Related papers: Linear Response Theory: A Modern Analytic-Algebrai…
We propose a new method for simulating electron dynamics in open quantum systems out of equilibrium, using a finite atomistic model. The proposed method is motivated by the intuitive and practical nature of the driven Liouville von-Neumann…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what…
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
In a recent paper we have shown that data collected from linear systems excited by persistently exciting inputs during low-complexity experiments, can be used to design state- and output-feedback controllers, including optimal Linear…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…
The ``black-box'' nature of deep learning models presents a significant barrier to their adoption for scientific discovery, where interpretability is paramount. This challenge is especially pronounced in discovering the governing equations…
We report a microscopic and general theoretical formalism for electrical response which is appropriate for both DC and AC weakly nonlinear quantum transport. The formalism emphasizes the electron-electron interaction and maintains current…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological…
The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response…
A quantum kinetic theory of the linear response to an electric field is provided from a controlled expansion of the Keldysh theory at leading order, for a multiband electron system with weak scalar disorder. The response is uniquely…
We consider an ergodic Schr\"odinger operator with magnetic field within the non-interacting particle approximation. Justifying the linear response theory, a rigorous derivation of a Kubo formula for the electric conductivity tensor within…
The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between…
In this work, a predictive control framework is presented for feedback stabilization of nonlinear systems. To achieve this, we integrate Koopman operator theory with Lyapunov-based model predictive control (LMPC). The main idea is to…
The neural mechanisms supporting flexible relational inferences, especially in novel situations, are a major focus of current research. In the complementary learning systems framework, pattern separation in the hippocampus allows rapid…
We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems…
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
Along with the proliferation of digital data collected using sensor technologies and a boost of computing power, Deep Learning (DL) based approaches have drawn enormous attention in the past decade due to their impressive performance in…