相关论文: Truncation scheme of time-dependent density-matrix…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
We introduce a non-linear differential flow equation for density matrices that provides a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal state. We use this equation to build a variational approach for…
The Hartree-Fock-Bogoliubov approximation is very useful for treating both long- and short-range correlations in finite quantum fermion systems, but it must be extended in order to describe detailed spectroscopic properties. One problem is…
We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
This paper investigates the time fractional sine-Gordon equation whose solution exhibits a weak singularity of type t^{\alpha}. By means of the Alikhanov formula we derive a fully discrete, linearized scheme. Using the more general…
We discuss effective field theory treatments of the problem of three particles interacting via short-range forces (range R >> a_2, with a_2 the two-body scattering length). We show that forming a once-subtracted scattering equation yields a…
We propose an efficient numerical method to compute the $k$-space second Chern number in four-dimensional (4D) topological systems. Our approach employs an adaptive mesh refinement scheme to evaluate the Brillouin-zone integral, which…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A…
The time evolution of $\ell$-spin reduced density operators is studied for a class of Heisenberg-type quantum spin models with long-range interactions. In the framework of the quantum Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy,…
We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges…
In a two-dimensional Bose-Einstein condensate the reduction in dimensionality fundamentally influences collisions between the atoms. In the crossover regime from three to two dimensions several scattering parameters have been considered.…
We extend a previously proposed rotation and truncation scheme to optimize quantum Anderson impurity calculations with exact diagonalization [PRB 90, 085102 (2014)] to density-matrix renormalization group (DMRG) calculations. The method…
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…
In this work, a new compact sixth order accurate finite difference scheme for the two and three-dimensional Helmholtz equation is presented. The main significance of the proposed scheme is that its sixth order leading truncation error term…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
We assess the validity of a single step Godunov scheme for the solution of the magneto-hydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally…
This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…
This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…