Gravitational-wave lensing beyond rays: a disordered-system approach

TL;DR

This paper introduces a novel theoretical framework for modeling gravitational wave propagation through stochastic lens distributions, extending beyond geometric optics by employing disordered-system techniques.

Contribution

It develops a path-integral formalism using the Schwinger Keldysh approach to describe wave interference, diffraction, and fluctuations in a unified manner.

Findings

Derived explicit form of the averaged density matrix for wave propagation.

Identified physical scales for coherence loss in gravitational wave signals.

Applicable to wave propagation in disordered media beyond gravitational lensing.

Abstract

We develop a framework to describe gravitational wave propagation through a stochastic distribution of weak gravitational lenses beyond the geometric optics limit. We model the lens distribution as a static random background field and formulate the problem in the language of quenched disorder, treating the disorder averaged density matrix as the fundamental object from which observables are computed. Using the Schwinger Keldysh formalism, we construct a path-integral representation of the averaged density matrix and derive its explicit form perturbatively for a suitable class of couplings. The result naturally separates into a quadratic exponential term, which governs the suppression of phase sensitive contributions in the averaged description, and a purely oscillatory contribution, which modifies coherent propagation through a disorder-induced correction to the propagation kernel. This provides a unified description of interference, diffraction, and statistical fluctuations of the lens distribution within a single framework. We also identify the physical scales controlling the onset of coherence loss and illustrate the formalism in the case of Gaussian wave packets. More generally, the derivation applies to any system described by the same class of actions, making the framework relevant beyond gravitational wave lensing to wave propagation in disordered media.