Related papers: Any order imaginary time propagation method for so…
In this work we develop EPOCH: Equilibrium Propagator by Orthogonal polynomial CHain, a computationally efficient method to calculate the time-dependent equilibrium Green's functions, including the anomalous Green's functions of…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
We study the time-sliced thawed Gaussian propagation method, which was recently proposed for solving the time-dependent Schr\"odinger equation. We introduce a triplet of quadrature-based analysis, synthesis and re-initialization operators…
The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrodinger equation in an explicitly iterative process. However, the method requires the spatial grid…
Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…
A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are…
We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and…
This thesis explores a particular class of distributed optimization methods for various separable resource allocation problems, which are of high interest in a wide array of multi-agent settings. A distinctly motivating application for this…
Prime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved…
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…
It is shown that if a complete set of mutually commuting operators is formed by constants of motion, then, up to a factor that only depends on the time, each common eigenfunction of such operators is a solution of the Schr\"odinger…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagator in each iteration of the plain parareal method together…