相关论文: Energy estimators for random series path-integral …

Carbon-hydrogen plasmas and hydrocarbon materials are of broad interest to laser shock experimentalists, high energy density physicists, and astrophysicists. Accurate equations of state (EOS) of hydrocarbons are valuable for various studies…

Path integral Monte Carlo simulations are applied to study dense atomic hydrogen in the regime where the protons form a Wigner crystal. The interaction of the protons with the degenerate electron gas is modeled by Thomas-Fermi screening,…

We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped He clusters. We describe the principles of PIMC,…

In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…

Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials…

Free energy sampling methods allow studying the full dynamics of activated processes. Unfortunately, the affordable accuracy of the potential describing the energy and forces of the system is usually rather low. Here we introduce a new…

Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation.…

Potential energy surfaces of the hydrogen molecular ion H$_2^+$ in the Born-Oppenheimer approximation are computed by means of the Riccati-Pad\'e method (RPM). The convergence properties of the method are analyzed for different states. The…

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of…

There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of…

In this educational paper, we will discuss calculations on the hydrogen molecule both on classical and quantum computers. In the former case, we will discuss the calculation of molecular integrals that can then be used to calculate…

We propose a new method to compute the free energy or enthalpy of fluids or disordered solids by computer simulation . The main idea is to construct a reference system by freezing one representative configuration, and then carry out a…

This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…

We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to…

Traditional dynamic security assessment faces challenges as power systems are experiencing a transformation to inverter-based-resource (IBR) dominated systems, for which electromagnetic transient (EMT) dynamics have to be considered.…

We demonstrate the accuracy of ground-state energies of the transcorrelated Hamiltonian, employing sophisticated Jastrow factors obtained from variational Monte Carlo, together with the coupled cluster and distinguishable cluster methods at…

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in…

We propose a bilinear sampling algorithm in Green's function Monte Carlo for expectation values of operators that do not commute with the Hamiltonian and for differences between eigenvalues of different Hamiltonians. The integral…

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of…

We propose a modified power method for computing the subdominant eigenvalue $\lambda_2$ of a matrix or continuous operator. Here we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers…