Related papers: Bosonization for disordered and chaotic systems
Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
Recently, general methods of bosonization beyond 1+1 dimensions have been developed. In this article, we review these bosonizations and extend them to the case with boundary conditions. In particular, we study the case when the bulk theory…
This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…
We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small…
A hard-core disordered boson system is mapped onto a quantum spin 1/2 XY-model with transverse random fields. It is then generalized to a system of spins with an arbitrary magnitude S and studied through a 1/S expansion. The first order 1/S…
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and…
We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the…
We introduce a new disordered system, the Super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pair-wise interactions. Its exact…
The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Recently it has been shown that transmon qubit architectures experience a transition between a many-body localized and a quantum chaotic phase. While it is crucial for quantum computation that the system remains in the localized regime, the…
We present a new and efficient optimization method to determine the structure of disordered systems in agreement with available experimental data. Our approach permits the application of accurate electronic structure calculations within the…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…
The passage of light or of electrons through a disordered medium is modified in the presence of resonances. We describe a simple model for this problem, and present first results.
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
BosonSampling is an intermediate model of quantum computation where linear-optical networks are used to solve sampling problems expected to be hard for classical computers. Since these devices are not expected to be universal for quantum…
The factorisation method commonly used in linear supersymmetric quantum mechanics is extended, such that it can be applied to nonlinear quantum mechanical systems. The new method is distinguishable from the linear formalism, as the…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…