Related papers: Any order imaginary time propagation method for so…
A method to compute the bound state eigenvalues and eigenfunctions of a Schr\"{o}dinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the…
Using a map between the Lindbladian evolution of dephasing in free fermions and the time evolution of imaginary-interaction Fermi-Hubbard models in bipartite lattices, we present an efficient classical algorithm to solve the Schr\"{o}dinger…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
This paper proposes two novel distributed continuous-time algorithms inspired by PID control to solve distributed optimization problems. The algorithms are referred to as first-order and second-order, respectively, depend on the intrinsic…
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the L\'evy flights; and the equation is derived as the macroscopic limit of the continuous time…
Self-gravitational force calculation for infinitesimally thin disks is important for studies on the evolution of galactic and protoplanetary disks. Although high-order methods have been developed for hydrodynamic and magneto-hydrodynamic…
This paper provides a provably quasi-optimal preconditioning strategy of the linear Schr\"odinger eigenvalue problem with periodic potentials for a possibly non-uniform spatial expansion of the domain. The quasi-optimality is achieved by…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
In this paper, we present a simple analytical method for obtaining a nonspreading solution of the time-dependent Schr\"odinger equation, which is given by the Airy function. The solution is derived by imposing a restriction on the phase…
We consider two approaches to calculate imaginary parts of effective actions in expanding space-times. While the first approach uses Bogolyubov coefficients, the second one uses the functional integral or the Feynman propagator. In…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
In this work we present the theoretical framework for the solution of the time-dependent Schr\"{o}dinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron's…
The Grassmann time-evolving matrix product operator method has shown great potential as a general-purpose quantum impurity solver, as its numerical errors can be well-controlled and it is flexible to be applied on both the imaginary- and…
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
We introduce and benchmark an improved algorithm for complex Langevin simulations of bosonic coherent state path integrals. Our approach utilizes a Strang splitting of the imaginary-time propagator rather than the conventional linear-order…
We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu,…
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of…
With growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schr\"odinger equation is of keen interest in modern electronic structure…
We introduce a simple and stable computational method for ill-posed partial differential equation (PDE) problems. The method is based on Schr\"odingerization, introduced in [S. Jin, N. Liu and Y. Yu, arXiv:2212.13969][S. Jin, N. Liu and Y.…
The semiclassical Schr\"odinger equation with time-dependent potentials is an important model to study electron dynamics under external controls in the mean-field picture. In this paper, we propose two multiscale finite element methods to…