相关论文: Fast and stable method for simulating quantum elec…
A fast and stable numerical method is formulated to compute the time evolution of a wave function in a magnetic field by solving the time-dependent Schroedinger equation. This computational method is based on the finite element method in…
A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We discuss a method to follow step-by-step time evolution of atomic and molecular systems based on QED (Quantum Electrodynamics). Our strategy includes expanding the electron field operator by localized wavepackets to define creation and…
Solving the time-dependent Schr\"odinger equation (TDSE) is pivotal for modeling non-adiabatic electron dynamics, a key process in ultrafast spectroscopy and laser-matter interactions. However, exact solutions to the TDSE remain…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…
Recent advancements of intermediate-scale quantum processors have triggered tremendous interest in the exploration of practical quantum advantage. The simulation of fluid dynamics, a highly challenging problem in classical physics but vital…
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still…
One of the unitary forms of the quantum mechanical time evolution operator is given by Cayley's approximation. A numerical implementation of the same involves the replacement of second derivatives in Hamiltonian with the three-point…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…
The central object in wave turbulence theory is the wave kinetic equation (WKE), which is an evolution equation for wave action density and acts as the wave analog of the Boltzmann kinetic equations for particle interactions. Despite recent…
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…
Efficient methods for generating samples of wave packet trajectories are needed to build machine learning models for quantum dynamics. However, simulating such data by direct integration of the time-dependent Schrodinger equation can be…