFNNs). By leveraging positivity system constraints, we employ a localized variant of the Aizerman…
We present a theoretical approach to calculate the {\it local} absorption spectrum of excitons confined in a semiconductor nanostructure. Using the density-matrix formalism, we derive a microscopic expression for the non-local…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
In fluids under temperature gradients, long-range correlations (LRCs) emerge generically, leading to enhanced density fluctuations. This phenomenon, characterized by the $\boldsymbol{q}^{-4}$ divergence in the static structure factor (where…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose…