A New Paradigm For Scattering Theory of Linear And Nonlinear Waves: Review And Open Problem

• URL: http://arxiv.org/abs/2408.14269v1
• Date: Mon, 26 Aug 2024 13:45:13 GMT
• Title: A New Paradigm For Scattering Theory of Linear And Nonlinear Waves: Review And Open Problem
• Abstract summary: I present a review of the recent advancements in scattering theory. I discuss a series of open problems, along with their significance and potential future applications in scattering and inverse scattering.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems, along with their significance and potential future applications in scattering and inverse scattering.

Related papers

• Open quantum spin chains with non-reciprocity: a theoretical approach based on the time-dependent generalized Gibbs ensemble [0.0]
  We study an open quantum spin chain with non-reciprocal dissipation using a theoretical approach known as time-dependent generalized Gibbs ensemble.<n>Our work constitutes a theoretical approach that is able to describe the physics of non-reciprocal open quantum spin chains beyond analyses based on non-interacting fermions.
  arXiv  Detail & Related papers  (2026-01-13T14:49:41Z)
• Diffusion models for inverse problems [57.87606622211111]
  We review the various different approaches that were proposed over the years.<n>We cover the extension to more challenging situations, including blind cases, high-dimensional data, and problems under data scarcity and distribution mismatch.
  arXiv  Detail & Related papers  (2025-08-04T01:26:06Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Kernel Approximation of Fisher-Rao Gradient Flows [52.154685604660465]
  We present a rigorous investigation of Fisher-Rao and Wasserstein type gradient flows concerning their gradient structures, flow equations, and their kernel approximations. Specifically, we focus on the Fisher-Rao geometry and its various kernel-based approximations, developing a principled theoretical framework.
  arXiv  Detail & Related papers  (2024-10-27T22:52:08Z)
• Eikonal Approximation for Floquet Scattering [3.004788114489393]
  The eikonal approximation (EA) is widely used in various high-energy scattering problems. In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians.
  arXiv  Detail & Related papers  (2024-07-20T05:14:04Z)
• Fourier Neural Differential Equations for learning Quantum Field Theories [57.11316818360655]
  A Quantum Field Theory is defined by its interaction Hamiltonian, and linked to experimental data by the scattering matrix. In this paper, NDE models are used to learn theory, Scalar-Yukawa theory and Scalar Quantum Electrodynamics. The interaction Hamiltonian of a theory can be extracted from network parameters.
  arXiv  Detail & Related papers  (2023-11-28T22:11:15Z)
• Causal Modeling with Stationary Diffusions [89.94899196106223]
  We learn differential equations whose stationary densities model a system's behavior under interventions. We show that they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2023-10-26T14:01:17Z)
• A Geometric Perspective on Diffusion Models [57.27857591493788]
  We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
  arXiv  Detail & Related papers  (2023-05-31T15:33:16Z)
• End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics [61.44793171735013]
  We introduce a novel unified architecture, termed latent variation models, which combines the latent learning of cutting-edge generative art approaches with an end-to-end variational framework. Our unified approach achieves a distribution-free distance to the truth of over 20 times less than non-latent state-of-the-art baseline.
  arXiv  Detail & Related papers  (2023-05-17T17:43:10Z)
• The foundations of quantum theory and its possible generalizations [0.0]
  Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The application of tachyonic field to overcome divergences arising in this equation is analyzed.
  arXiv  Detail & Related papers  (2021-03-09T11:44:48Z)
• Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning [7.400475825464313]
  We apply the multi-layer physics-informed neural networks (PINNs) deep learning to study the data-driven peakon and periodic peakon solutions of some well-known nonlinear dispersion equations. Results will be useful to further study the peakon solutions and corresponding experimental design of nonlinear dispersive equations.
  arXiv  Detail & Related papers  (2021-01-12T09:50:28Z)
• Transfer matrix in scattering theory: A survey of basic properties and recent developments [0.0]
  We start by surveying basic notions of potential scattering such as transfer matrix and its analyticity, multi-delta-function and locally periodic potentials. We then offer a simple derivation of the Lippmann-Schwinger equation and Born series, and discuss the Born approximation. Next, we outline a recently developed dynamical formulation of time-independent scattering theory in one dimension.
  arXiv  Detail & Related papers  (2020-09-22T12:53:56Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.