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We show that the physical mechanism for the equilibration of closed quantum systems is dephasing, and identify the energy scales that determine the equilibration timescale of a given observable. For realistic physical systems (e.g those…
Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic…
We present the Materials Learning Algorithms (MALA) package, a scalable machine learning framework designed to accelerate density functional theory (DFT) calculations suitable for large-scale atomistic simulations. Using local descriptors…
We develop a self-consistent first-principle method based on the density functional theory. Physical quantities, such as the density of states, Fermi energy and electron density are obtained using a time-dependent random state method…
Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem…
Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of…
Atomistic simulations provide insights into structure-property relations on an atomic size and length scale, that are complementary to the macroscopic observables that can be obtained from experiments. Quantitative predictions, however, are…
Electronic Structure Theory (EST) describes the behavior of electrons in matter and is used to predict material properties. Conventionally, this involves forming a Hamiltonian and solving the Schr\"odinger equation through discrete…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…
We present a method for the calculation of electronic structure of systems that contain tens of thousands of atoms. The method is based on the division of the system into mutually overlapping fragments and the representation of the…
This paper focuses on the scaling of the S-matrix for elastic nucleon-nucleon scattering at large Nc. It is argued that the logarithm of a typical S-matrix element is proportional to Nc in the regime where the large Nc limit is taken with…
A long-standing goal of science is to accurately solve the Schr\"odinger equation for large molecular systems. The poor scaling of current quantum chemistry algorithms on classical computers imposes an effective limit of about a few dozen…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
Understanding the non-equilibrium behavior of stainless steel under extreme electronic excitation remains a critical challenge for laser processing and radiation science. We employ a hybrid framework integrating density-functional tight…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and practical quantum…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…