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The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…
We propose a new approach to constructing a neural network for predicting expectations of stochastic differential equations. The proposed method does not need data sets of inputs and outputs; instead, the information obtained from the…
We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schr\"odinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator…
Applying machine learning models to meteorological data brings many opportunities to the Geosciences field, such as predicting future weather conditions more accurately. In recent years, modeling meteorological data with deep neural…
The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a…
By using the Lewis-Riesenfeld theory and the invariant-related unitary transformation formulation, the exact solutions of the {\it time-dependent} Schr\"{o}dinger equations which govern the various Lie-algebraic quantum systems in atomic…
We investigate the application of deep learning techniques employing the conditional variational autoencoders for semi-supervised learning of latent parameters to describe phase transition in the two-dimensional (2D) ferromagnetic Ising…
Transparent boundary conditions for the time-dependent Schrodinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the…
In this paper, we propose Galerkin-Legendre spectral method with implicit Runge-Kutta method for solving the unsteady two-dimensional Schrodinger equation with nonhomogeneous Dirichlet boundary conditions and initial condition. We apply a…
In this study, we theoretically analyzed a control protocol based on ``time-dependent resonance" in nearly adiabatic two-level quantum systems, demonstrating that it exhibits properties equivalent to adiabatic control. This protocol is…
A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schrodinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) method, the fast Fourier transform is used to…
We present theory and calculations for coherent high-fidelity quantum control of many-particle states in semiconductor quantum wells. We show that coupling a two-electron double quantum dot to a terahertz optical source enables targeted…
We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between…
This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…
In this paper, a linearized fully discrete scheme is proposed to solve the two-dimensional nonlinear time fractional Schr\"odinger equation with weakly singular solutions, which is constructed by using L1 scheme for Caputo fractional…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…