Related papers: Solving Caldeira-Leggett Model by Inchworm Method …
Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient…
We propose an efficient tensor-train-based algorithm for simulating open quantum systems with the inchworm method, where the reduced dynamics of the open quantum system is expressed as a perturbative series of high-dimensional integrals.…
The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature…
The Caldeira-Leggett model provides a compact characterization of a thermal environment in terms of a spectral density function. This simplicity has led to a variety of numerically exact quantum methods for reduced density matrix…
We present fast algorithms for the summation of Dyson series and the inchworm Monte Carlo method for quantum systems that are coupled with harmonic baths. The algorithms are based on evolving the integro-differential equations where the…
We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover,…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
The frozen Gaussian approximation, proposed in [Lu and Yang, [15]], is an efficient computational tool for high frequency wave propagation. We continue in this paper the development of frozen Gaussian approximation. The frozen Gaussian…
We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign…
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool…
This paper introduces an efficient tensor-vector product technique for the rapid and accurate approximation of integral operators within physics-informed deep learning frameworks. Our approach leverages neural network architectures to…
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
We show how the Gillespie algorithm, originally developed to describe coupled chemical reactions, can be used to perform numerical simulations of a granular intruder particle colliding with thermalized bath particles. The algorithm…
An explicit high order semi-Lagrangian method is developed for solving Lagrangian transport equations in Eulerian-Lagrangian formulations. To ensure a semi-Lagrangian approximation that is consistent with an explicit Eulerian, discontinuous…
A novel method, the Gaussian Integral Method (GIM), is presented for calculating void fractions in Computational Fluid Dynamics-Discrete Element Method (CFD-DEM) simulations. GIM is versatile and applicable to various grid types, including…
Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gradient used for iterations in seismic tomography.…
The simulation of entangled ground-states of quantum materials remains challenging for classical computational methods in more than one spatial dimension, and is a prime target for quantum computational advantage. To this end, an important…