Related papers: Classical eikonal from Magnus expansion
We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable | after the Heisenberg evolution associated with the…
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the…
We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
The all-order structure of scattering amplitudes is greatly simplified by the use of Wilson line operators, describing eikonal emissions from straight lines extending to infinity. A generalization at subleading powers in the eikonal…
Electronic transport through chaotic quantum dots exhibits universal behaviour which can be understood through the semiclassical approximation. Within the approximation, transport moments reduce to codifying classical correlations between…
We present a systematic diagrammatic investigation of the classical limit of observables computed from scattering amplitudes in quantum field theory through the Kosower-Maybee-O'Connell (KMOC) formalism, motivated by the study of…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Most elementary numerical schemes found useful for solving classical trajectory problems are {\it canonical transformations}. This fact should be make more widely known among teachers of computational physics and Hamiltonian mechanics. From…
We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic…
We discuss generation of series expansions for Ising spin-glasses with a symmetric $\pm J$ (i.e. bimodal) distribution on d-dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in…
We study the classical dynamics of spinning particles using scattering amplitudes and eikonal exponentiation. We show that observables are determined by a simple algorithm. A wealth of complexity arises in perturbation theory as positions,…
In this paper, working in the eikonal approximation, we present a proof for the exponentiation of the 2-body eikonal phase to {\it all orders in the eikonal expansion}, for scalar particles interacting electromagnetically or…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
An eikonal algebra ${\mathfrak E}(\Omega)$ is a C*-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are…
W. Magnus introduced a particular differential equation characterizing the logarithm of the solution of linear initial value problems for linear operators. The recursive solution of this differential equation leads to a peculiar Lie series,…