Subspace Hamiltonian technique.

Symplectic Model Reduction of Hamiltonian Systems

In this paper, a symplectic model reduction technique, proper symplectic decomposition (PSD) with symplectic Galerkin projection, is proposed to save the computational cost for the simplification of large-scale Hamiltonian systems while preserving the symplectic structure. As an analogy to the classical proper orthogonal decomposition (POD)-Galerkin approach, PSD is designed to build a symplect...

New technique for molecular-dynamics computer simulations: Hellmann-Feynman theorem and subspace Hamiltonian approach.

Two Qubit Quantum Computing in a Projected Subspace

A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This...

A Novel Noise Reduction Method Based on Subspace Division

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

Convexity of multi-valued momentum map

Given a Hamiltonian torus action the image of the momentum map is a convex polytope; this famous convexity theorem of Atiyah, Guillemin and Sternberg still holds when the action is not required to be Hamiltonian. Our generalization of the convexity theorem states that, given a symplectic torus action, the momentum map can be defined on an appropriate covering of the manifold and has as image a ...