Related papers: Lattice Green function for extended defect calcula…
A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers.…
False vacuum decay, a quantum mechanical first-order phase transition in scalar field theories, is an important phenomenon in early universe cosmology. Recently, real-time semi-classical techniques based on ensembles of lattice simulations…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we…
Measurements and analysis of orbit response matrix have been providing for decades a formidable tool in the detection of linear lattice imperfections and their correction. Basically all storage-ring-based synchrotron light sources across…
Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply…
Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on…
Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we…
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…
Average atom models are widely used to make equation of state tables and for calculating other properties of materials over a wide range of conditions, from zero temperature isolated atom to fully ionized free electron gases. The numerical…
A rigorous methodology is developed for computing elastic fields generated by experimentally observed defect structures within grains in a polycrystal that has undergone tensile extension. An example application is made using a near-field…
The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundaries of one and two-dimensional crystalline materials. The…
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular…
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…