Related papers: Symplectic integrators for spin systems

Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…

In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…

We propose new algorithms for numerical integration of the equations of motion for classical spin systems with fixed spatial site positions. The algorithms are derived on the basis of a mid-point scheme in conjunction with the multiple time…

We construct a symplectic structure on a disc that admits a compactly supported symplectomorphism which is not smoothly isotopic to the identity. The symplectic structure has an overtwisted concave end; the construction of the…

It is shown that a spin system is equivalent to a set of constrained harmonic oscillators. For finite, but large, systems, a continuous approximation to the density of states can be used, and the oscillator frequencies can be exactly…

Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a generalized Hamiltonian dynamics in an extra time variable $\tau$ which, at…

This survey gives a short and comprehensive introduction to a class of finite-dimensional integrable systems known as hypersemitoric systems, recently introduced by Hohloch and Palmer in connection with the solution of the problem how to…

In the Hilbert space of n qubits, we introduce the symplectic space (n odd) and the orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically…

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the…

We derive variational integrators for stochastic Hamiltonian systems on Lie groups using a discrete version of the stochastic Hamiltonian phase space principle. The structure-preserving properties of the resulting scheme, such as…

Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly…

In this article, we introduce $b$-semitoric systems as a generalization of semitoric systems, specifically tailored for $b$-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the…

Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…

We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that…

Adapting ideas of Daubechies and Klauder [J. Math. Phys. {\bf 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized…

In this article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way, the method of generating functions to 1-forms which are…

Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are…

The complete one-loop, planar dilatation operator of the N=4 superconformal gauge theory was recently derived and shown to be integrable. Here, we present further compelling evidence for a generalisation of this integrable structure to…

We study symplectic deformations of Gabor frames using the covariance properties of the Heisenberg operators. This allows us to recover in a very simple way known results. We thereafter propose a general deformation scheme by Hamiltonian…