Related papers: On Properties of Hamiltonian Structures for a Clas…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…
We study the properties of Hamiltonians defined as the generators of transfer matrices in quasi- one-dimensional waveguides. For single- or multi-mode waveguides obeying flux conservation and time-reversal invariance, the Hamiltonians…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
Semidiscretization in time is studied for a class of quasi-linear evolution equations in a framework due to Kato, which applies to symmetric first-order hyperbolic systems and to a variety of fluid and wave equations. In the regime where…
Given a Kaehlerian holomorphic fiber bundle whose fiber is a compact homogeneous Kaehler manifold, we describe the perturbed Hermitian-Einstein equations relative to certain holomorphic vector bundles. With respect to special metrics on the…
This paper is devoted to study measure solutions $\mu_t^h$ to perturbed nonlinear structured population models where $t$ denotes time and $h$ controlls the size of perturbation. We address differentiability of the map $h \mapsto \mu_t^h$.…
A variant of energy scale deformation is considered for the S = 1/2 antiferromagnetic Heisenberg model on polyhedra. The deformation is induced by the perturbations to the uniform Hamiltonian, whose coefficients are determined by the bond…
In the study of Hamiltonian systems on cotangent bundles, it is natural to perturb Hamiltoni-ans by adding potentials (functions depending only on the base point). This led to the definition of Ma{\~n}{\'e} genericity: a property is generic…
An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and…
We study a class of diffusion processes arising from random perturbations of conservative Hamiltonian systems. Under a set of abstract hypotheses -- including basic structural assumptions on the Hamiltonian, a weak Lyapunov structure, and a…
We show that solving the Maurer-Cartan equations is, essentially, the same thing as performing the Hamiltonian reduction construction. In particular, any differential graded Lie algebra equipped with an even nondegenerate invariant bilinear…
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…
We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra $\mathbb{V}$, so that it can be applied to non-canonical Hamiltonian systems. Given a Hamiltonian system that preserves a subalgebra $\mathbb{B}$ of $\mathbb{V}$,…
The $r$-KdV-CH hierarchy is a generalization of the Korteweg-de Vries and Camassa-Holm hierarchies parametrized by $r+1$ constants. In this paper we clarify some properties of its multi-Hamiltonian structures, prove the semisimplicity of…
We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the…
The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of periodic solutions which are the variational minimizers of Lagrangian actions.
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on $T^2$ and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange…