Related papers: Canonical symplectic structure and structure-prese…
Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give…
Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…
We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples we consider quantum mappings associated…
The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators…
Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations. We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation. We show that…
In this paper we discussed the self-adjointness of the Maxwell's equations with variable coefficients $\epsilon$ and $\mu$. Three different Lagrangian are attained. By the Legendre transformation, a multisymplectic Bridge's (Hamilton) form…
We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…
Due to the emergence of symplectic geometry, the geometric treatment of mechanics underwent a great development during the last century. In this scenario the pressence of symmetries in Hamiltonian systems leads naturally to the existence of…
In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
Obtaining exact solutions to the Schr\"odinger equation in complex quantum systems poses significant challenges. In this context, numerical methods emerge as valuable tools for analyzing such systems. This article proposes a numerical…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
On the basis of the covariant description of the canonical formalism for quantization, we present the basic elements of the symplectic geometry for a restricted class of topological defects propagating on a curved background spacetime. We…
In this contribution we propose an exponential update algorithm for magnetic moments appearing in the framework of micromagnetics and the Landau-Lifshitz-Gilbert (LLG) equation. This algorithm can be interpreted as the geometric integration…
Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated…
The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor {\theta} present; no…
Resonant solutions of the quantum Schr\"odinger equation occur at complex energies where the S-matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schr\"odinger…