Related papers: Basis-Independent Spectral Methods for Non-linear …
We present a Keldysh-based derivation of a formula, previously obtained by Oguri using the Matsubara formalisum, for the linear conductance through a central, interacting region coupled to non-interacting fermionic leads. Our starting point…
In this work, we develop a Legendre spectral element method (LSEM) for solving the stochastic nonlinear system of advection-reaction-diffusion models. The used basis functions are based on a class of Legendre functions such that their mass…
Motivated by the recent experimental progress in studying conventional and unconventional superconductors in a pump-probe setup, we perform a comprehensive theoretical analysis of the nonlinear response of a diffusive BCS conventional…
We theoretically demonstrate the ability of electron beams to probe the nonlinear photonic response with nanometer spatial resolution, well beyond the capabilities of existing optical techniques. Although the interaction of electron beams…
We derive a universal model for atom pairs interacting with non-resonant light via the polarizability anisotropy, based on the long range properties of the scattering. The corresponding dynamics can be obtained using a nodal line technique…
DC photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These…
We develop a non-equilibrium quantum field theory of the free-electron laser based on the Preparata model, using the real-time Keldysh formalism. Starting from a microscopic Lagrangian for a relativistic electron beam coupled to a single…
A closed-form expression that estimates the nonlinear interference of arbitrary modulation formats in Raman amplified links is presented. Accounting for any pumping schemes and inter-channel stimulated Raman scattering effect, the formula…
Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be…
The generation of engineered quantum states of light via nonlinear processes is fundamental for quantum technologies based on photons. Although embedding nonlinear materials within resonant structures allows for the enhancement and…
This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
In this article, we consider a non-linear hyperbolic-parabolic coupled system based on telegraph diffusion framework applied to image despeckling. A separate equation is used to calculate the edge variable, which improves the quality of the…
A general approach based on gauge invariance requirements has been developed for automatic construction of quantum kinetic equation in electron systems, far for equilibrium. Proposed theoretical scheme has high generality and automatism and…
We investigate the linear and non-linear optical response of two-dimensional (2D) interacting electron fluids confined by a strong non-parabolic potential. We show that such fluids may exhibit higher-harmonic spectra under realistic…
We present a method to reconstruct autocorrelated signals together with their autocorrelation structure from nonlinear, noisy measurements for arbitrary monotonous nonlinear instrument response. In the presented formulation the algorithm…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
Intense efforts have been made in recent years to realize nonlinear optical interactions at the single-photon level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other…
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…
A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(\epsilon^{-3/2})$ complexity…