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We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator…
I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
Multipolar expansions are a foundational tool for describing basis functions in quantum mechanics, many-body polarization, and other distributions on the unit sphere. Progress on these topics is often held back by complicated and competing…
We describe a method for removing the numerical errors in the modeling of linear evolution equations that are caused by approximating the time derivative by a finite difference operator. The method is based on integral transforms realized…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…
This paper proposes a novel approach to Hamiltonian simulation using Decision Diagrams (DDs), which are an exact representation based on exploiting redundancies in representations of quantum states and operations. While the simulation of…
In this work we present the general unified description for the unitary time-evolution generated by time-dependent non-Hermitian Hamiltonians embedding the bosonic representations of $\mathfrak{su}(1,1)$ and $\mathfrak{su}(2)$ Lie algebras.…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…
We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…
We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{_0}$…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
We describe the "Feynman diagram" approach to nonrelativistic quantum mechanics on R^n, with magnetic and potential terms. In particular, for each classical path \gamma connecting points q_0 and q_1 in time t, we define a formal power…
Given a Feynman parameter integral, depending on a single discrete variable $N$ and a real parameter $\epsilon$, we discuss a new algorithmic framework to compute the first coefficients of its Laurent series expansion in $\epsilon$. In a…
While current generative models have achieved promising performances in time-series synthesis, they either make strong assumptions on the data format (e.g., regularities) or rely on pre-processing approaches (e.g., interpolations) to…