Related papers: Time-ordering and a generalized Magnus expansion
For a renormalizability proof of perturbative models in the Epstein--Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction Lagrangian. This…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the `curl-curl' equation for the fields. We present a variational formulation based on classical field theory.…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
We consider the higher-order gravity theory derived from the quadratic lagrangian $R+\epsilon R^2$ in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of…
The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
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…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
After stating the measurement problem, physicists usually assume the problem to be coming from the measurement part. Since classical probabilities also collapse when updating information, there is nothing special about quantum state…
This paper provides an algebraic framework for the generation of order conditions for the construction of exponential integrators like splitting and Magnus-type methods for the numerical solution of evolution equations. The generation of…
We study time ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four wave mixing (SFWM) and frequency conversion (FC) using the Magnus expansion. Analytic approximations to the evolution operator that…
The renormalization method based on the Newton-Maclaurin expansion is applied to study the transient behavior of the solutions to the difference equations as they tend to the steady-states. The key and also natural step is to make the…
A general form of the Lions-Magenes theorems on solvability of an elliptic boundary-value problem in the spaces of nonregular distributions is proved. We find a general condition on the space of right-hand sides of the elliptic equation…