Here we propose the variational discrete action theory (VDAT) to study ground state properties of quantum many-body Hamiltonians. VDAT is a based on sequential product density matrix (SPD) ansatz, characterized by an integer $\mathcal{N}$, which monotonically approaches exact solution with increasing $\mathcal{N}$. To evaluate SPD, introduce and corresponding time Green's function. We use exact...

We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondence between continuous and discrete Hamiltonian mechanics, which arise from the continuousand discrete-time H...

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.

This paper will review recent advances in the formulation of a discrete version of geometric mechanics, based on the discretization of Hamilton’s variational principle, and progress that has been made in reduction theory for discrete variational mechanics in the form of Discrete Routh Reduction. To place discrete geometric mechanics on a firm mathematical foundation, we propose to develop a dis...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology o...