Related papers: Dispersion relations: foundations
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\geq 1$ when the density of states…
Deeper insight leads to better practice. We show how the study of the foundations of quantum mechanics has led to new pictures of open systems and to a method of computation which is practical and can be used where others cannot. We…
Over the past two decades, the rapid surge in data-intensive computational techniques for statistical modeling may have had the effect of diminishing the use of applied mathematics in causal scientific inquiry. In this paper, co-authored by…
Pion-loop corrections for Compton scattering are calculated in a novel approach based on the use of dispersion relations in a formalism obeying unitarity. The basic framework is presented, including an application to Compton scattering. In…
We outline a phenomenological programme for the search of effects induced by (string-motivated) canonical noncommutative spacetime. The tests we propose are based, in analogy with a corresponding programme developed over the last few years…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…
Proceeding from the main principles of the non-unitary quantum theory of relativistic bi-Hamiltonian systems, a system of Lagrangian fields characterized by a certain dispersion law (mass spectrum of particles), interactions between them…
A new minimal coupling method is introduced. A general dissipative quantum system is investigated consistently and systematically. Some coupling functions describing the interaction between the system and the environment are introduced.…
The purpose of these lectures is to give an accessible and self contained introduction to quantum scattering theory in one dimension. Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time…
The principle of common cause is discussed as a possible fundamental principle of physics. Some revisions of Reichenbach's formulation of the principle are given, which lead to a version given by Bell. Various similar forms are compared and…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
This paper is a companion to 'Quantum Diffusion with Drift and the Einstein Relation I' (jointly submitted to arXiv). Its purpose is to describe and prove a certain number of technical results used in 'Quantum Diffusion with Drift and the…
Hadronic resonance propagators which take into account the analytical properties of decay processes are built in terms of the dispersion relation technique. Such propagators can describe multi-component systems, for example, those when…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
We revisit sidewise dispersion relations as a method to relate the nucleon off-shell form factor to observable quantities, namely the meson-nucleon scattering phase shifts. It is shown how for meson-nucleon scattering a redefinition of the…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of…
In this paper we re-examine the traditional problem of connecting the internal fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also nonlinear processes. With…