Related papers: Basis-Independent Spectral Methods for Non-linear …
A non-perturbative model for graphene optical nonlinearity is developed for the study of ultrafast pulse propagation along a monolayer, as in the case of graphene-comprising nanophotonic integrated waveguides. This graphene `hot electron'…
We present a novel theoretical approach for computing and analyzing two-dimensional spectroscopy of bosonic collective excitations in disordered many-body systems. Specifically, we employ the Keldysh formalism to derive, within a…
We study the optical response of the alternating twisted trilayer graphene by making use of a unitary transformation for the trilayer Hamiltonian and the Kubo formulation of linear response theory. The layer-resolved optical conductivities…
We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random…
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…
A second-order accurate kernel-free boundary integral method is presented for Stokes and Navier boundary value problems on three-dimensional irregular domains. It solves equations in the framework of boundary integral equations, whose…
This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
This paper aims at an efficient strategy to solve drift-diffusion problems with non-linear boundary conditions as they appear, e.g., in heterogeneous catalysis. Since the non-linearity only involves the degrees of freedom along (a part of)…
A theoretical frame for two-photon photoemission is derived from the general theory of pump-probe photoemission, assuming that not only the probe but also the pump pulse is sufficiently weak. This allows us to use a perturbative approach to…
We develop a general framework for the electrostatic analysis of point charges in multilayer planar structures with arbitrary layer thicknesses and material parameters. Starting from a Hankel-transform analysis, we derive alternative…
The non-linear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n + 1 theorem…
We present a general non-perturbative method to determine the exact steady state of open quantum systems under perturbation. The method works for systems with a unique steady state and the perturbation may be time-independent or periodic,…
Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have aided multiple fields including chemistry, biology and physics. However, accurate quantum dynamical simulations based on model…
In this work we present a nonlinear adaptive suboptimal control strategy for uncertain nonlinear systems. Stochastic parametric uncertainty is dealt with by employing spectral decomposition of the random variables by means of the…
In the framework of the Keldysh technique, we formulate the nonlinear sigma model for disordered optical media with linear absorption or gain. The effective action for fluctuations of the matrix field about the saddle point acquires an…
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…
In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain of the system. We formulate a general nonparametric identification method as an infinite-dimensional…
We present a data-driven nonlinear predictive control approach for the class of discrete-time multi-input multi-output feedback linearizable nonlinear systems. The scheme uses a non-parametric predictive model based only on input and noisy…
A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz Ladik spectral problem (discrete version of the Zakharov-Shabat system). This 3-wave…