Related papers: Locality and Computational Reliability of Linear R…
Linear Recurrence Sequences (LRS) are a fundamental mathematical primitive for a plethora of applications such as the verification of probabilistic systems, model checking, computational biology, and economics. Positivity (are all terms of…
In the recent work of S. Sharma \emph{et al.}, (arxiv.org: arxiv:0912.1118), a single-electron spectrum associated with the natural orbitals was defined as the derivative of the total energy with respect to the occupation numbers at half…
The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility, known as quantum nonlocality, represents a milestone in the foundations of quantum theory. Quantum nonlocality is also…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
Single-electron capacitance spectroscopy precisely measures the energies required to add individual electrons to a quantum dot. The spatial extent of electronic wavefunctions is probed by investigating the dependence of these energies on…
The dynamical response of metallic clusters up to $10^3$ atoms is investigated using the restricted molecular dynamics simulations scheme. Exemplarily, sodium like material is considered. Correlation functions are evaluated to investigate…
Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest…
We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
Locality-preserving logical operators in topological codes are naturally fault-tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure…
We study electron localization in disordered quantum systems, focusing on both individual eigenstates and thermal states. We employ complex polarization as a numerical indicator to characterize the system's localization length. Furthermore,…
Quantitatively accurate electronic structure calculations rely on the proper description of electron correlation. A judicious choice of the approximate quantum chemistry method depends upon the importance of dynamic and nondynamic…
A nearest-neighbor tight-binding model on a tree structure is investigated. The full energy spectrum of the normalized Hamiltonian can be expressed in terms of successively increasing number of contributions at any finite step of…
Non-local correlations are not only a fascinating feature of quantum theory, but an interesting resource for information processing, for instance in communication-complexity theory or cryptography. An important question in this context is…
In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
In sufficiently strong scattering media, light transport is suppressed and modes are exponentially localized. Anderson-like localized states have long been recognized as potential candidate for high-Q optical modes for low-threshold, cost…
The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that…
Model checking large networks of processes is challenging due to state explosion. In many cases, individual processes are isomorphic, but there is insufficient global symmetry to simplify model checking. This work considers the verification…
The conflict between Quantum Mechanics (QM) and the intuitive concepts of Locality and Realism (LR) is manifest in the correlation between measurements performed in remote regions of a spatially spread entangled state. In this paper, it is…