Related papers: Hamiltonian preserving nonlinear optics
This paper describes the design and simulation of a proof-of-concept quasi-integrable octupole lattice at the University of Maryland Electron Ring (UMER). This experiment tests the feasibility of nonlinear integrable optics, a novel…
We analyze the effective Hamiltonian arising from a suitable power series expansion of the overlap integrals of Wannier functions for confined bosonic atoms in a 1d optical lattice. For certain constraints between the coupling constants, we…
This paper deals with the simultaneous estimation of the attitude, position and linear velocity for vision-aided inertial navigation systems. We propose a nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame…
To a very good approximation, particularly for hadron machines, charged-particle trajectories in accelerators obey Hamiltonian mechanics. During routine storage times of eight hours or more, such particles execute some $10^{8}$ revolutions…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
The harmonic oscillator Hamiltonian, when augmented by a non-Hermitian $\cal{PT}$-symmetric part, can be transformed into a Hermitian Hamiltonian. This is achieved by introducing a metric which, in general, renders other observables such as…
In this short note we give incremental algorithms for the following lattice problems: finding a basis of a lattice, computing the successive minima, and determining the orthogonal decomposition. We prove an upper bound for the number of…
In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows…
Nonlinear optical responses are becoming increasingly relevant for characterizing the symmetries and quantum geometry of electronic phases in materials. Here, we develop an expanded diagrammatic scheme for calculating spatially dispersive…
Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…
Nonlinear, completely integrable Hamiltonian systems that serve as blueprints for novel particle accelerators at the intensity frontier are promising avenues for research, as Fermilab's Integrable Optics Test Accelerator (IOTA) example…
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of…
We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…
We report on a study of the supersymmetric anharmonic oscillator computed using a euclidean lattice path integral. Our numerical work utilizes a Fourier accelerated hybrid Monte Carlo scheme to sample the path integral. Using this we are…
This paper presents three non-linear observers on three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This…
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…