Related papers: A sharper Magnus expansion bound woven in binary b…
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in…
The Magnus expansion offers a method to express a time-ordered exponential as an ordinary operatorial exponential. This representation has advantageous theoretical properties, while still solving the original differential equation. For any…
The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involving a linear operator. Since its discovery it has evolved…
In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a…
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…
Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their…
We investigate the Magnus expansion of the $N$-operator in relativistic quantum field theory, which is related to the $S$-matrix via $S = e^{iN}$. We develop direct methods to compute matrix elements of the $N$-operator, which we refer to…
New directions in research on master equations are showcased by example. Magnus expansions, time-varying rates, and pseudospectra are highlighted. Exact eigenvalues are found and contrasted with the large errors produced by standard…
In this report the emphasis is on an alternative representation of the Magnus series by proper operator (matrix) exponential solutions to differential equations (systems), both linear and nonlinear ODEs and PDEs. The main idea here is in…
We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian $A$ under a small geometrically local perturbation $\alpha B$. In certain regimes, the algorithm achieves the optimal scaling and outperforms the…
The logarithm of the time-evolution operator has been termed Magnusian, on account of the fact that its expansion describes the Magnus series. The diagrammatic expansion and computation of the classical Magnusian has been completely…
The classic Magnus embedding is a very effective tool in the study of abelian extensions of a finitely generated group $G$, allowing us to see the extension as a subgroup of a wreath product of a free abelian group with $G$. In particular,…
We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. The relation with the Malvenuto--Reutenauer Hopf algebra of…
We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results…
We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with…
Magnus expansion is used to identify effective Hamiltonians describing the coarse-grained dynamics of more complex problems. Here, we apply this method to a two-level system driven by an and AC field. We derive Stark and Bloch-Siegert shifs…
We rigorously derive an effective quantum mechanical Hamiltonian from N=4 gauge theory in the BMN limit. Its eigenvalues yield the exact one-loop anomalous dimensions of scalar two-impurity BMN operators for all genera. It is demonstrated…
A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…